United States
Environmental Protection
Agency
Air And Radiation
(6601J)
EPA402-R-96-016
June 1996
&EPA
Radiation Exposure And Risks
Assessment Manual (RERAM)
Risk Assessment Using
Radionuclide Slope Factors
Review Draft
Revision 2
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NOTICE
The policies set out in this document are intended solely as guidance to U.S. Environmental Protection Agency
(EPA) personnel; they are not final EPA actions and do not constitute rulemaking. These policies are not
intended, nor can they be relied upon, to create any rights enforceable by any party in litigation with the United
States. EPA officials may decide to follow the guidance provided in this document, or to act at variance with
the guidance, based on analysis of site-specific circumstances. EPA also reserves the right to change the
guidance at any time without public notice.
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ACKNOWLEDGMENTS
This manual was developed by the Radiation Assessment Branch of EPA's Office of Radiation and Indoor Air
(ORIA). Dr. Kung-Wei Yeh served as the Work Assignment Manager. Several individuals provided valuable
input regarding the content of this manual throughout its development, and their efforts are gratefully
acknowledged. Special acknowledgment and appreciation are extended to Christopher Nelson, Dr. Neal
Nelson, and Dr. Jerome Puskin of ORIA's Criteria and Standards-Division; Bruce Means and Jim Konz of
EPA's Toxics Integration Branch; and Dr. Keith Eckerman of Oak Ridge National Laboratory.
Technical assistance was provided by S. Cohen & Associates, Inc., under EPA Contract No. 68D20155, Work
Assignment 4-20.
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PREFACE
The Radiation Exposure and Risk Assessment Manual (RERAM) describes the methodology developed by
EPA's Office of Radiation and Indoor Air (ORIA) to derive ingestion, inhalation, and external exposure
radionuclide cancer slope factors for use in radiation risk assessment at a Comprehensive Environmental
Response, Compensation, and Liability Act (CERCLA or Superfund) site. Potential users of RERAM are
those involved in the remedy selection and implementation process, including risk assessors, risk assessment
reviewers, remedial project managers, and other decision-makers.
EPA encourages users to provide comments on the guidance provided in this document. Comments should
be sent to:
Dr. Rung-Wei Yeh
U.S. Environmental Protection Agency
Office of Radiation and Indoor Air (6603J)
401 M Street, SW
Washington, DC 20460
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IV
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EXECUTIVE SUMMARY
The U.S. Environmental Protection Agency (EPA) has developed radionuclide slope factors for estimating
excess cancer risks from radioactive materials at radio logically contaminated sites managed under the
Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA). These radionuclide
slope factors provide a methodology for evaluating radiation-induced cancer risk that is generally consistent
with that used for evaluating risks from chemical carcinogens. The slope factor is an estimate of the excess
probability of developing cancer per unit dose of a carcinogen over a lifetime. When multiplied by the total
lifetime exposure (inhalation, ingestion, or external exposure) to a given radionuclide, the slope factor provides
an estimate of the probability of developing cancer as a result of that exposure.
EPA has developed the Radiation Exposure and Risk Assessment Manual (RERAM): Risk Assessment Using
Radionuclide Slope Factors to supplement risk assessment.guidance presented in the series of publications
collectively entitled Risk Assessment Guidance for Superfund (RAGS). While the RAGS methodology
specifically includes consideration of risks from radioactive contaminants, it does not provide detailed
documentation of the methods used by EPA to derive the radionuclide slope factors. Since some CERCLA
sites are contaminated with both radioactive materials and hazardous chemicals, EPA recommends the use of
a consistent basis for evaluating cancer risks from radioactive materials and from nonradioactive hazardous
chemicals. In each case, the risk to potentially exposed human receptors is computed as the product of the
estimated lifetime intake or exposure for a contaminant of concern times a measure of the likelihood of excess
cancer induction per unit exposure (i.e., the slope factor). The RERAM guidance is designed to assist risk
assessors, remedial project managers, and others involved with the risk assessment and decision-making
process at radiologically contaminated sites in understanding the calculations and assumptions used by EPA
to estimate excess human cancer risks associated with radiation exposures.
Radionuclide slope factors express the lifetime excess cancer risk per unit exposure to a given radionuclide,
where exposure is measured in units of radioactivity intake for inhalation and ingestion (pCi inhaled or
ingested), or the product of soil concentration and exposure duration for external exposure [e.g., soil
concentration (pCi/g) x time (y) = pCi-y/g]. The slope factor is an estimate of the lifetime excess cancer risk
(fatal and nonfatal cancers) for all cancer sites, averaged over a population (all ages and both sexes). In
practice, the excess cancer risk for each cancer site is estimated separately based upon organ-specific dose rates
and risk coefficients, and the risks for these individual cancer sites are summed to estimate total excess risk.
Dose rates to each organ may vary as a function of age and time after exposure, and the organ-specific risk
coefficients may vary as a function of age and sex. Since the excess risk of cancer incidence resulting from
radiation exposure may not occur until many years after exposure, it is also necessary to account for competing
risks (i.e., risks from sources other than radiation exposure), through the use of vital statistics and mortality
data.
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The slope factor is derived from the integration of three principal types of data:
• Organ-specific dose rates for each tissue of interest (potential cancer site) over the lifetime of the
exposed population, resulting from chronic exposure, at a constant rate, to a given radionuclide;
• Risk factors, which express the lifetime excess cancer incidence risk per unit dose (e.g., expected
cancer cases per 106 rad) for specific cancer sites over the lifetime of the exposed population; and
• Vital statistics and mortality data for the reference population (currently the 1980 U.S.
population), which define the survival function for an average member of the population - i.e., the
probability of survival and projected years of life remaining at various ages in the reference
population, taking into account competing risks (mortality risks unrelated to radiation exposure,
e.g., accidents, illness).
For each age of exposure and for each cancer site considered, the excess risk of cancer at that site due to the
dose accumulated at that age from a given exposure pathway is calculated by multiplying the organ-specific
absorbed dose rate in that year (rad/y), the organ-specific cancer risk per unit absorbed dose at that age (rad"1),
and the survival function for the reference population (probability of survival to that year). The excess cancer
risk for each cancer site at each age is computed in this manner and summed to obtain the total number of
radiogenic cancers of all types expected in the life of the exposed population. This total is then divided by an
appropriate exposure term (i.e., the total quantity of the radionuclide inhaled or ingested over a lifetime for
inhalation or ingestion exposures, respectively, or the product of the radionuclide concentration in soil and
exposure duration in the contaminated area for external exposures) to compute the slope factor for each
exposure pathway. This procedure is followed for each radionuclide of concern. Risks from high-LET (alpha)
radiation are calculated separately from those due to low-LET radiations (beta and gamma), and these are
summed to obtain the slope factor for the radionuclide.
Radionuclide slope factors relate the lifetime cancer incidence risk attributable to given radionuclide exposure
conditions for an average member of the reference population. This estimate of excess risk is averaged over
all ages and both sexes for a population with specified mortality statistics (currently the U.S. population circa
1980). These slope factors are appropriate for assessing the average risk within this population, but are not
suitable for assessing the risk to a single individual of a particular age or sex. Estimates of radiogenic cancer
risk are subject to numerous sources of uncertainty, including the biokinetic and dosimetric models, tissue-
specific risk factors, mortality and survival characteristics of the population, and the extrapolation of
epidemiological data for populations exposed to high radiation doses to much lower levels characteristic of
environmental exposures.
Radionuclide slope factor values for more than 300 radionuclides have been tabulated in EPA's Integrated Risk
Information System (IRIS) and Health Effects Assessment Summary Tables (HEAST). These radionuclide
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slope factors are derived for the idealized conditions of chronic radionuclide intake or exposure, at a unit
radionuclide concentration, throughout the lifetime of the exposed individuals. These slope factors can be used
in conjunction with site-specific data describing the concentrations of radionuclides of concern in
environmental media (e.g., air, water, vegetation, soil, and foodstuffs) and with information describing the
exposure conditions (e.g., inhalation and ingestion rates; exposure times, frequencies and durations; etc.) to
estimate the cancer risk from inhaling contaminated air, eating contaminated food or soil, drinking
contaminated water, or from external exposure to contaminated ground surfaces for given site conditions.
Whether for inhalation, ingestion, or external exposure, the lifetime risk is related to the cumulative intake or
exposure to the given radionuclide. For inhalation and ingestion, the total radioactivity (pCi) inhaled or
ingested must be known. For external exposure, the soil concentration of the radionuclide of interest (pCi/g)
and the total duration of exposure in the contaminated area must be known, considering the effect of shielding
provided by buildings or other site features. For each radionuclide and exposure pathway, the excess cancer
risk is estimated as the product of the slope factor, the exposure point concentration in pertinent environmental
media, and the cumulative intake or exposure. The risks presented by each radionuclide (including radioactive
decay products) and exposure pathway in a given exposure situation should be assessed separately and summed
to estimate the total radiation risk.
VII
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VIM
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TABLE OF CONTENTS
Section Page
Notice j
Acknowledgments jj
Preface [[ \
Executive Summary v
List of Tables xj
List of Figures xj
Chapter 1. Introduction
1.1 Purpose and Scope \.\
1.2 Background - EPA Radiation Risk Assessment Methodology 1-1
1.3 Examples of the Use of Radionuclide Slope Factors 1-3
1.4 Special Considerations 1_7
1.5 Content of This Report 1_11
Chapter 2. Radionuclide Slope Factor Development
2.1 Basic Elements of Radionuclide Slope Factor Approach 2-1
2.2 Exposure Assumptions 2-5
2.3 Dosimetry Models 2-6
2.3.1 Internal Exposure - Overview of Internal Dosimetry Models 2-6
2.3.2 External Exposure - Overview of External Dosimetry Models 2-8
2.4 Cancer Risk Models 2-10
2.5 Reference Population Data: Mortality and Survival Statistics 2-12
Chapter 3. EPA Radiogenic Cancer Risk Models
3.1 Background 3_1
3.2 Cancer Risk from Low-LET Radiation 3_3
3.2.1 Dose Response Function and Dependence on Dose Rate 3-3
3.2.2 Risk Projection Models 3.5
3.2.3 EPA Assumptions for Estimating Radiogenic Cancer Risk
From Low-LET Radiation 3-6
3.3 Cancer Risk from High-LET Radiation 3-13
3.3.1 Relative Biological Effectiveness 3-14
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TABLE OF CONTENTS (continued)
Section Page
3.3.2 Dose Response Function 3-15
3.3.3 Estimates of Cancer Risk from Alpha Emitters 3-15
3.3.4 Estimates of Cancer Risk from Radon Decay Products 3-16
Chapter 4. Example Calculations of Radionuclide Slope Factors
4.1 Basic Considerations 4-1
4.2 Revised Methodology For Deriving EPA Radionuclide
Slope Factors 4-3
4.2.1 General Information 4-3
4.2.2 Illustrative Examples 4-5
4.3 Summary 4-10
Chapter 5. Uncertainty in Radionuclide Slope Factors
5.1 Sources of Uncertainty in Radiation Dosimetry 5-2
5.2 Sources of Uncertainty in Radiogenic Risk Models 5-4
5.3 Methods for Quantitative Uncertainty Analysis 5-6
References
References R'l
Appendices
A Radiation Dosimetry A-l
B Attributable Mortality Risk Coefficients B-l
C Pre-1994 EPA Radiogenic Cancer Risk Models & Slope Factors C-l
D Calculational Methods for Radiogenic Cancer Risk Estimates D-l
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LIST OF TABLES
Table page
1-1 Estimates of Cancer Mortality Risk per Unit Dose of Low-LET Radiation 1-10
1-2 Comparison of Radiation Risk Estimation Methodologies:
Slope Factor Approach vs. Dose-to-Risk Conversion Factor Approach 1-10
1-3 Comparison of Slope Factors for Radionuclides and Chemical Carcinogens 1-11
2-1 EPA Organ-Specific Risk Factors for Low-LET Radiation -
Low Dose, Low Dose Rate 2-11
3-1 Mortality Risk Coefficients for EPA Revised Risk Methodology 3-11
3-2 EPA Revised Radiogenic Cancer Risk Coefficients - Low Dose and
Low Dose Rate 3-\2
4-1 Survival Function Based on 1980 Decennial Life Table Data 4-4
4-2 Attributable Cancer Risk from Uniform Low-LET Radiation 4-6
4-3 Derivation of Attributable Cancer Risk Resulting from Chronic Exposure to
Gamma Radiation from Cs-137 Ground Contamination 4-8
4-4 Derivation of Attributable Cancer Risk Resulting from Chronic
Inhalation of Pu-238 4.9
4-5 Derivation of Attributable Cancer Risk Resulting from Chronic
Ingestion of Sr-90 4. \ \
LIST OF FIGURES
Figure page
1-1 Typical Radionuclide Exposure Pathways 1-3
1-2 Simplified Risk Equations 1_8
2-1 Basic Building Blocks Used to Calculate a Radionuclide Slope Factor 2-3
2-2 How are Radionuclide Slope Factors Derived? 2-14
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Chapter 1
Introduction
1.1 PURPOSE AND SCOPE
This document describes the methodology the U.S. Environmental Protection Agency (EPA) Office of
Radiation and Indoor Air (ORIA) utilizes to assess radiation risk through the use of radionuclide slope factors.
The purpose of this risk assessment guidance is to assist risk assessors, remedial project managers (RPMs),
and others involved with the risk assessment and decision-making process at Superfund sites in understanding
the calculations and assumptions used by the Agency to estimate human cancer risks associated with radiation
exposures.
1.2 BACKGROUND— EPA RADIATION RISK ASSESSMENT METHODOLOGY
EPA has developed guidance for evaluating risks to human health and the environment from exposure to
radioactive and nonradioactive hazardous substances at sites regulated under the Comprehensive
Environmental Response, Compensation and Liability Act of 1980, as amended (CERCLA or "Super-fund").
This guidance is documented in a series of EPA publications collectively entitled Risk Assessment Guidance
for Superfund (RAGS). The RAGS methodology was developed for use in the remedial
investigation/feasibility study (RI/FS) process at Superfund sites. This process, as specified in the National
Oil and Hazardous Substances Pollution Contingency Plan (NCP), the implementing regulation for CERCLA
(40 CFR 300), requires the selection of remedies that reduce, control, or eliminate risks to human health and
the environment. The RAGS methodology provides the framework for assessing baseline risks, developing
and refining preliminary remediation goals, and evaluating risks associated with various remedial action
alternatives.
The Risk Assessment Guidance for Superfund- considers two general categories of risk to human
health— carcinogenic risk and noncarcinogenic risk. However, in evaluating exposure to radioactive materials
at contaminated sites, only carcinogenic risk is considered for most radionuclides. Other types of detrimental
health effects that can also be associated with exposure to ionizing radiation include mutagenic, teratogenic,
and acute toxicity effects. However, these effects are generally less significant for doses associated with
environmental exposures. Therefore, EPA considers carcinogenic risk to be a sufficient basis for assessing
radiation-related human health risks at Superfund sites.
Previous EPA risk assessment guidance (EPA86) did not specifically address radioactive materials.
Traditionally, risks associated with exposure to radioactive materials and chemical hazards have been evaluated
using different methods. Since some CERCLA sites are contaminated with both radioactive materials and
hazardous chemicals, EPA recommends an approach for evaluating radiation- induced cancer risks that is
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generally consistent with that used for evaluating cancer risks from nonradioactive hazardous chemicals. In
each case, the risk to potentially exposed human receptors is computed as the product of the estimated lifetime
intake or external exposure1 for a contaminant of concern times a measure of the likelihood of incremental
cancer induction per unit exposure to that contaminant, termed the slope factor. The slope factor is an estimate
of the probability of a response—i.e., the probability of an individual developing cancer per unit intake of, or
external exposure to, a carcinogen over a lifetime; when multiplied by an estimate of the total lifetime intake
or external exposure, it may be used to estimate the probability of an individual developing cancer as a result
of that exposure.
Radionuclide slope factors are central estimates (i.e., approximately median or 50th percentile values) of the
age-averaged, lifetime cancer incidence (fatal and nonfatal cancer) risk per unit inhalation, ingestion, or
external exposure to a specific radionuclide. Values for more than 300 radionuclides have been tabulated in
EPA's Integrated Risk Information System (IRIS)(EPA96) and Health Effects Assessment Summary Tables
(HEAST)(EPA95). Ingestion and inhalation slope factors are central estimates of the age-averaged, lifetime
cancer incidence risk per unit of activity inhaled or ingested, expressed as risk per picocurie of a radionuclide
inhaled or ingested (risk/pCi). External exposure slope factors are central estimates of lifetime cancer
incidence risk for each year of exposure to external radiation from photon-emitting radionuclides distributed
uniformly in a thick layer of soil, and are expressed as risk/year per picocurie/gram of the radionuclide in soil
(risk per pCi-y/g). (See Appendix A for definitions of radiation units.)
Slope factors are used for several different purposes during various stages of the Superfund remedial action
process. For example, during the site assessment phase, slope factors are used in EPA's Hazard Ranking
System (HRS) to assign toxicity factor values to radionuclides for the purpose of calculating site scores.
During the remedial investigation and feasibility study (RI/FS), slope factors are used to determine baseline
site risk, to develop preliminary remediation goals, and to evaluate remedial alternatives.
In addition to this document, further discussion of the application of radionuclide slope factors in risk
evaluations may be found in the following EPA documents:
• Hazard Ranking System (HRS), Federal Register (55 FR 515320), December 1990 (EPA90).
• Risk Assessment Guidance for Superfund; Volume I - Human Health Evaluation Manual (RAGS), Part
A, Baseline Risk Assessment, EPA/540/1-89/002 (EPA89a).
• Risk Assessment Guidance for Superfund; Volume I- Human Health Evaluation Manual (RAGS), Part
B, Development of Risk-Based Preliminary Remediation Goals, OSWER Directive 9285.7-0 IB (EPA91a).
• Risk Assessment Guidance for Superfund; Volume I - Human Health Evaluation Manual (RAGS), Part
C, Risk Evaluation of Remedial Alternatives, OSWER Directive 9285.7-01C, (EPA91b).
LApplies only to radionuclides that emit gamma radiation or x-rays (see Appendix A).
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1.3 EXAMPLES OF THE USE OF RADIONUCLIDE SLOPE FACTORS
Radionuclide slope factors can be used to estimate the lifetime incremental cancer incidence risk attributable
to a given radionuclide exposure for an average member of an exposed population. The slope factors are used
in conjunction with site-specific data describing the concentrations of radionuclides of concern in
environmental media (e.g., air, water, vegetation, soil, and foodstuffs) and with information describing the
exposure conditions (e.g., inhalation and ingestion rates, exposure times, frequencies and durations, etc.) to
estimate the cancer risk from inhaling contaminated air, eating contaminated food or soil, drinking
contaminated water, or from external exposure to contaminated ground surfaces.
Exposure assessment for radionuclides is very similar to that for hazardous chemicals. The goal of the
exposure assessment is to estimate exposure point concentrations of the radionuclides of concern in
environmental media, and to estimate potential intakes or external exposures to potential receptors. This may
include direct measurements of environmental concentrations and/or mathematical modeling of radionuclide
fate and transport in the environment. Typical radionuclide exposure pathways are depicted in Figure 1-1.
Figure 1-1. Typical Radionuclide Exposure Pathways
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ng T
. *. . ** ~ • -, . • , - - •" *v
.'* *£•*.!* . * t «.-»*+ i*. "*s, >
Groundwater
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All radionuclides, by definition, undergo radioactive decay in which the radionuclide is transformed in atomic
number, mass, or excitation state. In many cases, the resulting decay products may also be radioactive and
undergo further decay. Consideration of all potential radioactive decay products is a key element of the
exposure assessment for radionuclides. Decay products may have different physical and chemical
characteristics that affect their environmental fate and transport, as well as different radiotoxicity
characteristics. The radiation dose estimates used to calculate EPA's radionuclide slope factors explicitly
consider the production of radioactive decay products within the body following inhalation or ingestion; the
dose estimates for external exposure, however, do not include contributions from radioactive decay products.
In each case, it is important that the exposure assessment address the intake of, or external exposure to,
multiple members of a radioactive decay chain, where appropriate.
For selected radionuclides where contributions to dose and risk from short-lived radioactive decay products
may be particularly significant, EPA's tabulations of radionuclide slope factors include entries with the suffix
"+D" (e.g., Ra-226+D, Cs-137+D); these slope factors explicitly incorporate the contribution to cancer risk
from decay chain members with radioactive half-lives less than 1 year (i.e., all decay chain members from the
parent radionuclide down to, but not including, the next radionuclide in the decay chain with a radioactive half-
life longer than 1 year), by assuming equivalent concentrations with the parent radionuclide in the environment
(i.e., secular equilibrium). This presumption of equilibrium may or may not be appropriate for a given set of
site conditions, and, where available, site-specific analytical data and models should be used to establish the
actual degree of equilibrium between each parent radionuclide and its decay products in each medium sampled,
rather than relying on these "+D" values. In some cases, it may be necessary to consider the combination of
risks from exposures to a parent radionuclide and its decay products over several sequential subchains (e.g.,
Ra-226+D and Pb-210+D).
Whether for inhalation, ingestion, or external exposure, the lifetime risk is related to the cumulative intake or
exposure to the given radionuclide. For inhalation and ingestion, the total activity (pCi ) inhaled or ingested
must be known. For external exposure, the soil concentration of the radionuclide of interest (pCi/g ) and the
total duration of exposure in the contaminated area must be known, considering the effect of shielding
provided by buildings or other site features. It should be emphasized that slope factors relate the lifetime, age-
averaged risk to the total exposure regardless of the time period over which the exposure occurs.
Three examples are presented below to illustrate the use of radionuclide slope factors in risk assessments—one
each for inhalation, ingestion, and external exposure. In an actual risk assessment, each pathway should be
assessed in greater detail, taking into account occupancy, building shielding, eating and drinking habits, and
sources of food and water.
The risks presented by each radionuclide in a given exposure situation must be assessed separately and
summed to estimate the total radiation risk. Normally, only a few radionuclides may dominate the radiological
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risks at a particular site. For the purposes of the following examples, however, it is assumed that exposure is
limited to a single radionuclide, and its radioactive decay products where appropriate.
External Exposure
For external exposure, we consider the case of the constant exposure to gamma rays emanating from soil
contaminated by Cs-137 to a level of 1 pCi/g. Approximately 94.6% of all Cs-137 atoms undergo radioactive
decay by beta emission to produce Ba-137m, while the remaining 5.4% of Cs-137 atoms decay to produce
nonradioactive Ba-137; the half-life for radioactive decay of Cs-137 is 30.17 years. For the purposes of this
example, Cs-137 is assumed to be in secular equilibrium with Ba-137m (i.e., 0.946 pCi/g of Ba-137m is
assumed to be present in soil along with the 1 pCi/g of Cs-137). For a given radionuclide, the contribution
to dose from radioactive decay products (if any) is not incorporated into the external dose estimates or the
derived radionuclide slope factors for external exposure; therefore, the effect of any radioactive decay products
must be considered by summing the appropriate slope factors for each radionuclide in the decay series.
Alternatively, for some radionuclides where the impact of radioactive decay products is considered particularly
significant, EPA has developed slope factors for both the individual radionuclides and for the radionuclide plus
its short-lived decay products; in the tabulations of radionuclide slope factors, the later cases are designated
by the suffix "+D" following the radionuclide name. For example, the radionuclide slope factors for Cs- 137+D
represent a composite of the values for Cs-137 and its daughter, Ba-137m; this distinction is particularly
important for this example because Ba-137m is a gamma-emitter, while Cs-137 is a pure beta emitter.
The slope factor for external exposure to Cs-137+D in soil is taken as 2.09 x 10'6 per pCi-yr/g of Cs-137 in
the soil (EPA95). The lifetime attributable cancer risk to a hypothetical individual who occupies this site for
12 hours/day over a period of 30 years is then:
Attributable Cancer Risk = Slope Factor x Concentration x Exposure Time
= 2.09 x lO'6 per pCi-y/g x 1 pCi/g x 30 y x 0.5
= 3 x lO'5,
where 0.5 represents the site occupancy factor (i.e., 12 hours/day / 24 hours/day).
It should be noted that the radionuclide slope factors for external exposure are derived assuming soil
contaminated constantly and uniformly to an infinite extent in depth and area. Risk estimates based on these
assumptions may be overly conservative for situations where the contamination is of limited areal extent and/or
depth, or located at some depth below the ground surface, etc.; furthermore, depletion of the radionuclide
concentration in soil due to radioactive decay or soil erosion is not considered in these slope factors, which may
also lead to conservative estimates of risk. To obtain more accurate estimates of risk, the slope factors should
be used in conjunction with the best available estimate of exposure conditions. Environmental fate and
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transport models which explicitly consider radioactive decay, deposition, erosion, site geometry and shielding
effects, and other important factors, may be used to estimate such exposures.
Inhalation Exposure
For inhalation, we consider an average individual exposed to air in which the measured concentration of Sr-90
is 1 pCi/m3. For this example, the slope factor for inhalation of Sr-90+D (i.e., Sr-90 in secular equilibrium
with its radioactive decay product, Y-90) is taken to be 6.93 x 10'" pCi'1 (EPA95). Assuming an average
exposed individual inhales a volume of 20 m3 of contaminated air per day for 250 days/year over a period of
7 years, the lifetime attributable cancer risk is estimated as:
Attributable Cancer Risk = Slope Factor x Concentration x Cumulative Intake
= 6.93 x 10'n pCi'1 x 1 pCi/m3 x 20 mVday x
250 days/y x 7 y
= 2X10-6.
The dose to body organs from inhalation of strontium, like many radionuclides, may differ depending on the
physical and chemical characteristics of the inhaled compound or carrier. For example, SrTiO3 is retained in
the lung for an extended period (ICRP lung clearance class Y), whereas other compounds are cleared much
more rapidly (ICRP lung clearance class D). Radionuclide slope factors are provided in IRIS and HEAST,
however, for only a single default case for each radionuclide - typically the most commonly encountered or
most conservative compound (i.e., the chemical form which results in the maximum dose per unit activity
inhaled). In this example, the slope factor for Sr-90+D assumes the ICRP lung clearance class D. Similarly,
the dose may vary as a function of the physical size of the inhaled particulate. In the development of
radionuclide slope factors, the size distribution for all particulates has been specified as the activity median
aerodynamic diameter (AMAD) of 1 micron. (Exceptions include radionuclides, such as radon, which exist
in gaseous form under normal conditions.) For exposure situations where the default parameters may not be
appropriate, users should contact the Remedial Guidance Section of ORIA at EPA-HQ. [Note that the ICRP
lung clearance class values specified for the radionuclide slope factors are provided for reference only, and
should not be used to correct, modify, or in any way adjust the radionuclide slope factors or intake
assumptions in the risk calculations.]
IngestJon Exposure
For ingestion, we consider an average individual exposed to drinking water contaminated by Pu-238 at a
concentration of 1 pCi/liter. The slope factor for ingestion of Pu-238 is taken to be 2.95 x IO'10 pCi'1 (EPA95).
Assuming an ingestion rate of 2 liters/day, 350 days/year for a period of 30 years, the lifetime attributable
cancer risk is estimated as:
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Attributable Cancer Risk = Slope Factor x Concentration x Cumulative Intake
= 2.95 x 10-'° pCi'1 x 1 pCi/L x 2 L/day x 350 days/y
x30y
= 6 x 10-6 .
Similar to the situation noted for inhalation exposures, the dose from ingestion of plutonium and other
radionuclides may vary depending on the chemical characteristics of the ingested compound. For ingestion,
this is expressed through the gastrointestinal (GI) tract absorption fraction, f,, which represents the fraction
of activity that is absorbed from the Gl-tract (typically only absorption from the small intestine is assumed)
to blood. For radionuclides which may have different values off, depending on the chemical form of the
ingested material, the radionuclide slope factors are typically specified in IRIS and HEAST only for the most
conservative case. For Pu-238, EPA specifies a slope factor only for f^lO'3 (EPA95). However, both EPA
(EPA88) and ICRP (ICRP86) recommend compound-dependent f, values of 10'5 for oxides, 10* for nitrates,
and 10~3 for other compounds or unknown mixtures of plutonium. For exposure situations where the default
parameters assumed for calculation of the slope factors may not be appropriate, users should contact the
Remedial Guidance Section of ORIA at EPA-HQ. [Note that the GI absorption factor (fj values specified
for the radionuclide slope factors are provided for reference only, and should not be used to correct, modify,
or in any way adjust the radionuclide slope factors or intake assumptions in the risk calculations. This differs
from the application of similar factors for chemical slope factors.]
Simplified equations for estimating excess cancer risk from exposure to radionuclides via inhalation, ingestion,
and external exposure to contaminated soil are presented in Figure 1-2. These simplified equations are
presented for illustrative purposes only. In an actual risk assessment for a contaminated site, an exposure
assessment would be conducted to determine the appropriate exposure pathways and exposure parameters for
use in estimating cumulative lifetime intake and external exposure to each radionuclide of concern.
1.4 SPECIAL CONSIDERATIONS
As discussed in the previous sections, radionuclide slope factors can be used to estimate excess cancer risks
resulting from radionuclide exposures in a manner analogous to that used for chemical contaminants at
Superfund sites—i.e., the estimates of lifetime intake/exposure from the exposure assessment are coupled with
the appropriate slope factors for each radionuclide and exposure pathway. The sum of the risks from all
radionuclides in all exposure pathways yields the lifetime cancer risk attributable to radiation exposure. This
approach differs from the method traditionally used to estimate radiation risk. Also, the radionuclide slope
factors differ from slope factors used to estimate chemical risks. These special considerations are discussed
below.
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Figure 1-2. Simplified Risk Equations '
External: RiskUxt = SFUxt x Ci)SOil x EF x ED x AF
Inhalation: RiskMnh - SFj>inh x Cuir x IR^ x EF x ED x AF
Ingestion: Risk^ = SFMng x Cijng x IR^ x EF x ED x AF
where,
Riski>p = Lifetime excess cancer risk from radionuclide / and pathway p
SF; p = Slope factor for radionuclide / and pathway p (risk per pCi inhaled or
ingested, or risk/y per pCi/g in soil for external exposure)
Q son = Concentration of radionuclide / in soil (pCi/g)
= Concentration of radionuclide / in air (pCi/m3)
i ing = Concentration of radionuclide / in ingested material
[e.g., drinking water (pCi/L), contaminated food products (pCi/g), etc.]
= Inhalation rate (m3/day)
IR;ng = Ingestion rate (g/day for soil or food products, L/day for water)
= Exposure frequency (days/year)
= Exposure duration (years)
=Adjustment factor for site-specific conditions (unitless)[e.g., radiation
shielding, indoor/outdoor exposure time, indoor/outdoor dust filtration, etc.]
Q air
EF
ED
AF
Radionuclide Slope Factors vs Dose
Traditionally, impacts from exposure to radioactive materials have been expressed in terms of dose. (See
Appendix A for a discussion of radiation dosimetry concepts and terminology—for the purpose of this
discussion, the term "dose" is used in a generic sense, rather than "absorbed dose" and "dose equivalent".)
Most radiation protection standards and requirements are specified in terms of a radiation dose limit (e.g.,
mrem/y) that may be allowable from a particular exposure source and/or exposure pathway.
Dose conversion factors (DCFs) for radionuclides represent the dose per unit intake or external exposure.
DCFs may be specified for specific body organs of interest, or as a weighted sum of individual organ doses,
termed the effective dose. These DCFs may be multiplied by the total activity of each radionuclide inhaled
or ingested per year or the external exposure to estimate the radiation dose to a receptor, in a manner analogous
to the use of the radionuclide slope factors for estimating risk. EPA-approved DCFs for inhalation and
ingestion exposure are published in Federal Guidance Report No. 11 (EPA88), and DCFs for external
exposure are published in Federal Guidance Report No. 12 (EPA93).
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Prior to the development of the radionuclide slope factors, cancer risk from radiation exposure was traditionally
estimated by multiplying the radiation dose computed using the DCFs by an estimate of the cancer risk per unit
dose (e.g., risk per person-rad), which is averaged over all organs and tissues. Recent estimates of the dose-to-
risk conversion factor are shown in Table 1 -1. EPA does not recommend this method, and estimates of risk
computed using this method are generally greater than those computed using the slope factor method; the
magnitude of this discrepancy depends on the particular radionuclides and exposure pathways for the site-
specific conditions, but can range from less than a factor of two to approximately one order of magnitude.
These differences may be attributed to factors such as the consideration of competing mortality risks and age-
dependent radiation risk models in the development of the slope factors, different distributions of relative
weights assigned to individual organ risks in the two methods, and differences in dosimetric and toxicological
assumptions. Some of these key differences are summarized in Table 1-2.
In evaluating sites contaminated with radioactive materials, it is generally useful to estimate both radiation dose
and health risk. DCFs should be used to compute radiation doses resulting from site-related exposures for
comparison with radiation protection standards and dose limits, and radionuclide slope factors should be used
to estimate cancer risk from radionuclide exposure to compare with EPA's target risk range (i.e., 10"4 to 10"6
lifetime excess cancer risk) for cleanup.
Comparison of Slope Factors for Radionuclides and Chemicals
At sites contaminated with both radionuclides and hazardous chemicals, the risks from both types of
contaminants should be considered to assess overall site conditions. However, risk estimates for radionuclides
and chemical contaminants should be assessed and presented separately in the risk characterization. Care
should be exercised in combining radiation and chemical risk estimates. The risk estimates for radionuclides
and chemicals may relate to different cancer endpoints, and slope factors for radionuclides and chemicals
incorporate several differences that may result in incompatibility; some of these differences are summarized
in Table 1-3.
For hazardous chemicals, evaluation of both carcinogenic and noncarcinogenic risks may be required. For
radionuclides, however, cancer risks generally will be limiting, and provide a sufficient basis for assessing
radiation-related human health risks at contaminated sites. One exception is uranium: for uranium, a kidney
toxin, chemical toxicity may be as important as, or more important than, radiotoxicity. For uranium, EPA
recommends consideration of both carcinogenic risk using the radionuclide slope factors and also noncancer
risk due to chemical toxicity using the reference dose.
Current knowledge of carcinogenesis from low-level exposures to radiation or chemicals in the environment
is very uncertain, and it is not known whether the impacts from multiple contaminants may be additive,
synergistic or antagonistic. However, in the absence of additional information, it is reasonable to assume that
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Table 1-1. Estimates of Cancer Mortality Risk per Unit Dose of Low-Level Low-LET Radiation
Source
EPA94a "
ICRP91
NAS90
EPA89b e
UNSC88
St88
NAS80
Fatal Cancer Risk
(per 10s person-rad)a
509
500
800
392
710
450
67-403
Comments
Incorporates a DDREF = 1 for breast and a DDREF = 2 for other sites.
Incorporates a DDREF = 2.
No DDREF incorporated (i.e., DDREF = 1); however, a DDREF = 2 to 10 is suggested
for low-level exposures.
No DDREF incorporated (i.e., DDREF = 1).
No DDREF incorporated (i.e., DDREF=1); however, a DDREF = 2 to 10 is suggested
for low-level exposures.
Incorporates a DDREF = 2 for breast and a DDREF = 3 for other sites
Incorporates a DDREF = 1 for the upper limit and a DDREF = 2.48 for the lower limit.
(a) Cancer risk per 10s person-rem for ICRP (1991). (b) Current EPA estimate - see Chapters 2-3 and Appendix D. (c) Pre-1994 EPA
estimate - see Appendix C. DDREF = Dose and dose rate effectiveness factor.
Table 1-2. Comparison of Radiation Risk Estimation Methodologies:
Slope Factor Approach vs. Dose-to-Risk Conversion Factor Approach
Parameter
Competing
Risks
Risk Models
Genetic Risk
Dose
Estimates
RBEfbr
alpha
radiation
Organs
Considered
Lung Dose
Definition
Integration
Period
Dosimetric/
Metabolic
Models
Slope Factor Approach
Persons dying from competing causes of death (e.g.,
disease, accidents) are not considered susceptible to
radiation-induced cancer.
Probability of dying at a particular age from competing risks
is considered based on the mortality rate from all causes at
that age in the 1979-1981 U.S. population.
Age-dependent and sex-dependent risk models for 14
cancer sites are considered individually and integrated into
the slope factor estimate.
Genetic risk is not considered in the slope factor estimates;
however, ovary is considered as a potential cancer site.
Low-LET and high-LET dose estimates considered
separately for each target organ.
20 for most sites (8 prior to 1 994)
10 for breast (8 prior to 1994)
1 for leukemia (1.1 17 prior to 1994)
Estimates of absorbed dose to 1 6 target organs/ tissues
considered for 1 3 specific cancer sites plus residual
cancers.
Absorbed dose used to estimate lung cancer risk computed
as weighted sum of dose to tracheobronchial region (80%)
and pulmonary lung (20%).
Variable length (depending on organ-specific risk models
and consideration of competing risks) not to exceed 110
years.
Metabolic model parameters for dose estimates generally
follow ICRP Publication 30 (ICRP79) recommendations;
exceptions include transuranic radionuclides (Su81).
Dose-to-Rtsk Conversion Factor Approach.
(Effective Dose Equivalent x Risk Factor)
Competing risks are not considered explicitly. (In some cases,
they may be incorporated into the derivation of the risk
factor— e.g., EPA94a.)
Risk estimate averaged over all ages, sexes, and cancer sites.
Effective dose equivalent value includes genetic risk component.
Dose equivalent includes both low-LET and high-LET radiation,
multiplied by appropriate Relative Biological Effectiveness (RBE)
factors (see below).
20 (all sites)
Effective Dose Equivalent (ICRP79) considers dose estimates to 6
specified target organs plus remainder (weighted average of 5
other organs).
Effective dose (ICRP91) considers dose estimates to 12 specified
target organs plus remainder (average of 10 other organs).
Average dose to total lung (mass weighted sum of
nasopharyngeal, tracheobronchial, and pulmonary regions).
Fixed integration period of 50 years typically considered.
Typically employ ICRP [Publication 30 (ICRP79) and/or Publication
60 (ICRP91)] models and parameters for radionuclide uptake,
distribution, and retention.
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Table 1-3. Comparison of Slope Factors for Radionuciides and Chemical Carcinogens
Parameter
Endpoints
Considered
Dose-Response
Model
Epidemiological
Basis
Statistical Level
Mechanism of
Cellular Damage
Exposure Routes
Special
Considerations
Uncertainties
Radionuclide Slope Factor
• Carcinogenic risk only (i.e., cancer as the cause of
death); however, for uranium only, noncarcinogenic
risk is considered separately, by comparison to its
Reference Dose (RfD)
• Linear non-threshold model
• Extrapolated from high dose exposures
• Risk estimates based primarily on human
epidemiological data
• Central estimate of mean
• Physical energy released during radioactive decay
ionizes biological tissue, producing free radicals
• Ingestion of water, soil, and food products
• Inhalation of participates and gases (radon)
• External gamma exposure
• Radioactive decay and ingrowth of radioactive decay
products: individual radionuclide concentrations may
decrease or increase with time
• Natural background is ubiquitous at levels exceeding
typical risk targets; natural variability in background
may swamp ability to distinguish small increments due
to contamination
Chemicaf Stops Factor
• Tumorigenic risk only; however, for some chemicals,
noncarcinogenic risks are considered separately
using appropriate RfD values
• Linear non-threshold model
• Extrapolated from hiqn dose exposures
• Risk estimates typically based primarily on animal
studies, with little human data
• 95% upper confidence limit on the mean
• Chemical action produces free radicals
• Ingestion of water, soil, and food products
• Inhalation of particulates and vdatites
• Dermal absorption on contaminants on skin
• Degradation products may include other carcinogens.
• Background levels in the environment typically tow
• For both chemicals and radionuclides, extrapolation from high dose and high dose rate exposure is generally required
to estimate risks of low-level exposures; this extrapolation typically constitutes one of the greatest sources of
uncertainty. For chemical carcinogens additional uncertainty may be introduced due to extrapolation of animal data to
humans. Slope factors for both radionudides and chemicals are used to estimate incremental cancer risk, which
typically represents a small increment over a relatively high baseline incidence.
excess cancer risks are additive for purposes of evaluating the overall potential human health hazard associated
with a contaminated site.
1.5 CONTENT OF THIS REPORT
The remainder of this report is organized as follows:
• Chapter 2 presents an overview of EPA's method of developing radionuclide slope factors. It
summarizes the integration of dosimetric and health effects models, with consideration of competing
risks, to estimate age-averaged excess lifetime cancer risk. [NOTE: In 1994, EPA adopted a revised
methodology for estimating radiogenic cancer risk and the calculation of radionuclide slope factors;
this new methodology is discussed in the body of this report. Similar information for the previous
methodology, used for estimating radiogenic cancer risk and radionuclide slope factors prior to 1994
is presented in Appendix C.]
• Chapter 3 presents a more detailed discussion of currently-recommended EPA models for estimating
cancer risk per unit radiation dose. Appendix C provides similar information on previously-
recommended EPA risk models.
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• Chapter 4 presents detailed numerical examples of the methods used to estimate cancer risks and slope
factors.
• Chapter 5 presents a brief overview of some of the important sources of uncertainty in the assessment
of risks from radionuclide exposures.
• Appendix A presents a summary of the models used for estimation of doses resulting from internal
and external exposures to radionuclides.
• Appendix B presents compilations of the attributable mortality risk coefficients used for developing
the radionuclide slope factors.
• Appendix C presents information on the methodology used by EPA for estimating radiogenic cancer
risk and radionuclide slope factors prior to adoption of the revised methodology in 1994. Appendix
C also includes numerical examples of the slope factor derivation using this previous methodology,
corresponding to those presented in Chapter 4 for the revised methodology.
• Appendix D presents calculational details of the radiogenic cancer risk models currently used by EPA
for derivation of the radionuclide slope factors (adapted from EPA94a).
Chapters 1 and 2 provide a general introduction to the radionuclide slope factors used by EPA for evaluating
radiation risks; this discussion is intended to address the needs of most readers in understanding the
interpretation and application of radionuclide slope factors. Chapter 3 presents additional discussion of the
radiogenic cancer risk models used in the development of the radionuclide slope factors; similar information
for the previous risk models (prior to 1994) is presented in Appendix C. Chapter 4 presents a series of
illustrative examples which may be helpful in understanding the calculational mechanics of the slope factor
derivation; corresponding examples for the methodology used by EPA for deriving slope factors prior to 1994
are presented in Appendix C. The discussion of uncertainties in Chapter 5 also should be of broad interest.
The summary of radiation dosimetry concepts and models in Appendix A is provided for reference purposes,
but is not essential to an understanding of the radionuclide slope factors. Similarly, the tabulations of risk
coefficients in Appendix B are provided for reference purposes only. Appendix D is very mathematically
oriented, and may be of limited interest, primarily to individuals desiring a more complete understanding of
the calculational mechanics of the radiogenic risk factor development.
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Chapter 2
Radionuclide Slope Factor Development
Chapter 2 presents an overview of the concepts and methods used to derive the radionuciide slope factors.
More complete discussions of the radiogenic cancer risk models, mathematical details of the calculational
methods, and examples of radionuciide slope factor development are provided in later chapters.
2.1 BASIC ELEMENTS OF RADIONUCLIDE SLOPE FACTOR APPROACH
The slope factor is an estimate of the incremental probability of developing cancer per unit dose/exposure of
a carcinogen over a lifetime. When multiplied by the total lifetime dose/exposure, the slope factor can be used
to estimate the probability of developing cancer as a result of that exposure.
Radionuciide slope factors are central estimates of the age-averaged, lifetime attributable cancer incidence
(fatal plus nonfatal cancer) risk per unit intake or external exposure to a specified radionuciide. EPA has
developed slope factors for estimating incremental cancer risks resulting from exposure to radionuclides via
inhalation, ingestion, and external exposure pathways. Ingestion and inhalation slope factors are central
estimates of the age-averaged, lifetime attributable cancer incidence risk per unit of activity inhaled or ingested
(risk/pCi). External exposure slope factors are central estimates of lifetime attributable cancer incidence risk
for each year of exposure to external radiation from photon-emitting radionuclides distributed uniformly in a
thick layer of soil (risk per year of exposure per pCi/g in soil). These values may be combined with site-
specific media concentration data and exposure assumptions to estimate lifetime attributable cancer risks to
current or future receptors at a site from radionuciide exposures. Slope factors for radionuclides are published
by EPA in IRIS (EPA96) and HEAST (EPA95).
The slope factors for radionuclides are based primarily on epidemiological data on human populations exposed
to high levels of "low-LET" (see Appendix A) ionizing radiation (high doses delivered at high dose rates).
For extrapolation of these data to the much lower doses typical of environmental radiation exposures, EPA
assumes that, for low-LET radiation, the risk per unit dose is reduced by a factor of two for ail cancer sites
except breast. In the range of environmental exposures, EPA assumes a linear non-threshold dose-response
mode! - i.e., that no lower threshold exists for radiation carcinogenesis, such that any level of exposure may
be associated with some probability of incremental cancer incidence. However, since the cancer risk is
stochastic (i.e., statistical or probabilistic) in nature, it is not possible to determine which cancers in an exposed
population are caused by radiation exposures. The extrapolation of epidemiological data for populations
exposed at high radiation doses and dose rates to much lower levels characteristic of environmental exposures
is a significant source of uncertainty in determining risks from low-level radiation.
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Radionuclide slope factors relate the lifetime cancer incidence risk attributable to given radionuclide exposure
conditions for an average member of an exposed population. This estimate of attributable risk is averaged over
age and sex for a reference population with specified mortality statistics. The slope factors estimate the
average risk within this population, but may not accurately indicate the risk to a single individual of a particular
age or sex. These estimates are only applicable under conditions where the incremental radiation-induced risks
do not appreciably alter the survival statistics of the reference population, i.e., where the radiation-induced
risks are very small relative to the competing risks experienced by the population; this condition is satisfied
under typical environmental radiation exposure situations.
Radionuclide slope factors are used to estimate the risk of developing cancer from exposure to a given
radionuclide under specific exposure conditions. Principal exposure parameters to be considered include: (I)
the radionuclide concentrations in air, soil, water and foodstuffs; (ii) intake factors such as breathing rates, and
drinking and eating habits; and (iii) exposure time, frequency, and duration.
The lifetime attributable cancer risk to the average individual from exposure to a given radionuclide is
computed as the number of radiation-attributable cancer cases expected in a uniformly exposed population
divided by the size of the population (or alternatively, the probability of a radiation-induced cancer in the
average member of the population). This estimate of lifetime attributable cancer risk is then divided by an
appropriate exposure term (i.e., the total activity inhaled or ingested over a lifetime or the product of the
radionuclide concentration in soil and occupancy time in the contaminated area for external exposures) to
compute the slope factors for each pertinent exposure pathway.
In EPA's development of radionuclide slope factors, the size of the exposed population (or alternatively, the
probability of survival of an average member of the population) is allowed to decrease over time to account
for competing risks of death (i.e., risks other than radiation exposure). This is accomplished by the use of an
actuarial "life table" based on age-specific mortality data, which provides the number of survivors of an
original population (or alternatively, the probability of survival for an average individual of that population,
termed the "survival function") on an annual basis'.
The basic calculational elements used to derive a radionuclide slope factor are depicted in Figure 2-1 and
summarized below:
• Specific exposure assumptions are used to calculate dose rates in various body organs of interest.
Exposures may occur by inhaling or ingesting radionuclides (internal exposures) or by absorbing gamma
rays that emanate from radionuclides in the soil (external exposure). Exposure rates are expressed in terms
of the rate of inhalation or ingestion (pCi/y) for internal exposures, or in terms of the concentration of
radionuclides in the soil (pCi/g) and occupancy in the contaminated area for external exposures. Constant
unit exposure rates are assumed—i.e., each member of the exposed population is assumed to inhale or
ingest a unit activity of the radionuclide of interest per year, or to be continuously exposed to a unit
concentration of the radionuclide in soil.
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Figure 2-1. Basic building blocks used to calculate a radionuclide slope factor.
Radiation risk:
Survival
(life table)
data
Radiation
risk models
1
Cancer
mortality
data*
Age specific
risk per unit
dose coefficient
*Used for relative risk model calculations.
External exposure:
Survival
(life table)
data
Age specific
risk per unit
dose coefficient
Dose per unit
exposure
(external) data
Average lifetime
risk per unit
exposure coefficients
Internal exposure:
Survival
(life table)
data
Age specific
risk per unit
dose coefficient
Biokinetic
uptake for
intakes
Average lifetime
risk per unit
intake coefficients
Dosimetric
data (internal)
Age specific
absorbed
dose rates
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• Biokinetic and dosimetric models are used to estimate time-dependent dose rates in various organs and
tissues of the body. The organ-specific dose rates may vary independently over time.
- The RADRISK computer code (Du80) is used to estimate dose rates from ingestion or inhalation of
radioactive materials. The dosimetric methods used in RADRISK are based primarily on models
recommended by the International Commission on Radiological Protection (ICRP) in ICRP
Publication 30 (ICRP79).
For external exposures to radionuclides in soil, dose estimates are calculated for each radionuclide
using volume and surface dose factors derived using the DFSOIL computer code (SJ84). These dose
factors account for photon energy flux attenuation and buildup in soil, assuming the radionuclide is
uniformly distributed in a large volume of soil. This method involves approximations which can
considerably overestimate dose rates to body organs, and resulting estimates of radiation risk, for small
volumes of contamination (small areal extent and/or depth). [The external dose coefficients from
Federal Guidance Report No. 12 (EPA93) are not yet incorporated in the radionuclide slope factors,
but are expected to be incorporated in future revisions.]
• Lifetime risk of developing a radiation-induced cancer in a body organ or tissue is assumed to be directly
related to the dose delivered to that organ or tissue across all ages. Each dose that is received and
accumulated adds an incremental risk of developing cancer at that site at a later time. The average risk
per unit intake/exposure for an average member of the exposed population can be calculated as the
expected risk per lifetime exposure, at a constant exposure rate, to a unit intake/concentration of the
radionuclide of concern.
EPA's radionuclide slope factors developed prior to 1994 were based primarily on radiation risk
models recommended by the National Academy of Sciences (NAS) Committee on the Biological
Effects of Ionizing Radiation (BEIR) in its BEIR III report (NAS80).
- In 1994, EPA published revised risk models for radiogenic cancer risks (EPA94a) which are
incorporated in the current slope factors. The revised methodology incorporates: revised risk models
based primarily upon recommendations of the ICRP (ICRP91), NRC (Gi91), andNCRP (NCRP85);
a revised dose and dose rate effectiveness factor (DDREF); and a revised relative biological
effectiveness (RBE) value for alpha radiation.
• In order to estimate the attributable cancer risk in the population of interest, actuarial life expectancy
statistics are used to predict depletion of the population over time as a result of death from causes other
than radiation exposure. The probability of dying at any age from competing risks is calculated from the
mortality rate at that age for all causes, as specified in actuarial life tables for the U.S. population. By not
modifying the survival function for the additional risk due to radiation, an asymptotic risk per unit dose
or exposure can be calculated. In a stationary population, the population age distribution function is
proportional to the survival function at each age.
Survival data and vital statistics for calculation of the current radionuclide slope factors have been
taken from the decennial U.S. population data for 1979-1981 (NCHS85,84,83,82). Previously, EPA
used life table data from the 1970 decennial U.S. population (NCHS75, 73) in the calculation of
radionuclide slope factors. Under the revised methodology, EPA also has adopted a more robust
method for integrating the vital statistics and risk models.
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• For each radionuclide, the cumulative number of radiation-induced cancers accumulated over the lifetime
of the exposed population is calculated by summing the attributable cancers at each cancer site projected
in survivors of all ages within the reference population in each year following the beginning of exposure.
The attributable cancer risk at each cancer site is computed for each age (0 to 110 y) as the product of the
dose to that site (rad/y), the cancer risk per unit dose for that site (risk/rad), and the survival function value
at that age (probability of survival to that age). This risk estimate represents the expectation value of
individual risk as well as the average risk within the reference population.
• Finally, this estimate of the lifetime attributable cancer risk is normalized for the cumulative lifetime
exposure to estimate the radionuclide slope factor. For ingestion and inhalation, the average lifetime
attributable cancer risk is divided by the cumulative lifetime activity intake of the exposed population, to
obtain a slope factor for that radionuclide. For exposures to gamma rays emanating from radionuclides
in the soil, the lifetime attributable cancer risk is divided by the product of the concentration of the
radionuclide in soil and the average lifetime of a member of the exposed population to obtain a slope
factor. In either case, the denominator represents the cumulative lifetime exposure an average individual
in the reference population.
The following sections address each of these components of the analysis in more detail. Example calculations
of the slope factor derivation for each exposure pathway are presented in Chapter 4.
2.2 EXPOSURE ASSUMPTIONS
For ingestion and inhalation, a constant activity intake rate (pCi/y) of a radionuclide is assumed. For the
external exposure pathway, a constant radionuclide concentration in soil is assumed, which yields a constant
dose rate in each body organ considered. The assumed rate of intake and concentration of radioactivity in soil
are each arbitrary at this point, because the radionuclide slope factor is obtained, in part, by dividing by the
total activity intake rate and duration, or by the total exposure duration in the case of external exposure.
Although arbitrary, these exposure assumptions are needed in order to calculate time-dependent dose rates in
body organs.
For ingestion and inhalation, additional important exposure assumptions include the chemical and physical
form of the radionuclide or its carrier. Many radionuclides may exhibit different biokinetic behavior in the
body depending upon the chemical and physical form—e.g., solubility and availability for absorption from the
gastrointestinal tract may vary as a function of the chemical form of the ingested material, and clearance of
inspired particulates from the lungs may vary as a function of both the physical dimensions of the inspired
particulate and the chemical complex. The effect of the chemical and physical form on the dose estimates is
further discussed in Section 2.2.2.1 and in Appendix A.
EPA has evaluated dose rates and cancer risks from appropriate chemical compounds of each radionuclide of
concern. However, radionuclide slope factors are generally provided only for the most conservative forms (i.e.,
the assumptions yielding highest estimates of dose and risk) expected for environmental exposures. In cases
where the measured chemical and physical forms of the radionuclides of concern in" an actual exposure
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situation differ from that assumed for the slope factors, this assumption may result in additional conservatism
which should be considered in the uncertainty analysis in a site-specific risk assessment. [In certain cases
where a radionuclide is present as an impurity rather than in a pure compound, use of the default parameters
can sometimes lead to an underestimation of the risk.] For exposure situations where the default parameters
may not be appropriate, users should contact the Remedial Guidance Section of ORIA at EPA-HQ.
2.3 RADIATION DOSIMETRY MODELS
Based upon the assumed exposure conditions, radiation dosimetry models are used to calculate doses to body
organs. For each exposure pathway and radionuclide, the dose rates to body organs vary independently over
time. The methods used for estimating dose rates to organs of interest is briefly summarized in the following
sections. Additional details are provided in Appendix A.
2.3.1 Internal Exposure - Overview of Internal Dosimetry Models
The RADRISK computer code (Du80) is used to estimate dose rates from ingestion or inhalation of radioactive
materials. The dosimetric methods used in RADRISK are based primarily on models recommended by the
International Commission on Radiological Protection Publication 30 (ICRP79). The principal difference
between RADRISK and the ICRP approach is that RADRISK computes estimates of absorbed dose rates to
specified target organs separately for high and low linear energy transfer (LET) radiation, whereas ICRP
Publication 30 considers committed dose equivalent to specified target organs. The time-dependent dose rates
are needed for the life-table calculations discussed in Section 2.2.4. Detailed discussion of the technical basis
and calculational methods used in RADRISK is provided elsewhere (Du80), and is only briefly summarized
here.
All calculations performed with RADRISK assume that the parent radionuclide of a possible chain of
radionuclides is taken into the body by inhalation or ingestion without any radioactive decay products. Intake
of radioactive daughters must be treated in a separate execution of the code. However, the ingrowth and
dynamics of daughters in the body after intake of the parent radionuclide are considered explicitly in the
calculation of dose rate. In addition, consideration is made for different metabolic properties of the various
radionuclides in the decay chain; this is another difference between the dose rate calculations conducted by
EPA using RADRISK and those of the ICRP (ICRP79), in that the ICRP calculations assume that all
radioactive decay products adopt the metabolic characteristics of the parent radionuclide. Exceptions are made
for lead-210 and radium-228, where EPA has adjusted the models so the predicted activity distribution
conforms more closely to other published data (see Appendix C). For most other radionuclides, the impact
of these different assumptions is minor.
RADRISK considers intake of a given radionuclide by inhalation or ingestion. Inhaled activity is assumed to
be originally deposited in the lungs; from the lungs, activity may be absorbed by the bloodstream or
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mechanically cleared to the stomach. The model used in RADRISK for paniculate deposition and retention
in the respiratory tract is based on the ICRP Task Group Lung Model (ICRP66), and considers four major
regions: the naso-pharyngeal, tracheobronchial, pulmonary, and lymphatic tissues. A fraction of the inhaled
activity is initially deposited in each of the naso-pharyngeal, tracheobronchial, and pulmonary regions.
Deposition and clearance of inhaled particulates in the lung are controlled by the physical size distribution of
the particulates and their solubility classification. The size distribution of the particulate is specified by the
activity median aerodynamic diameter (AMAD); an AMAD of 1 micron is assumed for all particulates in
deriving the radionuclide slope factors. The model employs three clearance classes, based on the chemical
properties of the element: classes D, W, and Y correspond to rapid (days), intermediate (weeks), and slow
(years) clearance, respectively, of material deposited in the respiratory passages. Special cases, where these
standard clearance classes are not used, include tritium vapor and noble gases.
Ingested activity is initially deposited in the stomach. It then is assumed to proceed sequentially through the
small intestine, upper large intestine, and lower large intestine; activity may be absorbed into the bloodstream
from any of the four segments of the gastrointestinal (GI) tract. The transfer rate of activity from one segment
to the next is assumed to be proportional to the activity in the segment, such that the initial activity in a
segment would decrease exponentially with time. While the model allows consideration of absorption from
any combination of the four segments, only activity absorbed from the small intestine is normally assumed;
the fractional absorption from the small intestine is traditionally denoted as f|.
Activity absorbed by the blood from the gastrointestinal or respiratory tract is assumed to be distributed among
systemic organs and tissues or excreted, as specified by fractional uptake, distribution, and excretion
coefficients. The list of organs and tissues in which activity is explicitly distributed (source organs) is element-
dependent, and may include such organs as bone or liver where sufficient metabolic data are available. This
list is complemented by an additional source region denoted as "OTHER", which accounts for that systemic
activity not distributed among the explicit source organs and tissues or excreted; uniform distribution of this
remaining activity within OTHER is assumed.
Radioactive material which enters an organ or tissue may be removed by both radioactive decay and biological
removal processes. For each source organ or tissue, the fraction of the initial activity remaining at any time
after intake is described by a retention function consisting of one or more exponentially decaying terms. The
metabolic models used in RADRISK calculations are described elsewhere (Su8I).
The time rate of change of activity in the body is modeled by a system of ordinary differential equations. The
activity of a given radionuclide in an organ or tissue may be divided among several conceptual compartments.
Each differential equation describes the rate of change of activity in a compartment. In each compartment,
there may be formation of radioactive decay products, which may have different chemical and physical
properties from those of the parent.
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The estimates of activity in various organs, tissues, and cr-
specified organs of the body. Activity deposited in an organ
for penetrating radiations (i.e., gamma radiation and x-rays).:
estimates of dose rate to an organ or tissue include contribute -:
(for penetrating radiations), activity within that organ or tiss* * .-
of dose. RADRISK calculates estimates of dose rate separ '
subsequent use in estimating health risk. Additional details ^
partments are used to estimate dose rates to
tissue may deliver a dose to that organ and,
other organs and tissues of the body. While
• from activity distributed throughout the body
generally contributes the principal component
:iy for low-LET and high-LET radiation, for
lais calculation are presented in Appendix A.
A revised set of mathematical models for estimating dose- • rom internal radionuclide exposures, which
provides more accurate estimates of dose rates to body or.; r,.; and tissues from ingestion and inhalation
exposures, is expected to be incorporated in future versions c' -lie radionuclide slope factors. These revised
dosimetric models and data incorporate organ/tissue-spec if;- biokinetics and age-dependence, along with
updated metabolic models and radionuclide decay data.
2.3.2 External Exposure - Overview of External Dosimetr^ 'odels
Radionuclide slope factors for external exposure are derived t:
by the DOSFACTER computer code (KoSla, b, c). This c,
organs and tissues, based on Monte Carlo simulations of the;;
of scattered photons in air resulting from a uniform concentrati
are calculated for each radionuclide and organ of interest by
photon energy associated with the radionuclide decay. Photo
contaminated with a given radionuclide throughout its extent.
breadth (i.e., a uniform radionuclide concentration in a soil y,
estimates for any given radionuclide do not include contribm:
dose rates from all radioactive decay products must be explici
from the external exposure pathway.
•: ng external dose conversion factors computed
. is used to estimate the dose rate in various
.^rbed dose rate in each tissue for the spectrum
of monoenergetic photon sources. Dose rates
taking the sum of the contributions from each
< are assumed to emanate from soil uniformly
which was assumed to be infinite in depth and
i'.h infinite area and depth). External dose rate
ns from any radioactive decay products, and
; v considered to estimate the total dose and risk
Dose rates from external exposure to contaminated ground sun", ices depend on the height of the receptor above
the surface and the angle of incidence of photons on the bod}. This is especially important for low-energy
photons, such as those that would reach the body after scattering in soil. The flux increases from the value for
photons incident from immediately below the receptor to a maximum for photons arriving from close to the
horizon. For the radionuclide slope factor calculations, a height of 1 meter above the ground is assumed. (The
slope factor calculation does not depend strongly on the exact height assumed.) Attenuation and buildup due
to scattering are considered in the calculations. Secondars scattering results in a distribution of photon
energies at the receptor, which increases the radiation flux above that calculated on the basis of attenuation.
The current slope factors for external exposure represent the excess cancer incidence from exposure to a source
of uniform activity per unit mass in soil (risk/y per pCi/g). Ho1 v-ver, the dose estimates on which these values
2-8
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are based represent the dose rate to various organs and tissues of the body from exposure to a uniform
radionuclide concentration on the ground surface (mrem/y per pCi/cm2). Consequently, conversion from a
surface source to a volume source distribution is required. The ratio of the unit dose or risk factors for a
volume concentration and for a surface concentration has the dimension of length and can be considered the
effective depth of the radionuclide in soil relative to the surface dose factor.
Prior to 1992, the slope factors for external exposure were expressed as the cancer incidence from exposure
to a source of uniform activity per unit surface area (risk/yr per pCi/cm2). Risk calculations using these slope
factors presumed an effective depth of 10 cm for all radionuclides in soil. Since soil concentrations are
typically expressed in units of activity per unit mass (pCi/g), risks were computed as the product of the surface
slope factors, the assumed effective depth (10 cm), the assumed soil density (1.43 g/cm3), and the soil
concentration. This effective depth value was expected to be reasonable for high-energy photon emitters, but
was expected to overestimate the risk for low-energy photon (i.e., gamma and x-ray) emitters. In the latter
case, it was expected that risk from internal exposures would be the predominant contributor to total risk, so
the overestimate of external exposure risk would not be significant. In practice, however, this approach led
to prediction of significant external exposure risks from radionuclides with low-energy photons, which were
inconsistent with reasonable expectations.
A revised approach for estimating the effective depth was adopted by EPA in 1992 to alleviate this problem.
The revised method uses volume and surface dose factors calculated with the DFSOIL computer code (SJ84),
and computes the radionuclide-specific effective depth as the ratio of these values. Estimates of the effective
depth using this approach range from over 5 cm for high-energy photon emitters to less than 0.05 cm for low-
energy photon emitters. Dose and risk estimates computed using the previous method exceed the values
computed with the revised method by factors ranging from less than 2 for some radionuciides with high-energy
photons to several hundred for low-energy photon emitters. Additional discussion of the external dose model
is provided in Appendix A.
The current estimates of dose and risk from external-exposure to radionuclides in soil presume that the source
is large in depth and areal extent. For small volumes of contamination (small areas and/or small depth), this
method can considerably overestimate dose rates and resulting estimates of radiation risk. Correction factors
to adjust for limited source areas are not currently considered in the slope factor derivation or application, but
may be considered in the future.
Revised tabulations of external dose conversion factors have been published in Federal Guidance Report No.
12 (EPA93), based on revised scattering calculations and radionuclide decay data. The revised method
provides more accurate estimates of dose rates to body organs and tissues from external exposure to
contaminated ground surfaces and from submersion in contaminated air and immersion in contaminated water.
Future revisions of the radionuclide slope factors are expected to incorporate these revised estimates.
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2.4 CANCER RISK MODELS
The estimated dose rates for each organ or tissue at specified times following the beginning of exposure are
used to estimate the number of incremental cancers in the exposed population attributable to the radiation
exposure. The incremental risk of radiation-induced cancer in a given organ or tissue is estimated from the
absorbed dose to the organ or tissue together with appropriate radiation risk factors for that organ or tissue.
The radiogenic cancer risk coefficients are often presented in terms of the probability of cancer expressed over
a lifetime in an exposed individual per unit of dose (lifetime attributable cancer risk per rad). 'Expression' of
a cancer means that the cancer becomes observable—i.e., the risk of developing cancer is estimated from
analyses of cancers that have been observed, sometimes decades after the radiation exposure that caused the
cancer. Often, the risk factors are expressed in terms of incremental cancer risk per collective dose (e.g.,
cancer cases per million person-rad), which more clearly expresses the fact that at very low levels of individual
exposure it is impossible to know exactly where or when a radiation-induced cancer will appear in an exposed
population, or if a radiation-induced cancer will appear in any particular individual. It can only be estimated
that a certain number of cancers are likely to appear somewhere, at some time, in the survivors of an irradiated
group.
For the purposes of risk assessment, cancers are considered to occur randomly within an exposed population.
It is assumed implicitly that only one radiation-induced cancer occurs per person. For purposes of developing
slope factors, it is also assumed that fatalities resulting from the radiation-induced cancers do not appreciably
change the survival characteristics of the exposed population.
EPA's radionuclide slope factors prior to 1994 were based primarily on radiation risk models developed by the
U.S. National Academy of Sciences (NAS) Committee on the Biological Effects of Ionizing Radiation, in its
BEIR III report (NAS80); however, these risk estimates also incorporated elements of observations and
models of the National Council on Radiation Protection and Measurements (NCRP), the United Nations
Scientific Committee on the Effects of Atomic Radiation (UNSCEAR), the International Commission on
Radiological Protection (ICRP), the National Cancer Institute, and the Radiation Effects Research Foundation
(RERF, formerly named the Atomic Bomb Casualty Commission).
In 1994, EPA adopted a revised methodology to estimate radiogenic cancer risk for use in development of the
radionuclide slope factors (EPA94a). The revised methodology reflects recent information pertaining to the
Japanese atomic bomb survivors. For most cancer sites, the risk model adopted by EPA is one in which age-
specific relative risk coefficients are obtained by taking a geometric mean of coefficients derived from the
atomic bomb survivor data, employing two different methods for transporting risks from the Japanese to U.S.
populations. These risk models have been used to estimate incremental cancer risks to specific organs and
tissues per unit dose, based on age-at-exposure and vital statistics of the 1979-1981 U.S. population.
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EPA's risk models address both cancer incidence and cancer mortality from radiation exposures, but
radionuclide slope factors are based on cancer incidence risk models only (i.e., fatal + nonfatal cancers), to
maintain consistency with the slope factors for chemical carcinogens. Both the original and revised EPA risk
models address the expected expression rates of solid tumors, bone cancer, and leukemia. The cancer sites
considered by EPA under the two risk methods are shown in Table 2-1, For use in the development of
radionuclide slope factors, these organ-specific risk factors are further broken down as appropriate for specific
age groups to consider age-dependent risk; examples of this application are presented in Chapter 4 and
tabulations of the age-specific risk coefficients for each cancer site considered are presented in Appendix B.
Table 2-1. EPA Organ-Specific Risk Estimates for Low-LET Radiation:
Low Dose, Low Dose Rate (lifetime attributable cancer risk per 10s rad [104 Gy])
Cancer
Site
Esophagus
Stomach
Colon
Liver
Lunq
Bone
Skin
Breast
Ovary
Bladder
Kidney
Thyroid
Leukemia
Remainder
TOTAL
Mortality
NESHAPs
9.1
46.0
22.9
49.6
70.1
2.5
_
55.4
_
11.8
5.9
6.4
44.8
19.3
392.1
Revised3
9.0
44.4
98.2
15.0
71.6
0.9
1.0
46.2
16.6
24.9
5.5
3.2
49.6
123.1
509.1
Incidence
NESHAPs
9.1
60.1
42.9
49.6
74.5
2.5
142.0
21.4
21.4
64.3
44.8
33.6
623.0
Revised3
9.5
49.3
178.5
15.8
75.4
1.3
1.0
92.5
23.8
49.7
8.4
32.1
50.1
173.4
760.6
a Dose and Dose Rate Effectiveness Factor (DDREF) is 1 for breast and 2 for all other sites. These risk coefficients are applicable to
doses less than 20 rad (200 mGy) and for total doses greater than 20 rad from dose rates less than 10 mrad/min (0.1 mGy/min). The
revised model incidence estimate for skin shown is for fatalities only; the entire incidence risk for skin would be about 500 times greater.
The thyroid incidence risk includes only malignant neoplasms and does not include benign tumors or nodules. For high-LET radiation,
risk estimates are increased by a factor of 20 (RBE=20) for all cancers except leukemia (RBE=1) and breast (RBE=10).
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Different risk factors are used for low-LET radiation (beta and gamma radiations) and for high-LET radiation
(e.g, alpha particles), to reflect differences in the ability of these different types of radiation to induce cancers.
In the development of radionuclide slope factors prior to 1994, a relative biological effectiveness (RBE) of
8 was used in calculating the risk from a given absorbed dose of alpha particle irradiation for all cancer
sites—i.e., the risk factor for alpha-particle irradiation is increased by a factor of 8 relative to low-LET
radiation; in 1992, the high-LET risk estimates for leukemia were modified, based on epidemiologicaj data,
to revise the alpha RBE from 8 to 1.117 for leukemia only. Under EPA's revised methodology, the RBE value
for alpha particles has been increased to 20, which is consistent with recommendations of the ICRP (ICRP91);
exceptions are made for leukemia, which is assigned an RBE of 1, and breast, which is assigned an RBE of
10.
Radiogenic cancer risk also may be a function of the magnitude of radiation dose and the dose rate at which
it is delivered. In the revised methodology, EPA has assumed a dose and dose rate effectiveness factor
(DDREF) of 2 (i.e., the risk per unit dose is reduced by a factor of 2 for low level radiation exposures) for all
cancer sites except breast, for which a DDREF of 1 is assigned. In the development of radionuclide slope
factors prior to 1994, a DDREF of 1 was assumed for all cancers.
Two basic types of risk projection models may be used to estimate excess risks attributable to radiation
exposures. In 'relative risk' models the expression rate of radiation-induced cancers is assumed to be
proportional to the rate at which cancers develop in the general population; since the baseline cancer rate for
most sites increases at later ages, the expression rate of radiation-induced cancers is also presumed to increase.
'Absolute risk1 models, on the other hand, are based on the assumption that the expression rate of radiation-
induced cancers is proportional only to the radiation dose and is independent of the baseline cancer rate in the
population.
In the current EPA methodology (EPA94a), absolute risk models are used to estimate radiogenic cancer risk
for bone, skin, and thyroid. Relative risk models are used for all other cancer sites considered. Previously,
EPA assumed absolute risk models for leukemia and bone cancer only, and relative risk models for all other
cancer sites.
Additional discussion of the models and assumptions used by EPA for estimating radiogenic cancer risk is
provided in Section 3. For detailed discussion of this topic, the reader should consult Estimating Radiogenic
Cancer Risks (EPA94a).
2.5 REFERENCE POPULATION DATA: MORTALITY & SURVIVAL STATISTICS
An important feature of the slope factor methodology is the use of actuarial data (e.g., life tables or survival
functions) to account for the time dependence of the radiation dose and risk and to allow for competing risks
of death in the estimation of risk due to radiation exposure. A life table or survival function consists of data
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describing the age-specific mortality rates from all causes of death for a given population. This information
is derived from data obtained on actual mortality within a real population.
Survival data and vital statistics for calculation of the current radionuclide slope factors have been taken from
the decennial U.S. population data for 1979-1981 (NCHS85,84,83,82). Previously, EPA used life table data
from the 1970 decennial U.S. population (NCHS75, 73) in the calculation of radionuclide slope factors. Risk
estimates for a different population could be obtained by modifying the survival function to reflect the age and
sex distribution and mortality rates of the particular population at risk.
The use of a life table or survival function in the study of risk due to low-level radiation exposure is important
because of the time delay inherent in radiation risk. After a radiation dose is received, there is a minimum
latency (or induction) period of several years before a cancer can be clinically observed. Following this
minimum latency period, the probability of occurrence of a cancer during a given year is assumed to persist
for a specified period, called the plateau period. The length of both the latency and plateau period depend
upon the type of cancer. If the latent and plateau periods are known, the survival function can be used to
estimate the number of individuals who will die from incremental radiation-induced cancers in the presence
of competing risk. This information also can be used to estimate the total number of years of life lost to those
dying of radiation-induced cancer, the average number of years of life lost per incremental mortality, and the
decrease in the population's life expectancy.
For internal exposure pathways, it is assumed that each member of the hypothetical exposed population is
exposed to a constant unit activity intake rate of each radionuclide of interest—e.g., each exposed individual
inhales or ingests 1 pCi/y beginning at birth and continuing throughout his/her lifetime. For external exposure
to contaminated ground surfaces, it is assumed that each member of the reference population is continuously
standing on a ground surface with a constant unit soil concentration of the radionuclide of interest. Since the
models used for estimating dose rate and risk are assumed to be linear, these results may be scaled to evaluate
other exposure conditions.
Absorbed dose rates computed for specific ages' throughout the assumed lifespan of 0 to 110 years for a
constant intake rate are interpolated using a cubic spline method to obtain values at any age. For a given
cancer site, the incremental mortality risk as a function of age is calculated as the product of the dose rate at
'The current library of absorbed dose rates for specific ages (times following the beginning of chronic
exposure) is an artifact of EPA's earlier calculational methodology. For the original RADRISK calculations, the
span from 0 to 110 years was divided into nine intervals, and the dose rates (rad/yr) at the midpoints of these
intervals (i.e., 1, 3, 6, 12, 20, 30, 42, 56, and 87 years) to specified organs and tissues were calculated as
estimates of the average annual dose during that interval. Dose rates at two additional times (50 and 70 years)
were also calculated for other purposes. While the radiogenic cancer risk models and calculational methodology
have been revised, the RADRISK library of absorbed dose rates is still used for internal dose pathways.
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Figure 2-2. How are radionuclide slope factors derived?
Step 1. Determine applicable exposure pathway: inhalation, ingestion, or external exposure.
Step 2. Determine dose rate per unit exposure for the radionuclide to each organ/tissue of interest.
Step 3. Determine incremental cancer risk per unit dose rate for each cancer site (risk factors).
Step 4. Determine survival function for the reference population (probability of survival for an average member of the
population at each age due to risks other than radiation exposure).
Step 5. Calculate lifetime attributable cancer risk by summing the attributable cancers at each cancer site predicted in
survivors of all ages within the reference population during each year of exposure [i.e., L DoseM (rad/y) x Risk^ (rad~
') x Survival., (probability) x Duration (1 y) for each cancer site, s, and each age, a (0 to 110 y)].
Step 6. Calculate radionuclide slope factor by dividing the lifetime attributable cancer risk by the cumulative lifetime
exposure [nominally estimated as the product of the unit exposure rate and the average life expectancy for the
reference population (e.g, 73.77 y for the 1980 U.S. population)].
that age and the corresponding mortality risk per unit dose of radiation at that age (see Tables B-2 through B-
17), weighted by the probability of survival to that age (see Table 4-1).
This quantity is divided by the lethality fraction (see Table B-l), and integrated from age 0 to 110 to obtain
the lifetime incidence risk at a constant intake (or exposure) rate. The estimates of the incidence risk for each
cancer site are then summed over all cancer sites to obtain the total number of radiation-attributable cancers
projected to develop during the lifetime of the exposed population.
The intake (or external exposure) rate is also integrated over the same interval to obtain the lifetime intake (or
exposure). Finally, the slope factor (the average lifetime incidence risk per unit intake or exposure) is
computed as the quotient of these two quantities—i.e., by dividing the lifetime attributable cancer risk by the
cumulative lifetime exposure.
This procedure is performed for each radionuclide of interest and for each of the three modes of exposure
(inhalation, ingestion, and external exposure), as appropriate (see Figure 2-2). Simplified example
calculations are presented in Chapter 4. Additional discussion of the calculational methodology is presented
in Appendix D.
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Chapter 3
EPA Radiogenic Cancer Risk Models
Chapter 3 presents a summary of the radiogenic cancer risk models used in the development of the
radionuclide slope factors. EPA's recently revised methodology for estimating radiogenic cancer risk is
discussed here; similar information on previously recommended risk models is presented in Appendix C.
More complete discussions of the two approaches are presented elsewhere (EPA94a for the recently adopted
methodology, EPA89b for the previous methodology).
3.1 BACKGROUND
The principal adverse biological reactions associated with ionizing radiation exposures from radioactive
substances in the environment are carcinogenicity, mutagenicity, and teratogenicity. Carcinogenicity is the
ability to produce cancer. Mutagenicity is the property of being able to induce genetic mutation, which may
be in the nucleus of either somatic (body) or germ (reproductive) cells. Teratogenicity refers to the ability of
an agent to induce or increase the incidence of congenital malformations as a result of permanent structural
or functional deviations produced during the growth and development of an embryo (these are more commonly
referred to as birth defects). Radiation can induce other deleterious effects at acute doses above about 25 rad
(0.25 Gy), but doses of this magnitude are not normally associated with radioactive contamination in the
environment.
Ionizing radiation causes injury by breaking constituent body molecules into electrically charged fragments
called "ions" and thereby produce chemical rearrangements that may lead to permanent cellular damage.
Ionizing radiation can also damage DNA structure. The degree of biological damage caused by various types
of radiation varies according to how close together the ionizations occur. Some ionizing radiations (e.g., alpha
particles) produce intense regions of ionization. For this reason, they are called high-LET (linear energy
transfer) particles. Other types of radiation, such as beta particles, are called low-LET radiations because of
the sparse pattern of ionization they produce. High-energy photons (e.g., x-rays and gamma rays) are not
charged particles and, strictly speaking, have no LET; however, their interactions with matter produce low-
LET electrons, and therefore they are generally classified with low-LET particles. In equal doses, the
carcinogenicity and mutagenicity of high-LET radiations are usually found to be roughly an order of magnitude
greater than those of low-LET radiations.
For environmental exposures to radioactive materials, carcinogenic risk is considered to be limiting. Acute
effects are observed only at very high doses. Radiation-induced genetic effects have not been observed in
human populations, and extrapolation from animal data indicates that risks per unit exposure are smaller than
the risk of cancer; moreover, these risks may be induced only during the reproductive years and expression
of the genetic risk may be spread over many generations. The risk per unit exposure of serious teratogenic
3-1
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effects may be greater than the risk of cancer; however, there is some indication of a threshold for teratogenic
effects and these effects can be induced only during gestation. Therefore, for purposes of developing the
radionuclide slope factors considered in this report, only carcinogenic effects are considered.
Whereas many, if not most, chemical carcinogens appear to be organ- or tissue-specific, ionizing radiation can
be considered pancarcmogenic. According to Storer (St75): "Ionizing radiation in sufficiently high dosage
acts as a complete carcinogen in that it serves as both initiator and promoter. Further, cancers can be induced
in nearly any tissue or organ of man or experimental animals by the proper choice of radiation dose and
exposure schedule." Radiation-induced cancers that have been reported in humans include those in the
following tissues: thyroid, female breast, lung, bone marrow (leukemia), stomach, liver, large intestine, brain,
salivary glands, bone, esophagus, small intestine, urinary bladder, pancreas, rectum, lymphatic tissues, skin,
pharynx, uterus, ovary, mucosa of cranial sinuses, and kidney (UNSC77, 82; NAS72, 80, 90; Be77, Ka82,
Wa83).
Studies of populations exposed to high levels of radiation have identified the organs at greatest risk following
radiation exposure. The major sources of human epidemiological data include: the survivors of the atomic
bomb explosions at Hiroshima and Nagasaki; a large group of patients who were given x-ray therapy for
ankylosing spondylitis of the spine during the years 1934 to 1954; several groups of women who were
exposed to x-rays during diagnostic radiation of the thorax or during radio-therapy for conditions involving
the breast; several groups of patients who were medically treated with x-rays to alleviate some benign
conditions; underground miners exposed to elevated levels of radon and its decay products; workers who
ingested radium-226 and radium-228 while painting watch and clock dials; and patients injected with
thorotrast (colloidal thorium dioxide) as an x-ray contrast medium.
In addition to this large body of human data, radiation-induced cancers also have been observed in many
animal species, including rats, mice, hamsters, guinea pigs, cats, dogs, sheep, cattle, pigs, and monkeys.
Induced through multiple routes of administration and at multiple dose levels, these cancers have occurred in
numerous organs and tissues. These animal studies have provided information on the significance of dose rate
compared with the age of the animals at exposure, the sex of the animals, and the genetic characteristics of the
test strain. They have shown that radiation-induced cancers become detectable after varying latent periods,
sometimes several years after exposure. The animal studies further show that the total number of cancers that
eventually develop varies proportional to the dose each animal receives. Experimental studies in animals have
also established that the carcinogenic effect of high-LET radiation (alpha radiations or neutrons) is greater than
that of low-LET radiation (x-rays or gamma rays).
Not all of the cancers induced by radiation are fatal, and the lethality fraction may differ for different cancer
sites. The BEIR committees and ICRP have estimated cancer lethality by site and sex (NAS80, ICRP91).
Their estimates range from about 10 percent fatal in the case of thyroid cancer to 100 percent fatal in the case
of liver cancer. On the average, females have about 2 times as many total cancers as fatal cancers following
radiation exposure, and males have about 1.5 times as many.
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In addition to the evidence that radiation is pancarcinogenic, and as such can induce cancers in many different
sites, it also appears that it can induce cancer by any route of exposure (dermal, inhalation, ingestion, and
injection). Exposure routes considered in the development of radionuclide slope factors include inhalation,
ingestion, and external exposures.
3.2 CANCER RISK ESTIMATES FOR LOW-LET RADIATION
The most important source of epidemic logical data on radiogenic cancer risks from low-LET radiation
exposures is the population of survivors of the atomic bomb detonations in Hiroshima and Nagasaki, Japan.
The atomic bomb survivors have been studied for more than 40 years in a carefully planned and monitored
epidemiological survey (Ka82, Wa83). They are the largest group that has been studied, and they provide the
most detailed information on the response pattern for organs, by age and sex, over a wide range of doses of
low-LET radiation.
Nevertheless, there are gaps in the human data on radiation risks. For example, no clear-cut evidence of excess
genetic effects has been found in irradiated human populations, perhaps due to the limited numbers in the
exposed cohort providing inadequate power to detect a dose-response. Likewise, no statistically significant
excess cancer risk has been demonstrated below about 10 to 20 rad (0.1 to 0.2 Gy), whereas the dose range
of interest from the standpoint of environmental exposures is much lower. Since the epidemiological data are
incomplete in many respects, risk assessors must rely on mathematical models to estimate the risk from
exposures to low-level ionizing radiation. The choice of models, of necessity, involves subjective judgments
but should be based on all relevant sources of data collected by both laboratory scientists and epidemiologists.
Thus, radiation risk assessment is a process that continues to evolve as new scientific information becomes
available.
3-2.1 Dose Response Function and Dependence on Dose Rate
Radiogenic cancers in humans have been observed, for the most part, only following doses of ionizing
radiation that are relatively high compared to those likely to result from a combination of background radiation
and environmental contamination. Therefore, a dose response model must be chosen to quantify the risks and
to characterize their uncertainties for small incremental doses above natural background. The primary types
of dose response models generally considered for radiogenic cancer risk include: (1) the linear model, in which
the number of effects (risk) is directly proportional to dose at all doses; (2) the linear-quadratic model, in which
risk is very nearly proportional to dose at very low doses and proportional to the square of the dose at high
doses; and (3) the quadratic model, where the risk varies as the square of the dose at all dose levels.
A comprehensive examination of this question was contained in NCRP Report 64 (NCRP80). Based primarily
on laboratory studies of cells, plants and animals, the report advocated a linear-quadratic dose response for
acute doses up to about 250-400 rad (2.5-4 Gy), above which the dose response begins to turn over due to cell
3-3
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killing effects. At low doses, the quadratic term is negligible in comparison to the linear term. The NCRP
committee defined the low dose region as 0-20 rad (0-0.20 Gy). Evidence was also cited to the effect that the
D2 term in the dose response function vanishes when the radiation is delivered at low dose rates, even for total
doses above 20 rad (0.2 Gy).
According to current theories of radiogenic cancer induction, the low-LET dose response should be linear at
low doses or dose rates, and with equal slopes. At higher doses and dose rates, multiple track events become
important, and the dose response should bend upward. In these circumstances, the response per unit dose at
low doses and dose rates will be overestimated if one extrapolates linearly from observations made at high
doses, acutely delivered (NCRP80). The degree of overestimation is commonly expressed in terms of a dose
and dose rate effectiveness factor (DDREF)—e.g., a DDREF of 2 means the risk per unit dose observed at high
acute doses should be divided by 2 before being applied to low dose and dose rate conditions.
NCRP has suggested DDREF values of 2 to 10 (NCRP80). These values are based on analysis of animal
studies that showed reduced effects at low doses for a number of biological endpoints, including radiogenic
cancer in animals, chiefly rodents. However, the data on humans seem to be somewhat at variance with the
data from animal studies. Atomic bomb survivor data on solid tumors suggest a linear dose response
relationship with no indication of a reduction in risk per unit dose at low doses. For leukemia, there is
evidence of a curvelinear dose response relationship, suggestive of a DDREF of about 2. Clinical studies of
radiation-induced breast and thyroid cancer have shown little or no reduction in risk with dose fractionation
(NAS80, LaSO, Sh84, DaS9, Ho92); this suggests a DDREF of 1 for these sites. Studies of tuberculosis
patients who had undergone repeated fluoroscopic examinations found an elevated risk of breast cancer from
fractionated doses of x-rays, but no indication of an excess lung cancer risk (Da89, Ho92); when compared
with observed lung cancer risk in the atomic bomb survivors, the results of these studies suggest that the
DDREF may be quite large for lung cancer induction, although the possibility of confounding by the
underlying disease cannot be ruled out.
The results on human solid tumors appear to differ from those obtained through laboratory studies, including
studies of radiation-induced tumorigenesis in mice and rats. For the most part, the laboratory studies suggest
a DDREF of about 2 or 3, and sometimes higher, depending on the endpoint; on the other hand, most evidence
on humans suggests a lower DDREF, possibly about 1 for most sites. There are also experimental data
indicating mat radiation-induced mutation may increase linearly with dose, and independently of dose rate,
in human cells but not in rodent cells (Gr85).
Current mechanistic explanations for a DDREF all involve DNA repair. The linearity of the dose response
at low doses suggests that DNA repair is maximal and independent of dose rate for doses below about 20 rad
(0.2 Gy). Repair of radiation-induced DNA damage is found to be largely complete within a few hours of an
acute exposure (Wh83, UI87). Consequently, protracting the dose beyond this time span should have little or
3-4
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no effect on the risk of cancer induction. It is expected, therefore, that repair will be maximal so long as no
doses above 20 rad (0.2 Gy) are delivered within a few hours.
While none of these examples is persuasive by itself, collectively they indicate that it may not be prudent to
assume that all kinds of cancers are reduced at low dose rates and/or low doses. However, it may be overly
conservative to estimate the risk of all cancers on the basis of the linearity observed for breast and thyroid
cancer.
3.2.2 Risk Projection Models
None of the exposed populations have been observed long enough to assess the full effects of their exposures
if, as currently thought, most radiogenic cancers occur throughout an exposed person's lifetime (NAS80, 90).
Therefore, another major choice that must be made in assessing the lifetime cancer risk due to radiation is to
select a risk projection model to estimate the risk for a longer period of time than currently available
observational data will allow.
To estimate the risk of radiation exposure that is beyond the period of observation, either a relative risk or an
absolute risk projection model (or suitable variations) may be used. The constant relative risk projection model
projects the currently observed percentage increase in annual cancer risk per unit dose into future years, i.e.,
the increase is proportional to the underlying (baseline) risk. An absolute risk model projects the average
annual number of excess cancers per unit dose into future years at risk, independent of the baseline risk.
Because the underlying risk of most types of cancer increases with age, the relative risk model predicts a larger
probability of excess cancer toward the end of a person's lifetime. In contrast, the absolute risk model predicts
a constant force of mortality across time. Therefore, given the incomplete data and less than lifetime follow-
up, a relative risk model projects a somewhat greater total lifetime cancer risk than that estimated using an
absolute risk model.
Recent evidence favors the relative risk projection mode! for most solid cancers. The epidemiological data
for the atomic bomb survivors indicate that, for solid cancers, relative risks have continued to remain constant
in recent years, while absolute risks have increased substantially (Ka82, NAS90). For cancers other than
leukemia, there is strong evidence of an increasing risk with age at expression, roughly in proportion to the
increase with age of baseline cancer mortality. The data are generally consistent with a constant relative risk
model in which the risk coefficients decrease with age at exposure. There is some suggestive evidence of a
fall-off in relative risk with time after exposure, especially for childhood exposures (NAS90, UNSC88), but
further epidemiological surveillance will be necessary to clarify the pattern of temporal change (Sh88).
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Smith and Doll (Sm78) reached similar conclusions on the trend in excess cancer with time among the
irradiated spondylitic patients. More recent analysis of the spondylitic data does show evidence of a fall-off
in relative risk after 25 years post-exposure, but the decrease is not yet statistically significant (Da86).
Although considerable weight should be given to the relative risk model for most solid cancers, the model does
not necessarily give an accurate projection of lifetime risk. The mix of tumor types varies with age so that the
relative frequency of some common radiogenic tumors, such as thyroid cancer, decreases for older ages. Land
has pointed out that this may result in overestimates of the lifetime risks when they are based on a projection
model using relative risks (La83). While this may turn out to be true for estimates of cancer incidence that
include cancers less likely to be fatal, e.g., thyroid, it may not be very important in estimating the lifetime risk
of fatal cancers, since the incidence of most of the common fata! cancers, e.g., breast and lung cancers,
increases with age.
Leukemia and bone cancer are exceptions to the general validity of a lifetime expression period for radiogenic
cancers. Most of the leukemia risk has apparently already been expressed in both the atomic bomb survivors
and the spondylitics (Ka82, Sm78). Similarly, bone sarcoma from acute exposure appears to have a limited
expression period (NAS80, Ma83). For these cancers, an absolute risk projection model with a limited
expression period appears to be adequate for estimating lifetime risk (NAS80).
The relative and absolute risk models used by EPA are age-dependent; that is, the risk coefficient changes,
depending on the age of the exposed persons. Observational data on how cancer risk resulting from radiation
changes with age are sparse, particularly so in the case of childhood exposures. Nevertheless, the explicit
consideration of the variation in radiosensitivity with age at exposure is a significant improvement in
methodology. It is important to differentiate between age sensitivity at exposure and the age dependence of
cancer expression. In general, people seem to be most sensitive to radiation when they are young. In contrast,
most radiogenic cancers seem to occur late in life, much like cancers resulting from other causes.
3.2.3 EPA Assumptions for Estimating Radiogenic Cancer Risk from Low-LET Radiation
Prior to 1994, EPA's estimates of cancer risks from low-LET radiation were based largely on the National
Academy of Sciences BEIR III report (NAS80). These estimates of radiation risk were based on a presumed
linear dose response function. A relative risk model with a lifetime expression period was assigned for all
cancer sites except for leukemia and bone cancer, where an absolute risk model with a 25-year expression
period was used. These risk estimates were used in the development of radionuclide slope factors prior to
1994. This methodology is summarized in Appendix C.
More recently, important new data have become available, especially revised dosimetry and further
epidemiological follow-up on the Japanese atomic bomb survivors. EPA has recently adopted a revised
methodology for estimating radiogenic cancer risks (EPA94a) to incorporate this new information. In addition,
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the revised approach utilizes more recent vital statistics forthe 1980 U.S. population, in place of the 1970 U.S.
vital statistics used previously. The revised methodology is summarized below.
Further epidemiological follow-up of the Japanese atomic bomb survivors since the publication of the BEIR
III report (NAS80) has lent additional support to the relative risk projection model for solid tumors. The
additional data provided by the follow-up reduces statistical uncertainties in the risk coefficients and fills in
important gaps pertaining to some organ-specific risks, particularly with respect to childhood irradiation
(Pr88).
Also subsequent to BEIR III, there has been a major reassessment of doses assigned to the atomic bomb
survivors, the effect of which, in general, is to increase the estimates of risk from low-LET radiation calculated
according to a particular model. The major differences between the dose estimates developed in 1965 (the
tentative 1965 dose estimates, T65) and the revised (Dosimetry System 1986, DS86) dose estimates are: (1)
the neutron dose in DS86 is decreased to 10 percent of its former value in Hiroshima and 30 percent in
Nagasaki (as a result, neutrons now contribute relatively little to the estimated excess of cancers in the two
cities); (2) the DS86 free-in-air gamma dose increases somewhat in Hiroshima but decreases in Nagasaki
relative to T65; (3) transmission of gamma rays through wooden structures is decreased by about a factor of
2 in DS86; and (4) transmission of gamma rays through the body to internal organs is generally increased,
partially nullifying the change associated with the decreased transmission through structures (Pr87, Sh87).
It appears that either a linear or linear-quadratic dose response is consistent with the survivor data, analyzed
according to the DS86 dose estimates (Pr87). However, as noted above, linear and linear-quadratic best fits
to the data differ only slightly in their predictions at low doses. It would also appear that the residual
difference in risk per unit dose between Hiroshima and Nagasaki is no longer statistically significant under
DS86 dosimetry (Sh87).
Risk estimates have been derived to reflect these new data in several recent reports (Sh88,90; UNSC88; St88;
NAS90; ICRP91; La91; Gi91). Based on a critical review of these studies and some ancillary information,
EPA has developed a revised methodology for estimation of radiogenic cancer risk.
3.2.3.1 Risk Models. EPA has adopted risk models developed by Land and Sinclair (La91) for the ICRP
(ICRP91) to develop nominal "best estimates" of radiogenic cancer risk to most organs of concern. For breast
cancer, however, the model developed by Gilbert (Gi91) for the NRC has been adopted by EPA.
The ICRP approach reflects a well defined, predetermined procedure in which the excess cancer mortality
observed in the atomic bomb survivors, by site, age, and sex, are used to calculate risk in the U.S. population,
and include relatively detailed information on the dependence of risk for specific cancer sites on age at
exposure. For the most part, the ICRP calculations make direct use of the age- and sex-specific relative risk
coefficients presented in RERF Report 11 (Sh88, Table 5A). Information in the RERF report is also used to
3-7
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incorporate three additional cancer sites into the model: esophagus, ovary, and bladder. Age-specific risk
coefficients for "residual" cancers are obtained by subtraction of specified cancers from the total cancers
expressed to date for the period of follow-up.
In the ICRP approach, three methods are used to transport risk estimates from the study population of atomic
bomb survivors to the reference population of interest. The additive projection model involves a direct
transport of age- and sex-specific absolute risk coefficients. The multiplicative projection model involves a
direct transport of relative risk coefficients. The NIH projection model is a hybrid of the additive and
multiplicative methods. For solid tumors, the total excess risk after the minimal latency period is projected
for the period of epidemiological follow-up (i.e., 10-40 years for the RERF data) using the absolute risk
coefficients of the additive model. However, it is considered to be distributed over time after exposure as a
multiple of the baseline rate. The NIH model relative risk coefficient yields the same risk over the follow-up
period as the absolute risk model. This coefficient is then used to project lifetime risk in the same way as for
the multiplicative model. With the NIH method, the excess risk varies with age, in proportion to the baseline
rates in the population of interest, but only weakly reflects differences between these baseline rates and those
in Japan.
A peculiarity of the NIH projection model is that it can artificially introduce age-dependent variability where
none can be discerned from the data. For example, in view of the very limited data on lung and colon cancer
mortality among the atomic bomb survivors exposed as children, the authors have assigned equal risk
coefficients for these cancers to the 0-9 year and 10-19 year age groups, for both the additive and multiplicative
models (Sh90, La91). However, if these age groupings are maintained, the derived NIH projection model will
contain significantly higher risk coefficients for the 0-9 year group, and a likely inflation of the risk estimates
associated with childhood exposures. To avoid this problem, the NIH risk coefficients for lung and colon are
calculated on the basis of treating the 0-19 year age group as a single group.
In developing organ-weighting factors, ICRP adopted an arithmetic average of the multiplicative and NIH
model projections for each cancer site. Land and Sinclair (La91) note that the multiplicative but not the
additive model provides a reasonable approximation to the epidemiologicat data; however, they also point out
that little information is available pertaining to the transfer across populations.
The NRC approach more explicitly incorporates expert judgement in the selection of risk coefficients, although
these coefficients do not generally represent statistical best estimates obtained from an analysis of
epidemiological data. Age-specific, constant relative risk models are recommended for all sites except
leukemia, bone, thyroid, and skin, for which absolute risk models are proposed. The models are designed to
be as simple as possible, but to yield estimates of risk on an age- and organ-specific basis, which are reasonably
central in view of the scientific uncertainties.
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3.2.3.2 Organ Risk Estimates. In view of the uncertainty in transportation of risk estimates from Japan to the
U.S. population, EPA has adopted a methodology in which most age- and site-specific risk coefficients are
taken to be the geometric means of the corresponding coefficients from the ICRP multiplicative and NIH
models; this method has been used to derive risk estimates for esophagus, stomach, colon, lung, ovary,
bladder, leukemia, and residual cancers. The choice of the geometric mean reflects a judgement regarding the
distribution of uncertainty associated with the transportation of risk, and is believed to provide a reasonable
central estimate of the risk, by organ and by age at irradiation. While giving weight to both the multiplicative
and NIH approaches, it tends to de-emphasize extreme values which may reflect large extrapolations based
on a few excess cancers observed among those exposed as children. In calculation of the geometric mean risk
estimates, EPA has also made adjustments for differences in the temporal assumptions in the multiplicative
and NIH models for leukemia, and for apparent anomalies in the risk coefficients presented by Land and
Sinclair for "residual" cancers in the 0-9 year age group.
For breast cancer, however, the model of Gilbert (Gi91) has been adopted by EPA. This model has the
advantage of being derived from data for North American women. This breast cancer model was based largely
on studies of women from the U.S. and Canada who received diagnostic or therapeutic doses of x-rays. This
model thus avoids the major issue of transporting risk estimates from Japan to the U.S., where the baseline
rates of breast cancer are much higher. Risk estimates using this model are in reasonable agreement with the
ICRP NIH model but are substantially lower than the projection made with the ICRP multiplicative model.
The model exhibits a sharp decrease in risk with age at exposure.
Estimates of kidney cancer risk are based upon the age- and sex-averaged excess relative risk coefficient from
the Atomic Bomb Survivor Study and the corresponding absolute risk coefficient reported by Shimizu et al.
(Sh88), adjusted from shielded kerma to absorbed dose. These risk coefficients are then used to estimate risks
through the ICRP multiplicative and NIH projection models, and the geometric mean of these two estimates
computed for use by EPA.
For liver cancer, EPA has adopted a constant relative risk model independent of age-at-exposure and sex. This
model is used in conjunction with a risk coefficient derived using the BEIR III and BEIRIV estimates of fatal
liver cancer induction by alpha particles (300 excess fatal liver cancers per million person-rad; 30,000 excess
fatal liver cancers per million person-Gy) and an assumed RBE of 10 for alpha particles (relative to acute high-
dose, high-dose-rate low-LET radiation).
As a basis for estimating radiation-induced bone sarcomas, EPA has adopted the BEIR IV risk estimate for
alpha irradiation by radium-224 (NAS88), with adjustment to convert from average skeletal dose to endosteal
dose by assuming a factor of 7.5 reduction in the risk estimate; this estimate is further adjusted using an
assumed RBE of 10 to estimate low-LET risk, and an assumed lethality fraction of 70%. Following BEIR III
(NAS80), a constant absolute risk model was selected for projecting risk, with an expression period extending
from 2 to 27 years after exposure.
3-9
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EPA's estimates of risk to the thyroid continue to be based on the recommendations of the NCRP (NCRP85).
Both the ICRP and NRC have also adopted this approach. The estimated fatality risk is calculated as one-tenth
the incidence risk. The estimated incidence and mortality risks are each reduced by a factor of 3 in the case
of exposures to iodine-125, -129, and -131; however, this reduction includes the effect of lowered dose rate
on the risk, and no additional DDREF should be used in the case of these radioiodine exposures.
Estimates of skin cancer risks are highly uncertain, but the mortality is known to be relatively low. For acute
exposures, EPA has adopted the ICRP mortality risk estimate (2 excess fatal cancers per million person-rad;
200 excess fatal cancers per million person-Gy); however, in contrast to ICRP, EPA has adopted a DDREF
of 2 for estimating skin cancer risk at low doses and dose rates. Due to the large uncertainty in available data,
EPA will ordinarily exclude nonfatal radiogenic skin cancers from its estimates of risk.
The site-specific risk coefficients for individual age groups are summarized in Table 3-1. Absolute risk models
are used for bone, skin, and thyroid cancers, whereas relative risk models are used for all other cancers.
3.2.3.3 Risk Estimates for Low-Level Radiation Exposures. For the revised estimates of radiogenic cancer
risk, EPA has adopted a dose and dose rate effectiveness factor (DDREF) value of 2 as a reasonable best
estimate. This value has recently been adopted by the ICRP (ICRP91), as well as by other organizations (Gi91,
CIRRPC92), and is expected to be widely applied for purposes of risk assessment and radiation protection
worldwide.
The DDREF is applied to all organ-specific risks except for the breast. There is epidemiological evidence that
dose fractionation has little or no effect on risk to the breast (NAS88); moreover, the risk model adopted by
EPA is based mainly on fluoroscopy studies in which the doses were in fact delivered as multiple small
fractions (NAS90, Gi91). Hence, EPA has adopted a DDREF of 1 for breast cancer. This choice assumes that
the risk (per unit dose) of highly fractionated exposures approximates the risk at low doses and dose rates.
EPA has defined specific conditions under which the DDREF should be applied (EPA94a). Although the
biological mechanisms are not yet elucidated, according to current thinking: at low doses, repair is maximal,
and the unrepaired DNA damage reflects single track events; at higher (acute) doses, repair decreases due to
damage caused by multiple tracks passing through the cell nucleus in close temporal proximity. It would
appear that repair efficiency is maximal for all doses below about 20 rad (0.2 Gy) (NCRP80). It also appears
that DNA repair is essentially completed within a few hours after radiation-induced damage (Wh83, U187).
Consequently, maximum repair efficiency should occur so long as the dose does not exceed 20 rad (0.2 Gy)
over a few hours. In view of these considerations, EPA has adopted UNSCEAR's recommendation that the
DDREF should be applied whenever the total dose is below 20 rad (0.2 Gy) or the dose rate is below 10
mrad/min(0.1 mGy/min) (UNSC93).
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Table 3-1. Mortality risk coefficients for EPA revised risk methodology
|.;[:;':;G^|ijCei|;:;; •£%&!&
'.]•£$$$&.-£ 'ft££i '£ s &;
Male:
Esophagus
Stomach
Colon
Liver
Lung
Bone
Skin
Breast
Ovary
Bladder
Kidney
Thyroid
Leukemia
Residual
Female:
Esophagus
Stomach
Colon
Liver
Lung
Bone
Skin
Breast
Ovary
Bladder
Kidney
Thyroid
Leukemia
Remainder
fiiili
R
R
R
R
R
A
A
R
R
R
R
A
R
R
R
R
R
R
R
A
A
R
R
R
R
A
R
R
0,2239
1.2337
2.1565
1.3449
0.4060
0.0927
0.0672
0.0
0.0
1.2191
0.3911
0.1667
672.16
0.7115
1.0418
3.4469
2.9680
1.3449
1.3753
0.0927
0.0672
0.7000
1.3163
1.0115
0.3911
0.3333
761.07
0.7119
0.2312
1.9165
2.1565
1.3449
0.4060
0.0927
0.0672
0.0
0.0
1.1609
0.3911
0.1667
244.07
0.7140
1.0896
4.2721
2.9680
1.3449
1.3753
0.0927
0.0672
0.7000
1.0382
0.9296
0.3911
0.3333
225.81
0.7174
0.2517
0.19051
0.2809
1.3449
0.0453
0.0927
0.0672
0.0
0.0
1;0736
0.3911
0.0833
323.47
0.1735
1.2492
4.0533
0.5755
1.3449
0.1921
0.0927
0.0672
0.3000
0.8829
1.0124
0.3911
0.1667
281.76
0.2932
0.2892
0.2881
0.4275
1.3449
0.1342
0.0927
0.0672
0.0
0.0
1.0544
0.3911
0.0833
228.86
0.1754
1.5831
0.5797
0.8186
1.3449
0.5440
0.0927
0.0672
Q.30QO
0.7678
1.1032
0.3911
0.1667
153.12
0.2963
0.3258
0.2524
0.0899
1.3449
0.1794
0.0927
0.0672
0.0
0.0
0.9639
0.3911
0.0833
142.51
0.1847
2.0211
0.4887
0.1870
1.3449
0.8048
0.0927
0.0672
0.1000
0.6367
0.979.2
0.3911
0.1667
154.28
0.3031
::; v:L^etHaJityjs:^
o. ::FiaCti0B:;!i::;S::
0.95
0.90
0.55
0.95
0.95
0.70
-
-
-
0.50
0.65
0.10
0.99
0.71
0.95
0.90
0.55
0.95
0.95
0.70
—
0.50
0.70
0.50
0.65
0.10
0.99
0.71
Notes:
Risk model type Coefficient units
Absolute (A) 10-6 (rad/y)'1 {10^ (Gy/y)'1 ]
Relative (R) lO^rad'1 (Gy1)
Lethality fractions (mortalfty:incidence ratios) are from Table B-19 of ICRP Publication 60 (ICRP91) except for remainder
and skin; lethality fraction for remainder is calculated from the corresponding value of (2-k) in Table B-20 of ICRP
Publication 60; for skin, only fatal cases are considered in the risk coefficients, and the much larger number of nonfatal
cases, most of which are easily treated, are omitted.
Based on the risk models discussed above and the DDREF value of 2, EPA has developed risk estimates for
excess cancer mortality risk resulting from exposure to radiation in low doses and dose rates for specific cancer
sites listed in Table 3-2. To obtain estimates of radiation-induced cancer incidence, each site-specific
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mortality risk estimate is divided by its respective lethality fraction, i.e., the fraction of radiogenic cancers at
that site which are fatal. With the exception of thyroid cancer, the lethality fraction is generally assumed to
be the same for radiogenic cancers as for the total cancers at that site. Site-specific cancer incidence risk is
calculated using ICRP's recommended lethality fractions (ICRP91), with the exception of skin. For skin
cancer, in the absence of data on what fraction of radiogenic skin cancer cases might be regarded as serious,
the incidence estimate reflects only fatal cases and omits the much larger number of nonfatal cases, most of
which are easily treated (see EPA94a). The site-specific estimates of radiogenic cancer mortality and incidence
risk are summarized in Table 3-2.
Table 3-2. EPA revised radiogenic cancer risk coefficients -
low dose and low dose rate [per 106 rad (per 104 Gy)]a
Cancer Site
Esophagus
Stomach
Colon
Liver
Lung
Bone
Skin
Breast
Ovary
Bladder
Kidney
Thyroid
Leukemia
Remainder
Total
Mortality
9.0
44.4
98.2
15.0
71.6
0.9
1.0
46.2
16.6
24.9
5.5
3.2
49.6
123.1
509.1
Incidence
9.5
49.3
178.5
15.8
75.4
1.3
1.0
92.5
23.8
49.7
8.4
32.1
50.1
173.4
760.6
Lethality
Fraction*1
0.95
0.90
0.55
0.95
0.95
0.70
-
0.50
0.70
0.50
0.65
0.10
0.99
0.71
~
* The Dose and Dose Rate Effectiveness Factor (ODREF) is 1 for breast and 2 for all other
sites. These risk coefficients are applicable to doses less than 20 rad (0.2 Gy) and for total
doses greater than 20 rad (0.2 Gy) from dose rates less than 10 mrad/minute ( 0.1
mGy/minute). The incidence estimate for skin is for fatalities only; the entire incidence risk for
skin would be 500 times higher. The thyroid incidence risk includes only malignant neoplasms
and does not include benign tumors or nodules.
h Lethality fractions (mortality:incidence ratios) except for remainder and skin are from Table B-
19 of ICRP Publication 60 (ICRP91); lethality fraction for remainder is calculated from the
corresponding value of (2-k) in Table B-20 of the same document. For skin, the incidence
estimate considers only fatal cases and omits the much larger number of nonfatal cases, most
of which are easily treated.
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For low-LET radiation, EPA's current estimate of the lifetime fatal cancer risk associated with uniform, whole-
body irradiation of the U.S. population has increased by 24% compared to the previous estimate, from 392 to
509 excess fatal cancers per 106 person-rad (per 104 person-Gy). It is estimated that about 70% of all cancers
induced by whole-body irradiation are fatal (nonfatal skin cancers excluded), corresponding to an incidence
risk estimate of 761 excess cancers per 106 person-rad (per 104 person-Gy). These increases occur despite the
change from a DDREF of 1 in the previous methodology (EPA89b) to a value of 2 in the revised methodology;
without this change, the risk estimates would have more than doubled.
For occupational exposures (assuming a constant exposure rate between ages 18 to 65), the mortality and
incidence risk estimates are 394 per 106 person-rad (per !04 person-Gy) and 567 per 106 person-rad (per 104
person-Gy), respectively.
3.2.3.4 Revised Life Table Analysis. In addition to the revised risk estimates noted above for specific cancer
sites, EPA also updated the vital statistics and adopted a revised approach for integrating the risk model and
vital statistics for the reference population. Male and female survival data (up to an age of 110 years) for the
U.S. population during 1979-1981 (NCHS85), have replaced the corresponding data for the 1970 decennial
U.S. population used previously. These data were used to calculate a combined life table for a male:female
live birth ratio of 1.051.
The vital statistics are discrete data, typically tabulated at one or five year intervals. Radiogenic risk models
used here are defined for several different age intervals and are inherently discontinuous. Previously, such risk
model calculations were implemented by adapting actuarial methods developed for life table calculations, using
the CAIRD computer code (Co78, Bu81). The revised method is to fit a cubic spline to discrete data and then
to calculate interpolated values, derivatives, and integrals directly from the spline coefficients. This method
admits almost any form of risk model and eliminates most of the ad hoc approaches that were necessary with
CAIRD.
3.3 CANCER RISK FROM HIGH-LET RADIATION
Radiobiological data indicate that high-LET alpha radiation has a larger biological effect than an equal
absorbed dose of low-LET radiation (NAS88, NCRP90, ICRP91). Unlike exposures to x-rays and gamma rays
where the resultant charged particle flux results in linear energy transfers (LET) of the order of 0.2 to 2 keV
per urn in tissue, 5-MeV alpha particles result in energy deposition of more than 100 keV per urn. The
radiobiological results, including those for tumor induction, are generally suggestive of a linear non-threshold
dose response for high-LET radiation, except for a possible fall-off in effectiveness at high doses. In contrast
to low-LET radiation, the effects of high-LET radiation may increase with fractionation or with a decrease in
dose rate.
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A number of cohorts exposed occupationally or medically to internally deposited alpha emitters have shown
an excess of cancer at heavily irradiated sites. Most important is the observed induction of: (1) lung cancer
in miners inhaling radon progeny; (2) bone sarcomas in patients injected with radium-224; (3) bone sarcomas
and head carcinomas in dial painters ingesting mixtures of radium-226 and radium-228; and (4) liver cancers
in patients injected with Thorotrast, an x-ray contrast medium containing isotopes of thorium. Although other
organs of the body received doses of alpha radiation in these populations, significant numbers of excess
cancers were generally not observed at sites other than those mentioned. As a result, only upper bounds to the
risk for these other organs can be estimated from studies of humans exposed to alpha irradiation.
Site specific cancer risk estimates for high-LET radiation (neutrons or alpha particles) are often calculated
utilizing human epidemiological data on low-LET radiation (e.g., from the Atomic Bomb Survivor Study) and
laboratory data on the relative biological effectiveness (RBE) of the high-LET radiation compared to a
reference low-LET radiation (NCRP90). Since the dose response relationship obtained for low-LET radiation
is typically linear or concave upward while that for high-LET radiation is linear or concave downward, the
RBE is dose dependent. EPA is primarily concerned with risks at low doses and dose rates, where the acute
high dose risk for low-LET radiation is reduced by the DDREF. Under these conditions, the dose responses
for both low and high LET radiations are thought to be linear, and the RBE takes on a constant (maximum)
value: RBEM.
Ranges of estimated values for neutron and alpha particle RBEu are wide, depending on both the biological
system and the observed end-point; the uncertainty in the RBEu estimate from an individual study is also
usually large, primarily due to the uncertainty in extrapolation of low-LET data to low doses. The
effectiveness of alpha emitters has been found to be 15 to 50 times that of beta emitters for the induction of
bone sarcomas, liver chromosome aberrations, and lung cancers (NCRP90). Since the LET of secondary
protons produced by fission neutrons in living tissue is comparable to that for alpha particles, data on the RBEs
of fission neutrons provides ancillary information relevant to the estimation of alpha particle RBE. Where the
dose response data on carcinogenic end-points are adequate to derive an estimate, fission neutrons have been
found to have an RBEj^ between 6 and 60 times that of low dose gamma rays (NCRP90).
3.3.1 Relative Biological Effectiveness
The ICRP (ICRP91) assumes that alpha radiation produces 20 times the risk, per unit absorbed dose, as low-
LET radiation. This relationship is meant to hold in the limit of low doses and dose rates. Thus, it already
takes into account the assumed DDREF of 2 for low-LET radiation; at high acute doses, the RBE would be
10. This must be kept in mind both when calculating alpha particle risks using models derived from low-LET
epidemiological data and when estimating low-LET risks (for bone and liver) based on high-LET studies.
Current NRC (Gi91) and NRPB (St88) recommendations also assume that at low doses the risk per unit
absorbed dose from alpha particles is 20 times that from gamma rays.
3-14
-------
The ICRP originally adopted the RBE value of 20 for alpha radiation in ICRP Publication 26 (ICRP77); prior
to that time, ICRP had assumed a RBE for alpha particle irradiation of 10, i.e., the biological effect from a
given absorbed dose of alpha particles was estimated to be 10 times that from an absorbed dose of low-LET
x-rays or gamma rays of the same magnitude. The ICRP decision to increase the RBE to 20 followed from
its decision to estimate the risk of low-LET radiations, in occupational situations, on the assumption that
biological effects were reduced at low doses and dose rates. There is evidence that the risks from high-LET
radiation are linear with dose and independent of dose rate (for low to moderate doses). Implicit in ICRP's risk
estimates for low dose/dose rate gamma radiation is a dose rate reduction factor of about 2.5. The EPA (linear)
risk model for low-LET radiation used prior to 1994 did not employ a DDREF (i.e., assumed DDREF=1);
therefore, in order to avoid an artifactual inflation in high-LET risk estimates, EPA assumed a RBE of 8
(20/2.5) for calculating the risks from alpha particles. [The alpha RBE used in EPA's risk estimates for
leukemia was revised from 8 to 1.117 in 1992, based on epidemiological data (see Appendix C).]
However, in EPA's revised methodology, a DDREF of 2 has been adopted whenever the total dose is below
20 rad (0.2 Gy) or the dose rate is below 10 mrad/min (O.l.mGy/min) for all cancer sites except breast, for
which a DDREF of 1 is assigned. The revised methodology also adopts the ICRP recommendation for a RBE
of 20 for alpha particles in this low dose and dose rate range. For higher doses or dose rates, however, EPA
assumes a value of 10 for the alpha particle RBE. An exception is made for leukemia, for which a RBE value
of 1 is adopted, consistent with available high-LET epidemiological data (NAS88, EPA9 Ic), and for breast,
for which a RBE of 10 is assigned. Risk estimates for radon decay products are also based directly on
epidemiological data, rather than on dose estimates and associated RBE values.
3.3.2 Dose Response Function
In the case of high-LET radiation, a linear dose response is commonly observed in both human and animal
studies. This response is not reduced at low dose rates (NCRP80). Some data on human lung cancer indicate
that the carcinogenic response per unit dose of alpha radiation is maximal at low doses (Ar81, Ho81, Wh83);
in addition, some studies with animals show the same response (Ch81, U182). However, at low doses,
departures from linearity are small compared to the uncertainty in the human epidemiological data, and EPA
believes a linear response provides an adequate model for evaluating risks in the general environment.
3.3.3 Estimates of Cancer Risk from Alpha-Particle Emitters
With the exception of radiation-induced breast cancer and leukemia, EPA has followed the ICRP
recommendation (ICRP91) in assuming an RBE for alpha particles of 20, in comparison to iow-LET radiation
at low doses and dose rates [i.e., for total doses of low-LET radiation below 20 rad (0.2 Gy) or dose rates
below 10 mrad/min (0.1 mGy/min)]. Where the comparison is made against acute high doses of low-LET
radiation, however, EPA assumes a value of 10 for the alpha particle RBE for these cancer sites. Thus the low-
LET radiation DDREF of 2 now used by EPA for these cancers is implicitly incorporated into the RBE value
3-15
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for alpha radiation. For breast cancer induction, a DDREF of ! has been adopted. Therefore, the RBE will
be independent of dose and dose rate. Since there is no DDKI-.F correction of the low-LET breast cancer risk
estimates at low doses and dose rates, it is assumed that the acute high dose RBE of 10 is also applicable to
breast cancer at low doses and dose rates.
There is evidence that alpha particle leukemia risks estimated on the basis of an RBE of 20 are too high
(EPA91). For this reason, EPA has adopted an alpha particle leukemia risk estimate of 5.0* 10~5 rad"1 (5xlO~3
Gy"1), consistent with the available high-LET epidemiologies! data (NAS88, EPA91c). Quantitatively, this
would correspond to an RBE of 1 for this site (relative to low dose, low-LET radiation). This is not to imply
that alpha radiation is no more carcinogenic than low-LET radiation in inducing leukemia. At least in part,
the lower than expected leukemia risk produced by alpha emitters may result from a nonuniform distribution
of dose within the bone marrow (i.e., average doses to sensitive target cells may be substantially lower than
calculated average marrow doses). Thus the RBE of 1 should be regarded as an "effective RBE," that reflects
factors other than just the relative biological sensitivity to high-and low-LET radiations. Since the spatial
distribution of the dose within the marrow will differ among alpha emitters, depending on the distribution of
the radionuclide within bone and the energies of the emitted alpha particles, the effective RBE may be
radionuclide dependent; however, this issue cannot be resolved with current data.
Estimates of the excess cancer mortality or incidence for specific cancer sites resulting from low doses and
dose rates of high-LET radiation may be obtained by multiplying the low-LET cancer risk estimates presented
in Table 3-2 (also see Appendix B) by the appropriate RBE value (I for leukemia, 10 for breast, and 20 for
all other cancer sites). For most cancer sites, the high-LET risk estimates have increased by more than the
corresponding low-LET estimates, reflecting the change in RBE from 8 to 20, which comes from adopting a
DDREF correction at low doses of low-LET radiation.
3.3.4 Estimates of Cancer Risk from Radon Decay Products
For estimating risks from radon decay products, EPA employs an epidemiological approach, based on human
epidemic logical data. When radon-222, a radioactive noble gas, decays, a number of short half-life
radionuclides (principally polonium-218, lead-214, bismuth-214, and poIonium-214) are formed. These decay
products, commonly referred to as "progeny" or "daughters," readily attach to respirable aerosol particles in
air. When inhaled, the radon progeny are deposited on the surfaces of the larger bronchi of the lung. Since
two of these radionuclides decay by alpha-particle emission, the bronchial epithelium is irradiated by high-LET
radiation. A wealth of data indicate that a range of exposures to the bronchial epithelium of underground
miners causes an increase in bronchial lung cancer, both in smoking and in nonsmoking miners, and in some
members of the general public. Recent reviews of radon risk data have been published by the NAS BEIRIV
Committee (NAS88) and the ICRP (ICRP87).
3-16
-------
The epidemiological approach to estimation of radon risks makes maximal use of the extensive human
epidemiological data and avoids uncertainties associated with estimating the bronchial dose delivered by the
inhaled radon progeny and selection of an appropriate RBE value. On this basis, EPA has adopted a central
risk estimate for excess radon exposure of 2.2 x 10"* fatal lung cancers per working level month (EPA92b,
Pu92).
3-17
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-------
Chapter 4
Example Calculations of Radionuclide Slope Factors
Chapter 4 presents simple numerical examples of the method used to derive the radionuclide slope factors.
As noted previously, the methodology used by EPA for derivation of the radionuclide slope factors was revised
in 1994. Example calculations are presented here for the revised methodology only; similar example
calculations for the previous methodology, used for development of the radionuclide slope factors prior to
1994, are presented in Appendix C.
4.1 BASIC CONSIDERATIONS
Radionuclide slope factors express the lifetime attributable cancer risk per unit exposure to a given
radionuclide, where exposure is measured in units of activity intake (pCi or Bq) for inhalation and ingestion,
or in units of soil concentration times exposure duration for external exposure [e.g., soil concentration (pCi/g
or Bq/g) x time (y) = pCi-y/g or Bq-y/gJ. The slope factor represents the total attributable cancer risk for all
organs and cancer sites. In practice, the attributable cancer risk for each organ or cancer site is estimated
separately based upon organ/tissue-specific dose rates and risk coefficients, and these estimates of risk to
individual organs and tissues are summed to estimate total attributable risk. Dose rates to each organ or tissue
may vary as a function of age and time after exposure, and the organ/tissue-specific risk coefficients may vary
as a function of age and sex.
In the derivation of radionuclide slope factors, chronic exposure, at a constant exposure rate, is assumed for
each radionuclide of concern. For chronic inhalation and ingestion exposures, dose rates to body organs and
tissues may increase with time following the beginning of exposure, as a result of the accumulation of activity
within the body. For the chronic external exposures, it is assumed that dose rates to each organ and tissue
remain constant with time. In all cases, the lifetime attributable cancer risk accumulates with age. The
methods used to estimate the dose rates to body organs and tissues of interest are summarized in Appendix A.
Since the radionuclide slope factors represent the attributable risk of cancer incidence, it is necessary to
account for "competing" risks (i.e., risks from sources other than radiation exposure). As described previously,
life tables and survival functions based on actuarial data are used to account for such competing risks, and to
estimate the probability of survival and projected years of life remaining at various ages in a reference
population. This estimate of the remaining years of life for the members of the exposed population at each age
is considered to be the period available for expression of the radiogenic cancer risk. As discussed in the
following sections, the methods used for implementation of the actuarial data in the slope factor calculations
differ under EPA's recently revised and previous methodologies, but the concept remains the same.
4-1
-------
Thus, for each age of exposure and for each cancer site considered, the attributable risk of cancer at that site
due to the dose accumulated at that age from a given exposure pathway is based on the organ/tissue-specific
absorbed dose rate in that year (rad/y or Gy/y), the organ/tissue-specific cancer risk per unit absorbed dose at
that age (rad'1 or Gy'1), and the survival function (see Section 4.4) or reference life table data. The attributable
cancer risk for each cancer site at each age is computed in this manner and summed to obtain the total number
of radiogenic cancers of all types expected in the life of the exposed population. This total is then divided by
the collective lifetime (person-years) of the exposed population and the lifetime activity intake rate to obtain
a slope factor for ingestion and/or inhalation. An analogous procedure is used for external exposure, except
the collective lifetime exposure is substituted for the lifetime intake. This estimate of attributable risk applies
to an age-averaged member of the exposed population.
This procedure is followed for each radionuclide. For alpha-emitters, the risks due to the high-LET (alpha)
radiation are calculated separately from those due to low-LET radiations (beta and gamma), and these are
summed to obtain the slope factor for the radionuclide.
Three principal types of data are required for the slope factor calculations:
• Dose rates in each body organ or tissue of interest over the lifetime of the exposed population. Dose rates
are calculated using the RADRISK code (Du80) for ingestion and inhalation assuming constant annual
intake of activity, e.g., a constant intake rate of 1 pCi/y (0.037 Bq/y). For external exposure, the codes
DFSOIL (Sj84) and DOSFACTER (KoSlc) are used to calculate the constant dose rates in body organs
and tissues that result from gamma photons emitted by a radionuclide in soil in which the concentration
of the radionuclide (pCi/g, Bq/g) is constant everywhere in the soil at all times considered, i.e., no
radioactive decay or other removal processes are considered. Additional information on the methods and
assumptions used to estimate dose rates is presented in Appendix A.
• Lifetime attributable cancer incidence risks per unit dose [e.g., expected cancer cases (risk) per 106 rad or
per 10" Gy] for specific cancer sites and ages. As discussed previously, the risk estimates used by EPA
for derivation of the radionuclide slope factors differ under the revised and previous methodologies; risk
estimates used in EPA's previous methodology were based primarily upon the National Academy of
Sciences BEIR III study (NAS80), whereas risk estimates under the revised methodology are based
primarily upon ICRP recommendations (ICRP91).
• Actuarial statistics for the reference population to account for competing risks, and to estimate the
projected years of life remaining at various ages in the reference population (i.e., the period available for
expression of the radiogenic cancer risk). EPA's derivation of radionuclide slope factors prior to 1994
utilized actuarial statistics for the 1970 decennial U.S. population, and the life-table analysis was
implemented using the CAIRD computer code (Co78). The revised methodology (EPA94a) utilizes vital
statistics for the 1980 decennial U.S. population; these data are fit by a cubic spline function, from which
interpolated values, derivatives, and integrals are calculated directly from the spline coefficients.
The use of these data to derive radionuclide slope factors is illustrated in the following sections.
4-2
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4.2 REVISED METHODOLOGY FOR DERIVING EPA RADIONUCLIDE SLOPE FACTORS
4.2.1 General Information
In 1994, EPA developed a revised methodology for estimating radiogenic cancer risk and the derivation of
radionuclide slope factors (EPA94a). The major changes include:
• Age- and sex-specific cancer incidence risk models (see Tables 3-1 and 3-2 and Appendix B) have been
revised based upon the recommendations of the ICRP (ICRP91), NRC (Gt91), andNCRP (NCRP85).
Absolute risk models are used for bone, skin, and thyroid cancer, whereas relative risk models are used
for all other cancer sites (esophagus, stomach, colon, liver, lung, breast, ovary, bladder, kidney, leukemia,
and remainder). Additionally, a dose and dose rate effectiveness factor (DDREF) of 2 has been adopted
for low-LET radiation at low doses and dose rates typical of environmental exposures for all cancer sites
except breast, for which a DDREF of 1 is assigned. (See Section 3 and EPA94a for additional discussion
of the revised risk models.)
• Vital statistics used in the revised methodology have also been updated. Age- and sex-specific mortality
data for the 1979-1981 U.S. population (NCHS85) have replaced the life table data for the 1970
population used previously. The survival function for the 1980 decennial U.S. life table data are shown
in Table 4-1.
• In both the revised and previous methodologies, organ-specific dose rates over the lifetime of the exposed
population were derived using: (1) the RADRISK computer code (Du80) for inhalation and ingestion
exposures, assuming constant annual intake of activity; and (2) the DOSFACTER (KoSlc) and DFSOIL
(SJ84) computer codes for external exposures to radionuclides in soil. However, it is anticipated that
future revisions of the radionuclide slope factors will incorporate revised methods for estimating
organ/tissue-specific dose rates. EPA has recently published revised dose rates for external exposure in
Federal Guidance Report Number 12 (EPA93), and a revised methodology for estimating dose rates from
internal exposures is currently under development. (See Appendix A for additional information on the
methods and assumptions used to estimate dose rates.)
Integration of these data is complicated by the different time periods considered in each. The risk factors are
for five age intervals: 0-9 y, 10-19 y, 20-34 y, 35-50 y, and 50+ y. RADRISK computes dose rates for the
midpoints of nine time intervals following the beginning of exposure (times 1, 3, 6, 12, 20, 30,42, 56, and 87
y). The survival function data are provided for each age in the population from 0 to 110 y. These data are
integrated by averaging over the age intervals of the risk data, where the data are weighted by the survivors'
collective person-years of life remaining at any age, or by the fraction of the time spent by survivors in the
smaller age intervals. This is accomplished by fitting the discrete mortality data to a cubic spline function and
then calculating interpolated values, derivatives and integrals directly from the spline function to estimate the
attributable cancer risk and the projected years of life remaining at various ages in the reference population.
Previously, these calculations were implemented by adapting actuarial methods developed for life table
calculations, using the CAIRD computer program (Co78). The revised approach is much more flexible with
respect to the form of risk models which may be used, and it eliminates most of the ad hoc approaches that
4-3
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Table 4-1. Survival Function Based on 1980 Decennial Life Table Data (probability)
Age
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
General
Population
1.0
9.8740E-01
9.8648E-01
9.8584E-01
9.8535E-01
9.8495E-01
9.8459E-01
9.8426E-01
9.8396E-01
9.8370E-01
9.8347E-01
9.8328E-01
9.8309E-01
9.8285E-01
9.8248E-01
9.8196E-01
9.8129E-01
S.8Q47E-01
9.7953E-01
9.7851 E-01
9.7741 E-01
9.7623E-01
9.7499E-01
9.7370E-01
9.7240E-01
9.7110E-01
9.6982E-01
9.6856E-01
9.6730E-01
9.6604E-01
9.6477E-01
9.6350E-01
9.6220E-01
9.6088 E-01
9-5951 E-01
9.5808E-01
9.5655E-01
9.5492E-01
Males
1.0
9.8607E-01
9.8508E-01
9.8436E-01
9.8379E-01
9.8333E-01
9.8291 E-01
9.8252E-01
9.821 7E-01
9.8186E-01
9.8160E-01
9.8139E-01
9.8119E-01
9.8090E-01
9.8043E-01
9.7972E-01
9.7878E-01
9.7762E-01
9.7628E-01
9.7479E-01
9.731 6 E-01
9.7141 E-01
9.6952E-01
9.6756E-01
9.6557E-01
9.6361 E-01
9.6169E-01
9.5980E-01
9.5795E-01
9.561 2E-01
9.5430E-01
9.5247E-01
9.5066E-01
9.4882E-01
9.4695E-01
9.4501 E-01
9.4297E-01
9.4081 E-01
Females.
1.0
9.8880E-01
9.8796E-01
9.8740E-01
9.8699E-01
9.8666E-01
9.8636E-01
9.8609E-01
9.8585E-01
9.8563E-01
9.8544E-01
9.8527E-01
9.8509E-01
9.8489E-01
9.8464E-01
9.8432E-01
9.8392E-01
9.8346E-01
9.8294E-01
9.8240E-01
9.8184E-01
9.8127E-01
9.8068E-01
9.8007E-01
9.7946E-01
9.7883E-01
9.7820E-01
9.7755E-01
9.7689E-01
9.7621 E-01
9.7551 E-01
9.7477E-01
9.7400E-01
9.7319E-01
9.7233E-Q1
9.7140E-01
9.7039E-01
9.6928E-01
Age
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
General
Population
9.531 7E-01
9.5129E-01
9.4926E-01
9.4706E-01
9.4465E-01
9.4201 E-01
9.391 3E-01
9.3599E-01
9.3256E-01
9.2882E-01
9.2472E-01
9.2021 E-01
9.1526E-01
9.0986E-01
9.0402E-01
8.9771 E-01
8.9087E-01
8.8348E-01
8.7551 E-01
8-6695E-01
8.5776E-01
8.4789E-01
8.3726E-01
8.2581 E-01
8.1348E-01
8.0024E-01
7.8609E-01
7.7107E-01
7.5520E-01
7.3846E-01
7.2082E-01
7.021 8E-01
6.8248E-01
6.6165E-01
6-3972E-01
6.1673E-01
5.9279E-01
5.6799E-01
Males
9.3852E-01
9.3607E-01
9.3345E-01
9.3062E-01
9.2754E-01
9.241 7E-01
9.2049E-01
9.1649E-01
9.1213E-01
9.0737E-01
9.021 4E-01
8.9639E-01
8.9007E-01
8.8317E-01
8.7570E-01
8.6761 E-01
8.5885E-01
8.4936E-01
8.3912E-01
8.281 3E-01
8.1634E-01
8.0370E-01
7.901 2E-01
7.7553E-01
7.5990E-01
7.4317E-01
7.2535E-01
7.0646E-01
6.8656E-01
6.6566E-01
6.4377E-01
6.2083E-01
5.9681 E-01
5.71 71 E-01
5.4557E-01
5.1856E-01
4.9088E-01
4.6272E-01
Average Life Expectancy =
Females
9.6807E-01
9.6675 E-01
9.6531 E-01
9.6374E-01
9.6200E-01
9.6009E-01
9.5799E-01
9.5570E-01
9.5320E-01
9.5047E-01
9.4748E-01
9.4419E-01
9.4060E-01
9.3669E-01
9.3245E-01
9.2788E-01
9.2294E-01
9.1760E-01
9.1185E-01
9.0567E-01
8.9903E-01
8.9187E-01
8.841 4E-01
8.7577E-01
8.6670E-01
8.5691 E-01
8.4641 E-01
8.3520E-01
8.2328E-01
8. 1061 E-01
7.971 2E-01
7.8269E-01
7.6720E-01
7.5055E-01
7.3273E-01
7.1368E-01
6-9340E-01
6.7186E-01
Age
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
73.777 years
General
Population
5.4239E-01
5.1599E-01
4.8878E-01
4.6071 E-01
4.3180E-01
4.0208E-01
3.7172E-01
3.4095E-01
3.101 2E-01
2.7960E-01
2.4961 E-01
2.2038E-01
1.9235E-01
1.6598E-01
1.4154E-01
1.1908E-01
9.8635E-02
8.031 8E-02
6.4236E-02
5.0429E-02
3.8842E-02
2.9389E-02
2.1854E-02
1.5982E-02
1.1503E-02
8.1530E-03
5.6958E-03
39250E-03
2.6702E-03
1.7947E-03
1.1928E-03
7.8447E-04
5.1093E-04
3.2979E-04
2.1110E-04
Males
4.3419E-01
4.0533E-01
3.7626E-01
3.471 4E-01
3.1810E-01
2.8925E-01
2.6074E-01
2.3282E-01
2.0586E-01
1 .8020E-01
1.5602E-01
1.3343E-01
1.1268E-Q1
9.3951 E-02
7.7322E-02
6.2748E-02
5.0120E-02
3.9323E-02
3.0247E-02
2.2794E-02
1.6834E-02
1.2215E-02
8.7148E-03
6.1181E-03
4.2296E-03
2.881 8E-03
1.9368E-03
1.2851E-03
8.4246E-04
5.461 3E-04
3.5037E-04
2.2262E-04
1.4020E-04
8.7570E-05
5.4285E-05
Females
6.491 OE-01
6.2506E-01
5.9960E-01
5.7253E-01
5.4372E-01
5.1315E-01
4.8098E-01
4.4744E-01
4.1289E-01
3.7772E-01
3.421 8E-01
3.0657E-01
2.7156E-01
2.3782E-01
2.0578E-01
1.7561 E-01
1.4747E-01
1.2172E-01
9.871 3E-02
7.8627E-02
6.1468E-02
4.7194E-02
3.5604E-02
2.6406E-02
1.9266E-02
1.3837E-02
9.791 OE-03
6.8305E-03
4.701 9E-03
3.1962E-03
2.1473E-03
1 .4269E-03
9.3855E-04
6.1153E-04
3.9498E-04
were necessary with the previous method. The survival function decreases monotonically, which accounts for
the fact that some deaths are expected to occur from causes other than radiation exposure at each age. This
consideration becomes more important at later ages, since the baseline mortality rates generally increase with
age. Accounting in this way assures that the radiation-induced excess cancer incidence risk is calculated for
only the surviving population at any age.
4-4
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4.2.2 Illustrative Examples
The examples presented here are designed to illustrate the principal features of the method for different
radionuclides, cancer sites, and pathways of exposure. These examples consider the following radionuclides
and exposure pathways: uniform low-LET radiation, exposure to external gamma rays due to Cs-137 in soil,
inhalation of Pu-238, and ingestion of Sr-90. The Pu-238 example illustrates how high- and low-LET
radiation dose rates and risks are combined to obtain the slope factor. Because of the large number of
calculations involved, the derivation of a slope factor is tedious and computer codes are used to compile and
organize the data and calculations that are required. Nevertheless, the purpose here is to present the basic
elements of the derivation using a few simplified examples to illustrate the principal considerations.
For illustrative purposes, these simplified examples deviate from the actual methodology used by EPA in that
the survival function, risk factors, and dose rates are averaged over the five discrete Risk Intervals, whereas
the actual EPA calculations perform the integration on continuous functions for each parameter using a cubic
spline function. For purposes of these examples, the survival function data from Table 4-1 have been averaged
over the age intervals (risk intervals) for the risk model as shown in Table 3-1 (i.e., 0-9 y, 10-19 y, 20-29 y,
30-39 y, and 40+ y). (Note that these risk intervals differ from those used in EPA's previous methodology, as
discussed in Appendix C.) Similarly, estimates of attributable cancer incidence risk per unit dose have been
averaged over each risk interval for the purposes of these examples only. EPA's actual risk calculations utilize
the more complete data sets for age-at-exposure values from 0 to 110 y for both the survival function (see
Table 4-1) and the attributable incidence risk per unit dose (see Appendix B).
4.2.2.1 Example A: Risk Estimate for Uniform Low-LET Radiation. Example A considers chronic exposure
to low-level low-LET radiation, where it is assumed that each member of the exposed population receives a
uniform, constant dose rate of 1 mrad/y (10'5 Gy/y) to all body organs. For purposes of this and the following
examples, the cohort survivors' life expectancy data from Table 4-1 have been aggregated over the age intervals
for the risk model as shown in Table 3-1 (i.e., 0-9 y, 10-19 y, 20-29 y, 30-39 y, and 40+ y). These five
intervals are denoted as "Risk Intervals" to distinguish them from other age intervals used in the calculations.
The survival function data from Table 4-1 are used in conjunction with the age-specific attributable cancer
incidence risk per unit dose to estimate the total lifetime attributable cancer incidence risk resulting from
uniform low-LET irradiation, assuming chronic equal dose rates to each body organ, as illustrated in Table 4-2.
The Survival Function values in Table 4-2 were derived as the arithmetic averages of the age-specific values
listed in Table 4-1 for each age contained in the respective Risk Interval. Similarly, the Interval Risk Factor
for each Risk Interval was derived as the arithmetic average of the age-specific mortality risk coefficients for
all cancer sites (see Table B-15), divided by an average lethality fraction of 0.67. Again, it is important to note
that averaging over each Risk Interval is performed here for purposes of illustration only, and the complete set
of age-specific risk coefficients and survival function values are utilized in EPA radiogenic risk calculations.
4-5
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Table 4-2. Attributable Cancer Risk from Uniform Low-LET Radiation
(chronic constant dose rate to all organs)
Risk Interval
M
0-9
10-19
20-29
30-39
40-110
Dose Rate
frad/vl
0.001
0.001
0.001
0.001
0.001
Survival Function
torobabttitv)
0.98665
0.98169
0.97175
0.95849
0.50565
Interval Risk Factor
frad-1)
1.6261 E-3
1.5937E-3
7.1977E-4
6.3740E-4
2.1452E-4
Attributable
Cancers*
1.60E-5
1.56E-5
6.99E-6
6.11E-6
7.59E-6
5.24E-5
Average individual risk = 5.24E-5 attributable cancers/(73.777 y x 1 E-3 rad/y)
= 7.1E-04 attributable cancers/rad
* Computed as the product of the length of the risk interval, survival function value, dose rate, and interval risk factor.
Within each risk interval, the radiation-attributable cancer risk is computed as the product of the pertinent dose
rate, survival function value, interval risk factor, and duration of the risk interval. The attributable cancer risks
projected for each risk interval are summed to estimate the total attributable cancer risk over the lifetime of
an average member of the exposed population under the assumed exposure conditions. Hence, a chronic dose
rate of 1 mrad/y (10~5 Gy) in each body organ results in a lifetime attributable cancer risk of approximately 5
x 10"s; for comparison, the current baseline cancer incidence risk from all causes is about 0.3. The estimated
lifetime attributable cancer risk per unit dose is computed as the lifetime attributable cancer risk divided by
the total lifetime dose (0.07377 person-rad), or approximately 7.1 x 10"4 attributable cancers per person-rad.
(Note that this estimate differs slightly from the value of 760 cancers per million person-rad in Table 3-1, due
to the simplified calculational assumptions noted above.)
This illustration is simplistic in that it assumes identical dose rates in all body organs at all times. In many
exposure situations, this is not the case, especially for internal exposures. In these cases, the dose rates at
various ages must be appropriately averaged in the discrete risk intervals, as illustrated in the following
examples.
4.2.2.2 Example B: External Exposure to Cs-137+D in Soil. Example B considers the case of chronic
exposure to gamma radiation from Cs-137 in soil contaminated at a uniform level of 1 pCi of Cs-13 7 per gram
ofsoil(l pCi/g or 0.037 Bq/g). Cs-137 is a pure beta-emitter, which decays to Ba-137m with a half-life of
approximately 30 years and a branching fraction of 0.946—i.e., 94.6% of all Cs-137 atoms decay to produce
Ba-137m. For this example, Cs-137 is assumed to be in equilibrium with its radioactive decay product Ba-
137m, i.e., the soil is also assumed to contain a uniform concentration of 0.946 pCi/g of Ba-137m per gram
of soil (0.946 pCi/g or 0.035 Bq/g). This is a case where inclusion of the radioactive decay products is
extremely important in estimating radiation risk, since the external pathway dose from this decay series is
4-6
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entirely from Ba-137m. The inclusion of radioactive decay products in radionuclide slope factors is indicated
as"Cs-137+D".
Although Cs-13 7 decays with a half-life of 30 years, the slope factor derivation assumes exposure to a constant
and uniform soil contamination level, and constant dose rates in the various body organs and tissues. The
decrease in radionuclide concentrations over time (i.e., by radioactive decay and also any physical removal
processes) should be accounted for in pathway modeling used in conjunction with the slope factors to estimate
risk. Conceptually, this can be accommodated by calculating the exposure-time integral in the appropriate
units (e.g., pCi-y/g) and multiplying by the slope factor to obtain the lifetime risk.
In this example, however, it is assumed that the ground contamination level is constant and uniform. Thus,
the dose rates in each body organ or tissue will also be constant over the lifetime of the exposed population.
However, since some body organs and tissues are shielded by other organs or tissues, each can be subjected
to a slightly different, but constant, dose rate. Since the dose rates in this example are constant over the life
of the cohort, averaging dose rates over the five risk intervals is unnecessary.
Table 4-3 shows the simplified calculations for estimating attributable cancer risk for this example. The first
column lists the risk intervals. The second lists the organ/tissue-specific dose rate for each risk interval. The
third column lists the probability of survival for each risk interval (survival function). The fourth column lists
the pertinent attributable cancer incidence risk per unit dose factors, derived from Appendix B. The last
column is the predicted attributable cancer risk in each risk interval, calculated as the product of the pertinent
dose rate, survival probability, interval risk factor, and interval duration. (As described in Section 4.2.2.1, the
values of the survival function and interval risk factor for each risk interval are computed as arithmetic
averages of the age-specific values within the respective risk interval.) This calculation is repeated for each
risk interval and for each of the 14 cancer sites considered.
The slope factor is then computed as the cumulative lifetime attributable cancer risk summed over all cancer
sites divided by the cumulative lifetime exposure. At the assumed constant soil contamination level of 1 pCi/g
(0.037 Bq/g), the attributable cancer risk is estimated as approximately 1.5 x 104. The cumulative exposure
duration of the average member of the exposed population is 73.777 years. Thus, the slope factor may be
calculated as
SF = 1.54E-4 attributable cancers/(73.777 y x 1 pCi/g)
— 2.09E-6 attributable cancers per pCi-y/g.
4-7
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Table 4-3. Derivation of Attributable Cancer Risk Resulting from Chronic Exposure to Gamma
Radiation from Cs-137+D Ground Contamination [1 pCi/g (0.037 Bq/g)]
Risk Interval
M
Dose Rate
frad/y)
Survival Function
(probability)
Interval Risk Factor
(rad'1)
Attributable
Cancers *
Breast
0-9
10-19
20-29
30-39
40-110
3.54E-3
3.54E-3
3.54E-3
3.54E-3
3.54E-3
0.98665
0.98169
0.97175
0.95849
0.50565
2.2382E-4
2.2486E-4
1.0275E-4
9.2426E-5
1.0664E-5
7.82E-6
7.81E-6
3.53E-6
3.14E-6
1.34E-6
2.36E-5
Lung
0-9
10-19
20-29
30-39
40-110
2.92E-3
2.92E-3
2.92E-3
2.92E-3
2.92E-3
0.98665
0.98169
0.97175
0.95849
0.50565
1.6406E-4
1.6486E-4
2.8309E-5
5.8202E-5
2.5979E-5
4.73E-6
4.73E-6
8.03E-7
1 .63E-6
2.69E-6
1.46E-5
[etc, for each of the 14 cancer sites]
Lifetime risk = 1 .54E-4 attributable cancers
Slope Factor = 1 .54E-4 attributable cancers/(73.777 y x 1 pCi/g)
= 2.09E-6 attributable cancers per pCi-y/g
Computed as the product of the length of the risk interval, survival function value, dose rate, and interval risk factor.
4.2.2.3 Example C: Inhalation of Pu-238. Example C considers the case of chronic inhalation of Pu-238 at
a constant rate of 1 pCi/y (0.037 Bq/y). In the calculation of ingestion and inhalation slope factors, it is
assumed that survivors in the cohort chronically ingest or inhale a constant amount of activity of a given
radionuclide each year (e.g., 1 pCi/y) throughout each survivor's lifetime. Unlike the cases considered above,
where the dose rates in body organs and tissues remained constant over time, in this example dose rates are
not constant as survivors age, and average dose rates in each risk interval must be calculated.
For this example, it is assumed that the chemical form of the particles carrying the Pu-23 8 is insoluble in body
fluids, i.e., the clearance time of the particles from the lung is very long (i.e., ICRP lung clearance class "Y";
see Appendix A). In this case, the dose rate to body organs and tissues increases rapidly during the first few
years of exposure, and then plateaus assymtoptically. For the purpose of this calculation, this means that dose
rates will vary significantly over the risk interval 0-9 y, and then become relatively constant for subsequent
intervals. Thus, an average dose rate for the 0-9 y interval must be calculated, taking into account the cohort
survival. This is done by calculating the fraction of the time spent by survivors in the age groups within this
risk interval. For the 0-9 y risk interval, three age groups are considered: 0-2,2-4, and 4-10. Dose rates in the
-------
middle of these age intervals, at 1,3 and 6 y of age, are used to estimate the average dose rate in the 0-9 y
interval. Similarly, a weighted average of the dose rate to each organ of interest is computed for each of the
five risk intervals.
Since Pu-238 is an alpha-emitter and weak photon emitter, both high- and low-LET dose rates must be
considered. The high-LET dose rates are adjusted for the greater relative biological effectiveness (RBE) of
the alpha particles in inducing lung cancer, relative to beta and gamma radiation. EPA's revised methodology
has adopted an RBE value of 20 for all cancer sites except leukemia, for which an RBE of 1 is assigned and
breast which is assigned an RBE of 10. (Previously, EPA's risk estimates assumed an RBE of eight for
estimating risks from alpha particles for all cancer sites; in 1992, the high-LET RBE for leukemia was reduced
from 8 to 1.117, based on epidemiological data.)
The weighted average dose rates for each organ and tissue of interest are combined with the corresponding
survival function data from Table 4-1 and the age-specific radiogenic cancer risk coefficients derived from
Appendix B to estimate the radiation-attributable cancer risk in each risk interval, as illustrated in Table 4-4.
Table 4-4. Derivation of Attributable Cancer Risk Resulting from Chronic Inhalation
of Pu-238 [1 pCi/y (0.037 Bq/y) constant intake rate]
S:*;Risic;Jfifeii&!3&^;:
ISSllli
l^i^iii^iep.;;:;
||h;^|M;|l;^
::::;J5tiryfcat" fiitifitibH:!^
IPi;|(ii'^a^!!3^P!^
•:;;ihie^a>:Risk':'£a'&b¥£:
\gl^gf^Wm
iMitiiiiii
-!; A 'ijrJiJiffi^iS&S
l^^^^^^^StM^iil^^^'1" :^^il^^Mis1t^ --'M^^KMi^Ki^llK
0-9
10-19
20-29
30-39
40-110
0-9
10-19
20-29
30-39
40-110
i^s^^^^^^i^^^^^^^ii^/-^1^.^^^^^^^^^
4.31 E-5
5.32E-5
5.33E-5
5.34E-5
5.35E-5
0.98665
0.98169
0.97175
0.95849
0.50565
20X1.6406E-4
20X1.6486E-4
20 x 2.8309E-5
20 x 5.8202E-5
20 x 2.5979E-5
1.40E-6
1.72E-6
2.93E-7
5.96E-7
9.84E-7
5.00E-6
iSS^t^^lS^'^^^^^ife'^0^ '-..-.•-'"'* ":':H;!i'-^i!!l!!f ii:!!l!0
9.07E-8
1.12E-7
1.12E-7
1.12E-7
1.12E-7
0.98665
0.98169
0.97175
0.95849
0.50565
1.6406E-4
1.6486E-4
2.8309E-5
5. 8202 E-5
2.5979E-5
It^H^^
1.47E-10
1.81E-10
3.08E-1 1
6.25E-1 1
1.03E-10
5.23E-10
Lifetime risk = 2.02E-6 attributable cancers
Slope Factor = 2.02E-6 attributable cancers/(73.777 y x 1 pCi/y)
= 2.74E-8 attributable cancers/pCi inhaled
Computed as the product of the length of the risk interval, survival function value, dose rate, and interval risk factor
4-9
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Under the assumed exposure conditions, the attributable cancer risk to an average member of the population
inhaling 1 pCi/y of Pu-238 (Class Y) is estimated as approximately 2 x 10"6. This attributable cancer risk may
be divided by the cumulative lifetime exposure (intake) to estimate the radionuclide slope factor as follows:
SF = 2.02E-6 attributable cancers / (73.777 y x 1 pCi/y)
= 2.74E-8 attributable cancers/pCi inhaled
4.2.2.4 Example D: Ingestion of Sr-90. Example D considers the case of chronic ingestion of Sr-90 at a
constant rate of 1 pCi/y over a lifetime. It is assumed here that the chemical form of the Sr-90 is soluble in
the gastrointestinal tract, with a Gl-tract-to-blood absorption fraction (fi) of 0.3. Since strontium accumulates
preferentially in the skeletal tissues, the dose rates to these tissues exceed those for other body organs or
tissues; therefore, this example focuses on attributable risk of bone sarcoma and leukemia (red bone marrow).
The annual dose rates computed by RADRISK for these tissues increase with time, due to the accumulation
of Sr-90 in these tissues—i.e., the deposition and retention of Sr-90 in bone surfaces and red bone marrow
greatly exceeds its biological and radiological removal rate.
Since the dose rates to bone surface and red marrow are not constant, average dose rates in each of the five risk
intervals are calculated. For each cancer site, the dose rate within each risk interval is calculated as a weighted
average based on the fraction of time spent by survivors in each age group within this risk interval.
Attributable cancer risk for this case is calculated as shown in Table 4-5. For each cancer site in each risk
interval, the average dose rates are multiplied by the probability of survival for that interval, and the
attributable cancer incidence risk per unit dose (derived from Appendix B) to estimate the attributable risk for
that interval. The sum of these products is divided by the total lifetime intake to obtain the slope factor.
Under the assumed exposure conditions, the attributable cancer risk is estimated at approximately 4 x 10'9;
this represents an average individual risk of approximately four chances in a billion, in this example. This
attributable cancer risk may be divided by the cumulative lifetime exposure (intake) to estimate the
radionuclide slope factor for ingestion of Sr-90 as
SF = 4.12E-9 attributable cancers / (73.777 y x 1 pCi/y)
= 5.59E-11 pCi'1 ingested.
4.3 SUMMARY
Radionuclide slope factors express the lifetime attributable cancer risk per unit exposure to a given
radionuclide, where exposure is measured in units of activity intake (pCi or Bq) for inhalation and ingestion,
or in units of soil concentration times exposure duration for external exposure [e.g., soil concentration (pCi/g
or Bq/g) x time (y) = pCi-y/g or Bq-y/g]. The slope factor represents the total attributable cancer risk for all
organs and cancer sites. In practice, the attributable cancer risk for each organ or cancer site is estimated
4-10
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Table 4-5. Derivation of Attributable Cancer Risk Resulting from Chronic fngestion
of Sr-90 [1 pCi/y (0.037 Bq/y) constant intake rate]
oi^Ftisk Interval J;;:
0-9
10-19
20-29
30-39
40+
0-9
10-19
20-29
30-39
40+
;:;:;:. pose 'Fiate;-;;!:
I;;;:;1:1';,; ^adjiy) :".;'•-;
!:i£Y;;iM-V;;W
2.96E-7
5.60E-7
6.28E-7
6.49E-7
6.51 E-7
0.98665
0.98169
0.97175
0.95849
0.50565
7.3982E-5
3.0404E-5
5.301 OE-5
6.0724E-5
3.1630E-5
4.89E-7
1.04E-7
1.27E-7
1.42E-7
1.47E-7
0.98665
0.98169
0.97175
0.95849
0.50565
1.6363E-6
1.6254E-6
1.6060E-6
1.5647E-6
6.8341 E-7
2.16E-10
1.67E-10
3.23E-10
3.78E-10
7.29E-10
1.81E-09
7.90E-12
1.66E-11
1.99E-11
2.13E-11
3.56E-1 1
1.01E-10
I etc. for each of the 14 cancer sites J
Lifetime risk = 4.12E-9 attributable cancers
Slope Factor = 4.12E-9 attributable cancers/(73.777 y x 1 pCi/y)
= 5.59E-1 1 attributable cancer/pCi ingested
* Computed as the product of the length of the risk interval, survival function value, dose rate, and interval risk factor.
separately based upon organ/tissue-specific dose rates and risk coefficients, and these individual organ risks
are summed to estimate total attributable risk. Dose rates to each organ and tissue may vary as a function of
age and time after exposure, and the organ/tissue-specific risk coefficients may vary as a function of age and
sex.
In the derivation of radionuclide slope factors, chronic exposure, at a constant exposure rate, is assumed for
each radionuclide of concern. For chronic inhalation and ingestion exposures, dose rates to body organs and
tissues may increase with time following the beginning of exposure, as a result of the accumulation of activity
within the body. For the chronic external exposures, it is assumed that dose rates to each organ and tissue
remain constant with time. In all cases, the lifetime attributable cancer risk accumulates with age.
Since the radionuclide slope factors represent the attributable risk of cancer incidence, it is necessary to account
for competing risks (i.e., risks from sources other than radiation exposure). Life tables and survival functions
based on actuarial data are used to account for such competing risks, and to estimate the probability of survival
and projected years of life remaining at various ages in a reference population. This estimate of the remaining
4-11
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years of life for the members of the exposed population at each age is considered to be the period available for
expression of the radiogenic cancer risk.
For each age of exposure and for each cancer site considered, the attributable risk of cancer at that site due to
the dose accumulated at that age from a given exposure pathway is based on the organ/tissue-specific absorbed
dose rate in that year (rad/y or Gy/y), the organ/tissue-specific cancer risk per unit absorbed dose at that age
(rad'1 or Gy'1), and the survival function or reference life table data. The attributable cancer risk for each cancer
site at each age is computed in this manner and summed to obtain the total number of radiogenic cancers of
all types expected in the life of the exposed population. This total is then divided by the collective lifetime
(person-years) of the exposed population and the lifetime activity intake rate to obtain a slope factor for
ingestion and/or inhalation. An analogous procedure is used for external exposure, except the collective
lifetime exposure is substituted for the lifetime intake. This estimate of attributable risk applies to an age-
averaged member of the exposed population.
This procedure is followed for each radionuclide. For alpha-emitters, the risks due to the high-LET (alpha)
radiation are calculated separately from those due to low-LET radiations (beta and gamma), and these are
summed to obtain the slope factor for the radionuclide.
In summary, the calculation of the radionuclide slope factor is based upon three principal types of data:
• Organ/tissue-specific dose rates are computed for each tissue of interest over the lifetime of the exposed
population. Dose rates are calculated using the RADRISK code (Du80) for ingestion and inhalation
assuming constant annual intake of activity, e.g., a constant intake rate of 1 pCi/y (0.037 Bq/y). For
external exposure, the computer code DFSOIL (SJ84) is used to calculate the constant dose rates in body
organs and tissues that result from gamma radiation emitted by a radionuclide uniformly distributed in soil
at a constant unit concentration (pCi/g or Bq/g).
• Lifetime attributable cancer incidence risks per unit dose [e.g., expected cancer cases (risk) per 106 rad or
per 104 Gy] have been computed for specific cancer sites and ages. As discussed previously, the risk
estimates used by EPA for derivation of the radionuclide slope factors differ under the current and
previous EPA methodologies. Risk estimates used in EPA's previous methodology were based primarily
upon the National Academy of Sciences BEIR III study (NAS80), whereas risk estimates under the revised
methodology are based primarily upon recommendations of the ICRP (ICRP91), NRC (Gi91), and NCRP
(NCRP85).
• Vital statistics and mortality data for the reference population are used to account for competing risks, and
to estimate the projected years of life remaining at various ages in the reference population (i.e., the period
available for expression of the radiogenic cancer risk). EPA's derivation of radionuclide slope factors prior
to 1994 utilized life table data for the 1970 decennial U.S. population, as implemented in the CAIRD
computer code (Co78). The revised methodology (EPA94a) utilizes vital statistics and mortality data for
the 1980 decennial U.S. population (NCHS85, 84, 83, 82) to estimate competing risks and the projected
years of life remaining at various ages in the reference population; the discrete mortality data are fit to a
4-12
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cubic spline function, from which interpolated values, derivatives, and integrals are calculated directly
from the spline coefficients.
Detailed discussion of the calculational methods, assumptions, and uncertainties in the EPA methodology for
estimating radiogenic cancer risk is provided in another EPA document, Estimating Radiogenic Cancer Risks
(EPA94a). A summary of the methodology used by EPA for derivation of radionuclide slope factors prior to
1994 is presented in Appendix C, and more detailed discussion of these calculations may be found in
Reference EPA89b.
4-13
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-------
Chapter 5
Uncertainty in Radionuclide Slope Factors
Estimates of health risk from low-level radiation exposures are inherently uncertain. Consideration of
uncertainties in estimates of risk is an important component of the risk assessment process (EPA89a, EPA92a).
This chapter presents a general discussion of the major sources of uncertainty in estimating risks from
environmental exposures to radioactive substances. The major sources of uncertainty in the radionuclide slope
factors are those pertaining to the underlying models used to estimate radiation dose and to relate dose to
radiation-induced cancer risk. Some of these uncertainties are not well quantified, and a quantitative
uncertainty analysis of the radionuclide slope factors has not been completed. However, a general
understanding of the uncertainty inherent in the radionuclide slope factors is important for the assessment and
management of radiation-related risks. Full disclosure of the limitations and uncertainties in risk estimates is
needed for informed risk management decisions.
Rather than using mathematical models to assess impacts of radioactive materials in the environment, it would
be preferable to measure the actual impacts directly; i.e., radionuclide concentrations and radiation fields in
the environment, radionuclide concentrations and absorbed doses in the various organs and tissues of the
exposed populations, and any increased incidence of cancer attributable to the exposures. However, this is not
possible because the radionuclide exposures are not generally detectable in members of the population, and
any excess cancers that may be attributable to radionuclide exposures cannot be identified in the presence of
the large numbers of baseline cancers in the population. Accordingly, the actual or potential impacts of
environmental radiation exposures must be predicted using calculational models, and the uncertainty in
radiation risk assessments must be discussed within the framework of the models and parameters used to
estimate risks that cannot be measured.
In the preceding discussions regarding radionuclide slope factors and their application in estimating radiation
risk, doses and risks from radiation exposure have been presented as discrete values; i.e., rad/year or lifetime
excess cancer risk. Each of these calculated values is an expression of impact on an individual or population.
These values are intended to be reasonable central estimates of risk, i.e., to not significantly underestimate or
overestimate risks and be of sufficient accuracy to support decision making. However, such values are of more
use to decision-makers when there is some characterization of their uncertainty. For a given exposure scenario,
a small risk may be calculated, e.g., 1 x 10~* lifetime risk of cancer for an individual. However, if the
uncertainty in this number is several orders of magnitude, the real risk from this source of exposure may in fact
be higher than another source of exposure which has a calculated risk of 1 x 10~5 lifetime risk of cancer but
has a small degree of uncertainty. Alternatively, an upper bound risk of 1 x IO'2 lifetime risk may be calculated
and appear to represent an unacceptable risk. However, the actual risk may be orders of magnitude smaller.
This situation may occur when, due to limited information and uncertainty in the calculational parameters,
conservative assumptions (i.e., assumptions likely to overestimate actual values) are used throughout the
5-1
-------
calculation in order to ensure that the risks are not underestimated. This can result in a risk estimate that is
near or beyond the upper limit of what is plausible, because it is based on a very unlikely combination of
conservative assumptions for each parameter.
5.1 SOURCES OF UNCERTAINTY IN RADIATION DOSIMETRY
Radiation dosimetry models are designed to simulate the uptake, distribution, retention and removal of
radioactive materials in the human body. At best, these models can only approximate real situations in organs
and-tissues in humans. In applying the internal dosimetry models in current use, the primary sources of
uncertainty are attributed to model formulation and parameter variability produced by measurement error or
natural variation. These sources include:
• Uncertainty in the formulation of the mathematical models for
- deposition of activity in the lung and translocation of inhaled activity into blood,
- translocation and absorption of ingested activity into the blood,
- distribution and retention of activity from blood to various systemic organs and tissues, and
- calculation of the absorbed dose to an organ or tissue from activity in that and other organs and tissues;
• Uncertainty in the model parameters, including
- parameters in the biokinetic and dose models (e.g., GI absorption fraction, lung clearance class, organ
deposition fractions and retention times, organ masses and geometries, etc.), and
- anatomical and physiological data for characterizing the population of interest.
The dosimetric models and data have been developed primarily in the context of radiation protection for adult
workers, and represent average adult male members of the population; consequently, they do not account for
variability in the physiological and metabolic characteristics among individuals within a population or across
populations, or in the metabolic behavior of radionuclides, which vary depending on age, sex, and dietary
intakes of an individual at the time of exposure. Despite the obvious differences between risk assessment and
occupational radiation protection, the dosimetric formulations of the latter have been generally adopted, often
with little or no modifications, in risk assessment activities. This approach permits use of a substantial body
of information assembled by international experts from the occupational setting and provides models that avoid
the complex problems encountered in biokinetic modeling of radionuclides for the general public in an
age-dependent sense. More recently, dosimetric models and data which incorporate organ/tissue-specific
biokinetics and age-dependence have become available (ICRP89,93,95a, 95b). These estimates of dose per
unit exposure tend to be higher for children than for adults by factors ranging up to approximately an order
of magnitude. These age-dependent dose estimates, however, are not yet incorporated into the radionuclide
slope factors.
The radionuclide slope factors represent the risk to an average individual due to chronic lifetime exposures.
Variation in dosimetric parameters between people and between age groups is of reduced importance in this
context because such variation gets averaged over a population and/or over a lifetime. Nevertheless, parameter
5-2
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variability can contribute substantially to the uncertainty in the dose and risk estimates, and it should be kept
in mind that some individuals in a population are going to be at higher or lower risk from a g,ven exposure.
Parameter variation among individuals contributes uncertainty to the models by causing random errors in any
measuredhumandataupon which the dosimetric models are based. To the extent that the subjects from whom
such data are collected are atypical of the U.S. population (e.g., with respect to health status), parameter
variation may also be a source of bias. Since the parameters contained in the dosimetric models were estimated
primarily for adult males, they may not provide an adequate basis for calculating the average dose or risk m
cases where age- and sex-related variations in these parameters are large. This problem becomes more
significant in light of the generally higher risks associated with a given dose for childhood exposures; if doses
are also higher in childhood, the enhanced effect on risk will be compounded. In addition, some of the
biokinetic models used for dosimetry calculations are based on very limited observational data in humans or
constructed largely from animal data.
Also the distribution of an element within an organ or tissue may not be uniform, particularly with respect to
biological targets of interest. This can be a serious problem with respect to the estimation of relevant doses
from internallydepositedalphaemitters, given the short range of alpha particles in nutter.-For example, where
an alpha emitter is distributed nonuniformly in bone, the calculation of doses to sensitive cells in the bone and
the bone marrow will be difficult. Another example is the uncertainty in estimating doses to cells lining the
GI tract from ingested alpha emitters passing through the tract; in some cases, the mucus Immg may
effectively shield the target cells from irradiation.
Estimates of external dose also suffer similar limitations. These estimates are based on assumptions of uniform
radionuelide concentrations within a semi-infinite geometry of the source region. The radiation field between
the feet and the head of a person standing on contaminated ground is not uniform, but for photon energies
greater than about 10 keV, the variation about the value at 1 meter becomes minimal. A more significant
source of error is the assumption of a uniform radionuelide concentration in soil. Kocher (KoSlb) has shown
that sources would have to be approximately uniform over distances of as much as a few hundred meters from
the receptor forthe dose rate factors to be accurate for ground surface exposures. Factors such as penetration
of deposited radionuclides into the ground surface, ground surface roughness, terrain irregularities, and
shielding provided by any buildings or structures that may be present, are likely to reduce actual doses below
the theoretical estimates.
Additional uncertainty arises from the factors used to relate the dose in air above a contaminated ground
surface to the dose in various organs of the body. These factors assume that the radiation field for the ground
surface source is isotropic and has the same energy distribution as for immersion in contaminated air. These
assumptions clearly do not hold true, but more precise estimates of these distributions are not likely to change
the organ dose rate factors substantially.
5-3
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5.2 SOURCES OF UNCERTAINTY IN RADIOGENIC RISK MODELS
Important sources of uncertainty inherent in current estimates of risk from whole body, low-LET radiation
include:
- the extrapolation of risks observed in populations exposed to relatively high doses, delivered acutely
to populations recewing relatively low dose chronic exposures-i.e., the form of the dose-response
Junction and any dependence on dose rate;
- the projection of risk over a full lifespan, including consideration of age at exposure, sex, and other
factors (e.g., the extent to which high relative risks seen over a limited follow-up period among
individuals exposed at young ages carry over into later years of life when baseline cancer incidence rates
are high); and
- tiie"transport"[°f risks observed in one population to another population of different characteristics (eg
different baseline cancer risks, diets, and lifestyles).
The most important source of epidemiological data on radiogenic cancer is the Atomic Bomb Survivor Study.
The population of survivors of the atomic bomb detonations in Hiroshima and Nagasaki have been studied for
more than 40 years in a carefully planned and monitored epidemiological survey. They are the largest group
that has been studied, and they provide the most detailed information on the response pattern for organs by
age and sex, over a wide range of doses of low-LET radiation. However, use of these data for estimating risks
to the U.S. population from exposure to low doses and dose rates of radiation is subject to each of the three
major uncertainties noted above. Most of the epidemiological data pertain to acute doses of 50 rad (0.5 Gy)
or higher; extrapolation of these data to much smaller chronic doses incremental to the natural background
level of about 100 mrad/yr (1 mGy/yrXexcluding indoor radon) is highly uncertain. Since epidemiological
follow-up of the irradiated population is still incomplete, projection beyond the period of observation is
required to obtain lifetime risk estimates.
Also, the transportation of the atomic bomb surviyor data to the U.S. population is an area of significant
uncertainty. Baseline rates for specific cancer types vary from population to population, and over time within
a given population. For example, stomach cancer rates are substantially higher in Japan than in the U.S., while
the reverse is true for lung, colon, and breast cancer; moreover, the incidence rates for lung and breast cancer,
particularly, have been increasing in both populations during recent years. Despite the observed rough
proportionality between radiation risk and baseline cancer rates by age, the radiation risk will not necessarily
vary m proportion to the baseline cancer rate between different populations. Information on how to transport
risk estimates between populations is currently very limited; the available information suggests that the
method may be dependent on the specific cancer site. Given this uncertainty in the transportation or risks
across populations, EPA has adopted a model in which age- and site-specific risk coefficients are taken as the
geometric means of two models proposed by the ICRP for transporting risks from the Japanese to U.S.
populations.
5-4
-------
In addition to these model uncertainties, errors in dosimetry and random statistical variations also contribute
to the uncertainty in the risk estimates for the atomic bomb survivors. Significant errors were identified and
corrected in the estimates of radiation doses received by the exposed population, leading to the replacement
of the "T65" (tentative dose 1965)doseestimatesbythe"DS86"(dosimetry system 1986) dose estimates. The
residual error of the DS86 dosimetry is generally estimated to be a relatively minor contributor to the overall
uncertainty, with an overall uncertainty in individual doses on the order of ± 30% (Ka89). Recent estimates
of neutron doses (Pr93) may lead to further revision of these uncertainty estimates.
The precision of risk estimates is also limited by sampling uncertainties due to the limited sample size.
Uncertainties due to sampling error are larger where data are sparse, e.g. with respect to risks for specific age
groups or specific cancer sites (Sh88). Finally, there will be some error in ascertaining cancer cases, such as
under-reporting of cases or mislabeling of cancer type. Both of these types of error tend to bias risk estimates
slightly downward.
Additional sources of epidemiological data on exposures to low-LET radiation include medical exposures of
specific tissues, notably the thyroid and breast. These data are also subject to the same types of uncertainties
noted above.
Uncertainties in risk estimates for internally deposited alpha emitters are often greater than for low-LET
radiation, with the notable exception of lung cancer risk from inhalation of radon decay products. For many
organs and tissues, no human epidemiological data are available for alpha exposures, so extrapolation from
low-LET radiation is required. For other sites where epidemiological data are available, risk estimates are
complicated by uncertainties in dosimetry. Excess cancers have been observed in certain human populations
exposed occupationally or medically to internally deposited alpha emitters, including: (1) lung cancer in miners
inhaling radon decay products; (2) bone cancer in patients injected with radium-224; (3) bone sarcomas and
head carcinomas in watch dial painters ingesting mixtures of radium-226 and radium-228; and (3) liver cancers
in patients injected with Thorotrast, an x-ray contrast medium containing isotopes of thorium. Although other
organs and tissues of the body received doses of alpha radiation in these populations, excess cancers were
generally not observed at sites other than those listed. As a result, only upper bounds to the risk for these other
organs and tissues can be estimated directly from studies of humans exposed to alpha radiation.
For other sites, cancer risk estimates for high-LET radiation are often derived from human epidemiological
data on low-LET radiation and laboratory data on the relative biological effectiveness (RBE) of the high-LET
radiation. The assumptions regarding the RBE for alpha irradiation are generally derived from high dose
experiments on animals. The available evidence on cells, animals, and humans points to a linear dose response
relationship for the risk from alpha emitters (NAS88). The extrapolation to low doses is therefore considered
to be less important as a source of uncertainty for alpha irradiation than for low-LET irradiation. There is,
however, considerable variability in the RBE determined from animal studies; the extrapolation of these results
to humans is also a significant source of uncertainty.
5-5
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Ar81
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Appendix A
Radiation Dosimetry
A-1
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[ This page is blank intentionally. ]
A-2
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CONTENTS
Section Page
A.1 INTRODUCTION A-5
A.2 BASIC CONCEPTS A-5
A.2.1 Activity A-6
A.2.2 Radioactive Half-Life A-6
A.2.3 Radionuclide Chains A-7
A.2.4 Biological Half-Life A-7
A.2.5 Internal and External Exposures to Radionuclides A-7
A.2.6 Absorbed Dose and Absorbed Dose Rate A-7
A.2.7 Linear Energy Transfer (LET) A-8
A.2.8 Dose Equivalent and Dose Equivalent Rate A-8
A.2.9 Effective Dose Equivalent and Effective Dose Equivalent Rate A-9
A.2.10 Relationship of the Dose Equivalent and the Effective Dose
Equivalent to Risk A-10
A.2.11 Radon Decay-Product Units A-l 1
A.2.12 Customary and SI Units A-I1
A.3 EPA DOSIMETRIC MODELS A-ll
A.3.1 Internal Dose Models A-12
A.3.2 External Dose Models A-21
A.5
REFERENCES
A-24
A-3
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Table
A-l
A-2
A-3
A-4
TABLES
Quality factor for various types of radiation ...................................... A-9
Tissue weighting factors recommended by the ICRP for stochastic risks ............... A-10
Comparison of Customary and SI Special Units for Radiation Quantities .............. A- 12
Target organs and tissues considered in EPA dose calculations ...................... A-13
FIGURES
Figure Pa8e
A-l ICRP Lung Model A-18
A-2 ICRP schematic representation of radioactivity movement among respiratory
tract, gastrointestinal tract, and blood A-19
A-4
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Appendix A
Radiation Dosimetry
Appendix A highlights the internal and external dosimetric models used by EPA to assess the dose to
individuals exposed to radionuclides. Much of this information has been presented in detail elsewhere
(EPA89, EPA93), and is discussed briefly here for the convenience of the reader. Special dosimetric methods
for radon are presented elsewhere (EPA92) and are not discussed here.
A.1 INTRODUCTION
The evaluation of risks from environmental exposures to radionuclides requires an assessment of the doses
received by individuals who are exposed by coming into contact with radiation sources. Two forms of
potential radiation exposures can occur from these sources — internal and external. Internal exposures can
result from the inhalation of contaminated air or the ingestion of contaminated food or water. External
exposures can occur when individuals are immersed in contaminated air or water or are standing on
contaminated ground surfaces. Internal or external doses can result from either direct contact with the radiation
from radionuclides at the site area or from radionuclides that have been transported from these sites to other
locations in the environment. The quantification of the doses received by individuals from these radiation
exposures is called radiation dosimetry.
The models for internal dosimetry consider the quantity of radionuclides entering the body, the factors
affecting their movement or transport through the body, and the energy deposited in organs and tissues from
the radiation that is emitted during spontaneous decay processes. The models for external dosimetry consider
only the photon doses to organs of individuals who are immersed in air or are exposed to a contaminated
ground surface. In addition, the uncertainties associated with each model will be discussed.
A.2 BASIC CONCEPTS
Radioactive materials produce radiation as their constituent radioactive nuclides undergo spontaneous
radioactive decay. The forms of emitted energy are characteristic of the decay process and include energetic
charged particles (alpha and beta particles) and photons (gamma rays and x-rays). Alpha particles are nuclei
of helium atoms and carry two positive charges compared to electrons which carry a single negative charge.
These particles can produce dense ionization tracks in the biological material that they traverse. Beta particles
are electrons or positrons emitted in radioactive decay. Their penetration power in material is greater than that
of alpha particles. Gamma and x-rays are electromagnetic radiation and, depending on energy, can have very
great penetrating power in material.
A-5
-------
D =
dm
I .. Ae
- hm
Am
(rad)
(A-6)
Internal and external exposures from radiation sources are not usually instantaneous but are distributed over
extended periods of time. The resulting time rate of change of the absorbed dose to a small volume of mass
is referred to as the absorbed dose rate, D
• dD ,. AD
D = = hm
dt Ar-o Af
(mradly)
(A-7)
The customary unit of absorbed dose rate is any quotient of the rad (or its multiple or submultiple) and a
suitable unit of time. In this report, absorbed dose rates are generally given in mrad/yr.
A.2.7 Linear Energy Transfer (LET)
The linear energy transfer, L., is a quantity that represents the energy lost, by collision, per unit length by
charged particles in an absorbing medium. It represents the increment of the mean energy lost, AE, to tissue
by a charged particle of specified energy in traversing a distance, AX:
L =
dE ,. s
— = lim
dX AI-O
(keV mm
(A-8)
For photons, U, represents the energy imparted by the secondary electrons (electrons that are knocked out of
their orbitals by primary radiation) resulting from secondary interactions between the photons and tissue
material. High-LET radiation (alpha particles) imparts more energy per unit length of organ tissue than does
low-LET radiation (x-rays, gamma rays, and beta particles). Consequently, the former are more effective per
unit dose in causing biological damage.
A.2.8 Dose Equivalent and Dose Equivalent Rate
Dose equivalent is a special radiation protection quantity that is used to express the absorbed dose in a manner
that considers the difference in biological effectiveness of various kinds of ionizing radiation. The ICRU has
defined the dose equivalent, H, as the product of the absorbed dose, D, and the quality factor, Q, at the point
of interest in biological tissue (ICRU80; an additional "modifying factor", N, is no longer used). This
relationship can be expressed in the following manner:
A-8
-------
H = D Q (rent)
(A-9)
The quality factor is a dimensionless quantity that depends on the collision stopping power for charged
particles, and it accounts for the differences in biological effectiveness found among varying types of radiation.
By definition, it is independent of tissue and biological endpoint The ICRP values for quality factors for high-
and low-LET radiation, which are used by EPA, are given in Table A-l.
Table A-1. Quality factor for various types of radiation (ICRP77, ICRP91")
^SiSi^^^^SS§iiiiiik^l^K'M
x-ravs. aamma ravs. and electrons
alpha particles
WiiiiiU^^i^SK >li
1
20
" ICRP Publication 60 designates as "radiation weighting factors".
The dose equivalent rate, ff, is the time rate of change of the dose equivalent to organs and tissues and is
expressed as:
dH „ Aff
,,
H = - = lun
dt A(-o
, , ,
(mremly)
(A-10)
A.2.9 Effective Dose Equivalent and Effective Dose Equivalent Rate
The ICRP has defined the effective dose equivalent, HE, as:
W
T *AT
{rent)
(A-ll)
where HT is the dose equivalent in tissue and w is the weighting factor, which represents the estimated
proportion of the stochastic risk resulting from tissue, T, to the stochastic risk when the whole body is
uniformly irradiated (ICRP77). The weighting factors recommended by the ICRP are listed in Table A-2.
More recently, ICRP (ICRP91) has adopted the use of effective dose, E, defined in a similar manner to H& but
with a different set of tissue weighting factors, as shown in Table A-2. In addition to the revised tissue
weighting factors, the tissue labeled "Remainder" is defined differently in the ICRP 30 and ICRP 60 methods.
A-9
-------
Table A-2. Tissue weighting factors recommended by the ICRP for stochastic risks
Gonads
Breast
Red Bone Marrow
Lung
Thyroid
Bone Surfaces
Remainder
0.25
0.15
0.12
0.12
0.03
0.03
0.30
;; : v;> >;: : ;:<; JGRP :PublicafiOn:66;fl(JRR9l|::i: : -^
Blftr Tis|e. ; - ;: : v ;::;; ;^;;:;;^i-; ' ;}
Gonads
Red Bone Marrow
Colon
Lung
Stomach
Bladder
Breast
Liver
Esophagus
Thyroid
Skin
Bone Surface
Remainder
0.20
0.12
0.12
0.12
0.12
0.05
0.05
0.05
0.05
0.05
0.01
0.01
0.05
The effective dose equivalent rate is the time derivative of the dose equivalent and is expressed as He, where
W
(mrem/y)
(A-12)
A.2.10 Relationship of the Dose Equivalent and the Effective Dose Equivalent to Risk
The dose equivalent was formally defined by the International Commission on Radiation Units and
Measurements (ICRU) in 1 962. Using this construct, the biological effects of absorbed doses of different types
of radiation can be compared for radiation protection purposes. Subsequently, the effective dose equivalent
was introduced to provide a radiation protection quantity to compare detriment from dose equivalents
distributed nonuniformly in the body. By convention, these concepts, in combination with the ICRP-
recommended quality factors and organ-weighting factors, are widely used in radiation protection. These
recommended factors, however, are based on models that differ significantly from those used to estimate risk.
To calculate risk, EPA first calculates age-specific, high- and low-LET absorbed dose rates, by organ, for a
uniform intake or external exposure rate. The radiogenic risk associated with this dose is then calculated using
the procedure described in Chapters 3 and 4 in conjunction with age- and organ-specific risk models.
These models assume a linear dose-response relationship and a lifetime relative risk projection for cancers
other than bone, skin, and thyroid cancers, for which absolute risk projection is employed. These risks are
integrated over the lifetime exposure period to arrive at the lifetime excess cancer risk.
A-10
-------
In calculating dose equivalents and effective dose equivalents, the ICRP Publication 30 convention was
employed, including the same quality factor and organ-weighting factors. However, in calculating the
radiogenic cancer risk from a given absorbed dose of alpha particle irradiation, RBEs shown in Table B-1 were
used. The ICRP organ-weighting factors shown in Table A-2 do not stand in the same proportions the organ
risks calculated using the EPA models for cancer induction or genetic mutations.
Furthermore, EPA considers somatic and genetic risks separately. Thus, even if attention is restricted to low-
LET radiation, the EPA estimated risk from a given effective dose equivalent will vary, depending on how the
absorbed dose is distributed within the body.
To summarize, because EPA risk models differ from those underlying the ICRP radiation protection
recommendations, the effective dose equivalent derived using ICRP quality factor and organ weighting factors
are not strictly proportional to risks calculated by the EPA.
A.2.11 Radon Decay-Product Units
The working level is a unit that has been used as a measure the radon decay-product activity in air. It is
defined as any combination of short-lived radon daughters (through polonium-214) per liter of air that will
result in the ultimate emission of 1.3 x 105 MeV of alpha energy. An activity concentration of 100 pCi/L of
radon-222 in equilibrium with its short-lived daughters gives rise to a potential alpha-energy concentration of
approximately 1 WL. Sometimes, the WL unit is also used" for thoron (radon-220) daughters. The potential
alpha energy exposure is commonly expressed in units of working level months (WLM). One WLM
corresponds to an exposure to a concentration of 1 WL for the commonly used reference period of 170 hours.
A.2.12 Customary and SI Units
The relationship between the customary units used in this text and the international system of units (SI) for
radiological quantities is shown in Table A-3. While the SI radiological units are almost universally used in
other countries for radiation protection regulation, the United States has not yet officially adopted their use for
such purposes.
A.3 EPA DOSIMETRIC MODELS
The EPA dosimetric models, to be discussed in the following sections, have been described in detail in
previous publications (Du80, Su81, Ko81 a, Ko81 b). Information on the elements treated in these sections was
taken directly from those documents or reports. In most cases, the EPA models are similar or identical to those
recommended by the ICRP (ICRP79, ICRP80, ICRP81). [Differences in model parameters did exist for some
A-11
-------
Table A-3. Comparison of Customary and SI Special Units for Radiation Quantities
Quantity
Activity (A)
Absorbed dose (D)
Dose equivalent (H)
Linear energy
transfer (L»)
1 ": : •'••'-''' •"'•''* '-'- ' - : Gu^tbnlaryiy^rtft:1 :^ :"^ : : : L '.
•\ •. iNartie : ^'-^-^•^^
Curie (Ci)
rad
rem
kiloelectron
volts per
micrometer
(keV unr1)
i^^^^i
3.7x1010s-1
10'2Jkg-1
lO^Jkg-1
1.602x1 a10 Jnrr1
-./- • ;.-: ::.;:::.: : ^i^^^^^^ife^^^lS
".:. •:SI;:Urtit^^-^;i^i:;:;S;l:
becquerel (Bq)
gray (Gy)
sieved (Sv)
1.0s'1
LOJkg-1
LOJkg'1
J = Joules; m = meter; s = seconds; kg = kilogram
radionuclides until 1983-1984 when EPA changed to the ICRP models for all radionuclides, except the
transuranics.] The basic physiological and metabolic data used by EPA in calculating radiation doses are
taken from ICRP reports (ICRP75, ICRP79).
A.3.1 Internal Dose Models
EPA implements contemporary models to estimate absorbed dose rates as a function of time to specified organs
in the body. Estimates of the doses resulting from the deposition and retention of inhaled particulates in the
lung and their subsequent absorption into the blood and clearance into the gastrointestinal (GI) tract are made
using the ICRP Task Group Lung Model (ICRP66).
A.3.1.1 Generalized Scheme for Estimating Organ Absorbed Dose Rates
A.3.1.1.1 Distribution of Activity of Radionuclides in the Body. The complex behavior of radionuclides is
simplified conceptually by considering the body as a set of compartments. A compartment may be any
anatomical, physiological, or physical subdivision of the body throughout which the concentration of a
radionuclide is assumed to be uniform at any given time. The terms "compartment" and "organ" are often used
interchangeably, although some of the compartments considered in this report may represent only portions of
a structure usually considered to be an organ, while some compartments may represent portions of the body
usually not associated with organs. Examples of compartments used in this report are the stomach, the
pulmonary region of the lung, the blood, or the bone. Within a compartment, there may be more than one
"pool" of activity. A pool is defined to be any fraction of the activity within a compartment that has a
A-12
-------
biological half-life which is distinguishable from the half-time(s) of the remainder of activity within the
compartment.
Activity entering the body by ingestion is assumed to originate in the stomach compartment; activity entering
through inhalation is assumed to originate in a compartment within the lung (the tracheo-bronchial, pulmonary,
or naso-pharyngeal region). From the stomach, the activity- is viewed as passing in series through the small
intestine, the upper large intestine, and the lower large intestine, from which it may be excreted. Also, activity
reaching the small intestine may be absorbed through the wall into the bloodstream, from which it may be
taken in parallel into any of several compartments within the skeleton, liver, kidney, thyroid, and other organs
and tissues.
The list of organs or regions for which dose rates are calculated is found in Table A-4. Activity in the lung
may reach the bloodstream either directly or indirectly through the stomach or lymphatic system. The
respiratory system and gastrointestinal tract models are discussed further in later sections.
Table A-4. Target organs and tissues considered in EPA dose calculations
Target Organ/Tissue
Lungsa
Stomach wall
Small intestine wall
Upper large intestine wall
Lower large intestine wall
Adrenals
Bladder Wall
Kidneys
Liver
Breast
Ovaries
Pancreasb
Brain
Red Bone Marrow
Endosteum (Bone Surface)
Skin
Spleen
Testes
Thymus
Thyroid
Uterus
• Since 1983, doses are also computed for three separate lung regions (naso-pharyngeal region, tracheo-bronchial region,
and pulmonary region) for inhalation exposures, plus intestinal wall, other, remainder, gonads, and effective.
b The pancreas is also used as a surrogate organ for calculating the cancer risk for all other organs and tissues.
A-13
-------
EPA models separately consider the intake and subsequent behavior of each radionuclide in the body. The
models also allow for the formation of radioactive decay products within the body, and it is assumed that the
movement of internally produced radioactive daughters is governed by their own metabolic properties rather
than those of the parent. This is in contrast to the ICRP assumption that daughters behave exactly as the
parent.
If A^t) denotes the activity of the ith species of the chain in organ k and if that activity is divided among
several "pools" or "compartments" indexed by subscript 1, then the time rate of change of activity can be
modeled by a system of differential equations of the following form:
(A-13)
at
- 1.
where compartment 1 is assumed to have L^ separate pools of activity, and where
the activity of species i hi compartment I of organ k;
(In 2) / Tf, where 1^ = radioactive half of species i;
rate coefficient (time'1) for biological removal of species i from compartment 1 of
organ k;
number of exponential terms in the retention function for species i in organ k;
branching ratio of nuclide j to species i;
inflow rate of the i* species onto the organ k; and
the fractional coefficient for nuclide i in the 1* compartment of organ k.
Pik
The subsystem described by these L* equations can be interpreted as a biological compartment in which the
fractional retention of radioactive species is governed by exponential decay. Radioactivity that enters an organ
may be lost by both radioactive decay and biological removal processes. For each source organ, the fraction
of the initial activity remaining at any time after uptake at time t = 0 is described by a retention function
consisting of one or more exponentially decaying terms:
(A-14)
The subscript 1 in the above equation represents the 1th term of the retention function, and the coefficients cilk
can be considered as "pathway fractions."
A-14
-------
A3.1.1.2 Dose Rates to Target Organs. The activity of a radionuclide in a compartment is a measure of the
rate of energy being emitted in that compartment, at any time, t, and can be related to the dose rate to a specific
organ at that time. This requires estimating the fraction of the energy emitted by the decay of the radionuclide
in each compartment that is absorbed by the specific organ.
The absorbed dose rate, I}(X;t) to target organ X at time t due to radionuclide species i in source organs
Y!,Y2,...., YM is estimated by the following equation:
D.(X;T) = tDfX-Ytf) (A-15)
where
P(X~Yk;t) =
A&(t) = activity, at time t of species i in source organ Yk,
S^X-YJ, called the S-factor, represents the average dose rate to target organ X from one unit of activity of
the radionuclide uniformly distributed in source organ or compartment Yk (Sn74). It is expressed in the
following manner:
where
c = a constant that depends on the units of dose, energy, and time being used;
fm = intensity of decay event (number per disintegration);
Em = average energy of decay event (Mev); and
$ra(X^Yk) = specific absorbed fraction, i.e., the fraction emitted energy from source organ Yk
absorbed by target organ X per gram of X, where the summation is taken over all
events of type m.
The units for S-factors depend on the units used for activity and time; thus, the S-factor units may be rad/Ci-
day. The S-factor is similar in concept to the SEE factor (specific effective energy) used by the ICRP
Committee 2 in Publication 30 (ICRP79). However, the SEE factor includes a quality factor for the type of
radiation emitted during the transformation.
The above equations are combined to produce the following expressions for the absorbed dose rates to target
organs at any time due to one unit of activity of radionuclide species, i, uniformly distributed in source organs
Y, - Yk:
A-15
-------
The corresponding dose equivalent rate, Hf(X;t), can be estimated by inclusion of the quality factor, Qm:
Q
Implicit in the above equations is the assumption that the absorbed dose rate to an organ is determined by
averaging absorbed dose distributions over its entire mass.
Alpha and beta particles are usually not sufficiently energetic to contribute a significant cross-irradiation dose
to targets separate from the source organ. Thus, the absorbed fraction for these radiations is generally assumed
to be just the inverse of the mass of organ X, or if the source and target are separated, then <|>m(X-Y) = 0.
Exceptions occur when the source and target are in very close proximity, as is the case with various skeletal
tissues. Absorbed fractions for cross-irradiations by beta particles among skeletal tissues were taken from
ICRP Publication 30 (ICRP80). The energy of alpha particles and their associated recoil nuclei is generally
assumed to be absorbed in the source organ. Therefore, (J>m(X-X) is taken to be the inverse of the organ mass,
and m(X-Y) = 0 if X and Y are separated. Special calculations are performed for active marrow and
endosteal cells in bone, based on the method of Thorne (Th77).
A.3 .1.1.3 Monte Carlo Methodology to Estimate Photon Doses to Organs. The Monte Carlo method uses a
computerized approach to estimate the probability of photons interacting within target organ X after emission
from source organ Y. The method is carried out for all combinations of source and target organs and for
several photon energies. The body is represented by an idealized phantom in which the internal organs are
assigned masses, shapes, positions, and attenuation coefficients based on their chemical composition. A mass
attenuation coefficient, u^ is chosen, where fj0 is greater than or equal to the mass attenuation coefficients for
any region of the body. Photon courses are simulated in randomly chosen directions, and potential sites of
interactions are selected by taking distances traversed by them as -In r///0, where r is a random number
distributed between 0 and 1 . The process is terminated when either the total energy of photons has been
deposited or the photon escapes from the body. The energy deposition for an interaction is determined
according to standard equations (Sn74).
A.3 . 1 . 1 .4 Effects of Decay Products. In calculating doses from internal and external exposures, the in-growth
of radioactive decay products (or daughters) must be considered for some radionuclides. When an atom
undergoes radioactive decay, the new atom created in the process, which may also be radioactive, can
contribute to the radiation dose to organs or tissues in the body. Although these decay products may be treated
A-16
-------
as independent radionuclides in external exposure, the decay products of each parent must be followed through
the body in internal exposure situations. The decay product contributions to the absorbed dose rates, which
are included in EPA calculations, are based on the metabolic properties of the individual daughters and the
organ in which they occur.
A.3.1.2 Inhalation Dosimetry - ICRP Respiratory Tract Model. As stated earlier, individuals immersed in
contaminated air will breathe radioactive aerosols or particulates, which can lead to doses to the lung and other
organs in the body. The total internal dose caused by inhalation of these aerosols can depend on a variety of
factors, such as breathing rates, particle sizes, and physical activity. Estimating the total dose to individuals
over a specific time period requires specifying the distribution of particle depositions in the respiratory tract
and the mathematical characteristics of the clearance parameters. The EPA currently uses assumptions
established by the ICRP Task Group on Lung Dynamics (TGLM)(ICRP66). This section will summarize the
essential features of that model. For a more comprehensive treatment, the reader is referred to the actual
report.
The basic features of the ICRP lung compartmental model are shown in Figure A-1. According to this model,
the respiratory tract is divided into four regions: naso-pharyngeal (N-P), tracheo-bronchial (T-B), pulmonary
(P), and lymphatic tissues. In the model, the regions N-P, T-B, and P are assumed to receive fractions D3, D4,
and D5 of the inhaled particulates, where the sum of these is less than 1 (some particles are removed by prompt
exhalation). The values D3, D4, and D5 depend on the activity median aerodynamic diameter (AMAD) of the
inspired particles. For purposes of risk calculations, EPA uses a default AMAD value of 1 micron. The lung
model employs three clearance classes, D, W,and Y, corresponding to rapid, intermediate, and slow clearance,
respectively, of material deposited in the respiratory passages. The clearance class depends on chemical
properties of the inhaled particles.
Like the ICRP, EPA assumes that the absorbed dose rate to the N-P region can be neglected. Unlike the ICRP,
however, EPA averages the dose over the pulmonary region of the lung (compartments e through h), to which
is assigned a mass of 570 g, including capillary blood (ICRP75). In addition, it is assumed that the total
volume of air breathed in one day by a typical member of the general population is 22,000 liters. This value
was determined by averaging the ICRP Publication 23 adult male and female values based on 8 hours of
working "light activity," 8 hours of nonoccupational activity, and 8 hours of resting.
A.3.1.3 Ingestion Dosimetry - ICRP GI Tract Model. According to the ICRP 30 GI tract model, the
gastrointestinal tract consists of four compartments: the stomach (S), small intestine (SI), upper large intestine
(ULI), and lower large intestine (LLI). The fundamental features of the model are shown in Figure A-2. It
is assumed that absorption into the blood occurs only from the small intestine (SI).
A-17
-------
Figure A-1. The ICRP Task Group lung model for particulates.
Inhaled particulates
B
0
c;
L)
>
k
i
a
c
e
3.
A &*
.:. 4
De§>
h
- r
T R
1 - D
S~
f
ff '
P
*
lg
b
d
^
1
T
R
T
N-P
(D3 - 0.030)
T-B
(D4 - 0.08)
P
-------
Figure A-2. ICRP schematic representation of radioactivity
movement among the respiratory tract, gastrointestinal tract, and blood.
INGEST10N
t
Respiratory
tract
f
B
L
0
0
D
S_>
SI
ULI
ab
LLI
= 24 day'
SI
XSI = 6 day1
ULI
Xuu = 1.85 day'1
LLI
"LLI
S = stomach
SI = small intestine
ULI = upper large intestine
LLI - lower large intestine
X = elimination rate constant
This model postulates that radioactive material entering the compartments of the GI tract is exponentially
removed by both radioactive decay and biological removal processes, and that there is no feedback.
Absorption of a particular nuclide from the GI tract is characterized by fj, which represents that fraction of the
nuclide ingested which is absorbed into body fluids if no radiological decay occurs, where
A-19
-------
/I -
, ab
^•SI
(A-19)
'57
the absorption coefficient (s"1)
the transfer coefficient from the small intestine to the large intestine (s"1)
Figure A-1 graphically presents the role of these coefficients in the gastrointestinal model. The kinetic model,
as formulated by the ICRP, does not permit total absorption of a nuclide (ft = 1). (The maximum value used
in EPA's calculations is f{ = 0.95.)
A.3.1.4 Dose Rate Conversion Factors. EPA uses the computer code RADRISK (Du80) for calculating age-
specific radiation dose rates resulting from a chronic unit intake rate of a radionuclide for a lifetime exposure.
These calculations are performed for inhalation and ingestion exposure pathways.
Following the beginning of chronic exposure, the activity in each organ of the body increases monotonically
until a steady state is achieved, at which time the activity remains constant. The instantaneous dose rates at
various times after the start of chronic exposure provide a reasonably accurate (and conservative) estimate of
the total annual dose for chronic exposure conditions. Since the rate of change in activity levels in various
organs is more rapid at early times after exposure, annual dose rates for use in risk calculations are averaged
over progressively longer periods.
A.3.1.5 Special Radionuclides
Tritium and Carbon-14 Most radionuclides are nuclides of elements found only in trace quantities in the body.
Others like tritium (hydrogen-3) or carbon-14 must be treated differently since they are long-lived nuclides of
elements that are ubiquitous in tissue. An intake of tritium is assumed to be completely absorbed and to be
rapidly mixed with the water content of the body (Ki78a).
The estimates for inhalation include consideration of absorption through the skin. Organ dose estimates are
based on the steady-state specific-activity model described by Killough et al. (Ki78a).
Carbon-14 is assumed to be inhaled as CO2 or ingested in a biologically bound form. Inhaled carbon-14 is
assumed to be diluted by stable carbon from ingestion (Ki78b). This approach allows separate consideration
of the ingestion and inhalation pathways. The specific-activity model used for organ dose estimates is also that
of Killough etal. (Ki78a). Short-lived carbon radionuclides (e.g., carbon-11 or carbon-15) are treated as trace
elements, and the organ doses are calculated accordingly.
A-20
-------
Radon Decay Products EPA estimates radiogenic cancer risk resulting from inhalation of radon decay products
based on an epidemic logical, based on human epidemiological data. In this approach, the airborne
concentration, expressed in WL (see A.2.1I), and exposure duration are used in conjunction with a
corresponding risk factor (risk per WLM), and absorbed dose rates or dose equivalent rates are not computed.
A.3.2 External Dose Models
This section is concerned with the calculation of dose rates for external exposure to photons from radionuclides
dispersed in the environment. Two exposure models are discussed: (1) immersion in contaminated air and (2)
irradiation from material deposited on the ground surface. The immersion source is considered to be a uniform
semi-infinite radionuclide concentration in air, while the ground surface irradiation source is viewed as a
uniform radionuclide concentration on an infinite plane. In both exposure modes, the dose rates to organs are
calculated from the dose rate in air.
Dose rates are calculated as the product of a dose rate factor, which is specific for each radionuclide, tissue,
and exposure mode, and the corresponding air or surface concentration. The dose rate factors used were
calculated with the DOSFACTOR code (Ko8 la,b). Note that the dose rate factors for each radionuclide do
not include any contribution for decay products. For example, the ground surface dose factors for cesium-137
are ail zero, since no photons are emitted in its decay. To assess surface deposition of cesium-137, the
ingrowth of its decay product, metastable barium-137, which is a photon emitter, must first be calculated.
A.3.2.1 Immersion. For immersion exposure to the photons from radionuclides in air, EPA assumes that an
individual is standing at the base of a semi-infinite cloud of uniform radionuclide concentration. First, the dose
rate factor (the dose rate for a unit concentration) in air is calculated for a source of photons with energy Er
At all points in an infinite uniform source, conservation of energy considerations require that the rates of
absorbed and emitted energy per unit mass be equal. The absorbed energy rate per unit mass at the boundary
of a semi-infinite cloud is one-half that value. For a photon of energy E^,
-k^- (A-20)
2 p
where
a
Dy(EY) = the dose rate per in air from immersion in a unit air concentration (rad-mVCi-s);
ET = emitted photon energy (MeV);
k = units conversion factor
1.62E-13 (J/MeV) x 3.7E+10 (dis/s-Ci) x l.OE+3 (g/kg) x 100 (rad kg/J)
5.93E+2 (rad-g/MeV-Ci-s) [or 1.602E-10 Gy-g/MeV-Bq-s]; and
p = density of air (g/m3).
A-21
-------
The above equation presumes that for each nuclide transformation, one photon with energy ET is emitted. The
dose rate factor for a nuclide is obtained by adding together the contributions from each photon associated with
the transformation process for that radionuclide.
A.3.2.2 Ground Surface Irradiation. In the case of air immersion, the radiation field was the same throughout
the source region. This allows the dose rate factor to be calculated on the basis of energy conservation without
having to consider explicitly the scattering processes taking place. For ground surface irradiation, the radiation
field depends on the height of the receptor above the surface, and the dose rate factor calculation is more
complicated. The radiation flux per unit solid angle is strongly dependent on the angle of incidence. It
increases from the value for photons incident from immediately below the receptor to a maximum close to the
horizon. Attenuation and buildup due to scattering must be considered to calculate the dose rate factor.
Secondary scattering provides a distribution of photon energies at the receptor, which increases the radiation
flux above mat calculated on the basis of attenuation. Trubey (Tr66) has provided a useful and reasonably
accurate expression to approximate this buildup:
where
Baen = the buildup factor (i.e., the quotient of the total energy flux and that calculated for
attenuation) for energy in ah-;
ua = attenuation coefficient at the energy of the released photon (m"1);
r = distance between the photon source and the receptor; and
Ca, Da = Berger buildup coefficients in air, which are dependent on energy and the scattering
medium.
The buildup factor is dimensionless and always has a value greater than unity. The resulting expression for
the dose rate factor at a height z (m) above a uniform plane is
exp(-(l -/>>„*)] (A-22)
\ a'
where
s
DY(EY,z) = dose rate in air per unit exposure (rad-m3/Ci-s) to a uniform surface concentration;
z = reference height above the ground surface (1m);
(Ma/P). = me mass energy-absorption coefficient (m2/g) in air at Ey; and
E| = the first order exponential integral function, i.e.,
A-22
-------
E.
= /
exp(-u)du
(A-23)
The dose rate at a height, z, above a soil volume uniformly contaminated with a radionuclide emitting
monoenergetic photons of energy Ey is computed as (SJ84):
(A-24)
where
CS,DS
the dose rate in air per unit exposure to a uniform volume concentration in soil (rad-
m3/Ci-s);
thickness of soil corresponding to 100 cm of air;
the mass energy-absorption coefficient (m2/g) in soil;
Berger energy buildup coefficients in soil at energy EY; and
the second order exponential integral function.
The thickness of soil corresponding to 100 cm of air, x,, is calculated as the depth for which the dose at the
soil surface from a plane source has the same value as Dys(EY,z) from Eqn A-22. For z=100 cm, the values
of xa are in the range of about 0.01 to 0.08 mm.
The dose factor for a given radionuclide is computed as the sum over all its characteristic photon releases of
the product of the corresponding energy-specific dose factor and intensity. The effective depth, xe, for each
radionuclide is computed as the ratio of the volume dose factor to the surface dose factor (DYDS). This
radionuclide-specific estimate of the effective depth is used by EPA in conjunction with the surface dose rate
factors to estimate the dose and risk from external exposure to radionuclides in soil, as discussed in Section
2.2.2.2.
A.3.2.3 Organ Doses. The dose rate factors in the preceding two sections are for the absorbed dose in air.
For estimating health risks, the absorbed doses in specific tissues and organs are needed. For this purpose,
Kerr and Eckerman (Ke80a,b) have calculated organ dose factors for immersion in contaminated air. Their
calculations are based on Monte Carlo simulations of the absorbed dose in each tissue or organ for the
spectrum of scattered photons in air resulting from a uniform concentration of monoenergetic photon sources.
Kocher (Ko8 la,b) has used these data to calculate values of the ratio of the organ dose factor to the air dose
factor, Gk(Ey), for 24 organs/tissues at 15 values of Ey ranging from 0.01 to 10 MeV.
A-23
-------
The dose rate factor for organ k, DYk, from immersion in contaminated air is
= G
(A-25)
For a given nuclide, the dose rate factor is obtained by taking the sum of the contributions from each photon
energy associated with the radionuclide decay. Ideally, a separate set of CftEJ values would be used for the
angular and spectral distributions of incident photons from a uniform plane source. Since these data are not
available, Kocher has used the same set of Gk(EY) values for calculating organ dose rate factors for both types
of exposure (Ko81a,b).
A.5 REFERENCES
Du80 Dunning, D.E. Jr., Leggett, R.W, and Yalcintas, M.G., "A Combined Methodology for
Estimating Dose Rates and Health Effects from Exposure to Radioactive Pollutants," ORNI/TM-
7105, 1980.
EPA89 U.S. Environmental Protection Agency, "Environmental Impact Statement, NESHAPS for
Radionuclides, Background Information Document - Volume 1, Risk Assessment Methodology,"
EPA/520/1-89-005, September 1989.
EPA92 U.S. Environmental Protection Agency, "Technical Support Document for the 1992 Citizens
Guide to Radon," EPA 400-R-92-011, May 1992.
EPA93 U.S. Environmental Protection Agency, "High-Level and Transuranic Radioactive Wastes,
Background Information Document for Proposed Amendments," EPA 400-R-93-007, January
1993.
ICRP66 ICRP Task Group on Lung Dynamics, "Depositions and Retention Models for Internal Dosimetry
of the Human Respiratory Tract," Health Phvs.. 12(2): 173-207, 1966.
ICRP75 International Commission on Radiological Protection, Report on the Task Group on Reference
Man. ICRP Publication No. 23, Pergamon Press, Oxford, 1975.
ICRP77 International Commission on Radiological Protection, "Recommendations of the International
Commission on Radiological Protection," ICRP Publication 26, Annals of the ICRP, Vol. 1, No.
3, Pergamon Press, Oxford, 1977.
ICRP79 International Commission on Radiological Protection, "Limits for Intakes of Radionuclides by
Workers," ICRP Publication No. 30, Pergamon Press, Oxford, 1979.
ICRP80 International Commission on Radiological Protection, "Limits for Intakes of Radionuclides by
Workers," ICRP Publication 30, Part 2, Annals of the ICRP, Vol. 4 (3/4), Pergamon Press,
Oxford, 1980.
ICRP81 International Commission on Radiological Protection, "Limits for Intakes of Radionuclides by
Workers," ICRP Publication 30, Part 3, Annals of the ICRP, Vol. 6 (2/3), Pergamon Press,
Oxford, 1981.
A-24
-------
ICRP84 International Commission on Radiological Protection, "A Compilation of the Major Concepts and
Quantities in Use by ICRP," ICRP Publication No. 42, Pergamon Press, Oxford, 1984.
ICRP91 International Commission on Radiological Protection, "1990 Recommendations of the
International Commission on Radiological Protection," ICRP Publication No. 60, Annals of the
ICRP, 21 (1-3), Pergamon Press, Oxford, 1991.
ICRU80 International Commission on Radiation Units and Measurements, ICRU Report No 33,
Washington, D.C., 1980.
KeSOa Kerr, G.D., andEckerman, K.F., Oak Ridge National Laboratory, private communication; see also
Abstract P/192 presented at the Annual Meeting of the Health Physics Society., Seattle,
Washington, July 20-25, 1980.
KeSOb Kerr., G.D., "A Review of Organ Doses from Isotropic Fields of X-Rays," Health Phys.. 39(1):3,
1980.
Ki78a Killough, G.C., Dunning, D.E Jr., Bernard, S.R. and Pleasant, J.C., Estimates of Internal Dose
Equivalent to 22 Target Organs for Radionuclides Occurring in Routine Releases from Nuclear
Fuel Cvcle Facilities. Vol. 1, Report No. ORNL/NUREG/TM-190, Oak Ridge National
Laboratory, Tennessee, June 1978.
Ki78b Killough, G.C., and Rohwer, P.S., "A New Look at the Dosimetry of I4C Released to the
Atmosphere as Carbon Dioxide," Health Phvs.. 34(2):141, 1978.
KoSla Kocher, D.C., "Dose-Rate Conversion Factors for External Exposure to Photons and Electrons,"
NUREG/CR-1918, ORNL/NUREG-79, Oak Ridge National Laboratory, Oak Ridge, TN, 1981.
Ko81b Kocher, D.C., "Dose-Rate Conversion Factors for External Exposure to Photon and Electron
Radiation from Radionuclides Occurring in Routine Releases from Nuclear Fuel-Cycle Facilities,"
Health Phys.. 38(4):543-621. 1981.
NCRP71 National Council on Radiation Protection and Measurements, Basic Radiation Protection Criteria.
NCRP Report No. 39, Washington, D.C., 1971.
Sn74 Snyder W.S., Ford, M.R., Warner, G.G., and Watson, S.B., A Tabulation of Dose Equivalent per
Microcurie-Day for Source and Target Organs of an Adult for Various Radionuclides. Oak Ridge
National Laboratory, ORNL-5000,1974.
Su81 Sullivan, RE., Nelson, N.S., Elicit, W.H., Dunning, D.E. Jr., Leggett, R.W., Yalcintas, M.G. and
Eckerman, K.F., Estimates of Health Risk from Exposure to Radioactive Pollutants. Report No.
ORNL/TM-7745, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 1981.
Th77 Thorne, M.D., "Aspects of the Dosimetry of Alpha-Emitting Radionuclides in Bone with
Particular Emphasis on 226Ra and 2,39Pu," Phvs. Med. Biol.. 22:36-46, 1977.
Tr66 Trubey, D.K., A Survey of Empirical Functions Used to Fit Gamma-Rav Buildup Factors. Oak
Ridge National Laboratory Rep., ORNL-RSIC-10, 1966,
A-25
-------
-------
Appendix B
Attributable Mortality Risk Coefficients
B-1
-------
CONTENTS
Section Page
B Attributable Mortality Risk Coefficients B-3
TABLES
Table Page
B-I Risk Models, DDREFs, RBEs and Lethality Fractions
Assumed by EPA for Specific Cancer Sites for Radiation Risk Assessment B-4
B-2 Attributable Mortality Risk Coefficients: Esophagus (DDREF=2XSVI) B-5
B-3 Attributable Mortality Risk Coefficients: Stomach (DDREF=2)(SV1) B-6
B-4 Attributable Mortality Risk Coefficients: Colon (DDREF=2)(SV1) B-7
B-5 Attributable Mortality Risk Coefficients: Liver (DDREF=2XSv') B-8
B-6 Attributable Mortality Risk Coefficients: Lung (DDREF=2XSV1) B-9
B-7 Attributable Mortality Risk Coefficients: Bone (DDREF=2XSv-') B-10
B-8 Attributable Mortality Risk Coefficients: Skin (DDREF=2)(SV1) B-l 1
B-9 Attributable Mortality Risk Coefficients: Breast (DDREF=lXSv'1) B-12
B-10 Attributable Mortality Risk Coefficients: Ovary (DDREF=2)(SV1) B-13
B-l 1 Attributable Mortality Risk Coefficients: Bladder (DDREF^XSV1) B-14
B-12 Attributable Mortality Risk Coefficients: Kidney (DDREF=2)(Svl) B-l5
B-13 Attributable Mortality Risk Coefficients: Thyroid (DDREF=2)(Sv1) B-16
B-14 Attributable Mortality Risk Coefficients: Leukemia (DDREF=2)(SV1) B-17
B-15 Attributable Mortality Risk Coefficients: Residual (DDREF=2)(SV1) B-18
B-16 Attributable Mortality Risk Coefficients: All Cancers (Sv1) B-l 9
B-17 Attributable Mortality Risk Coefficients: Radon Daughter Inhalation (WL'1) B-20
B-2
-------
Appendix B
Attributable Mortality Risk Coefficients
Appendix B presents attributable mortality risk coefficients for EPA's revised radiation risk assessment
methodology. In addition to the individual cancer sites considered in the revised risk methodology, risk
coefficients are also tabulated for all cancers combined and the special case of radon daughter inhalation.
Absolute risk models are employed for bone, skin, and thyroid cancer. Relative risk models are used for all
other cancer sites. Corresponding values for attributable cancer incidence risk coefficients may be derived by
dividing these values by the appropriate lethality fraction (see below). The baseline mortality data used to
derive these risk coefficients (for the relative risk models) are those of the 1980 decennial U.S. population
(1979-1981). For each cancer site considered, risk coefficients are tabulated for each age at exposure, T^ for
males, females, and the general population (based on male:female birth ratio of 1.051).
The risk coefficients presented in the following tables are applicable to low-LET radiation. Corresponding
risk coefficients for high-LET radiation may be derived by multiplying these values by the appropriate relative
biological effectiveness (RBE): 1 for leukemia, 10 for breast, and 20 for all other cancer sites. Furthermore,
these risk coefficients are applicable to low dose and low dose rate exposure conditions [<0.2 Gy (<20 rad)].
The dose and dose rate effectiveness factors (DDREFs) assumed for these estimates are indicated in the
heading for each table. A DDREF value of 2 is used for all cancer sites except breast, for which a DDREF
of 1 is used.
B-3
-------
Table B-1. Risk Models, DDREFs, RBEs and Lethality Fractions
Assumed by EPA for Specific Cancer Sites for Radiation Risk Assessment
Cancer Site
Esophagus
Stomach
Colon
Liver
Lung
Bone
Skin
Breast
Ovary
Bladder
Kidney
Thyroid
Leukemia
Residual
Risk Model
Absolute
Absolute
Absolute
Absolute
Absolute
Relative
Relative
Absolute
Absolute
Absolute
Absolute
Relative
Absolute
Absolute
DDREF
2
2
2
2
2
2
2
1
2
2
2
2
2
2
RBE
20
20
20
20
20
20
20
10
20
20
20
20
1
20
Lethality
Fraction
0.95
0.90
0.55
0.95
0.95
0.70
0.002 "
0.50
0.70
0.50
0.65
0.10
0.99
0.71
Skin cancer incidence is calculated only for those cases that are fatal, i.e., the mortality rate is divided by 1.
B-4
-------
Table B~2. Attributable Mortality Risk Coefficients: Esophagus (DDREF=2)(Sv1)
0
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
8.0710E-04
8.1739E-04
8.1815E-04
S.1868E-04
8.1908E-04
8.1941E-04
8.1970E-04
8.1997E-04
8.2022E-04
8.2044E-04
8.3745E-04
8.5442E-04
8.5458E-04
8.5477E-04
8.5503E-04
8.5544E-04
8.5601E-04
8.5671E-04
8.5752E-04
8.5837E-04
9.1313E-04
9.6808E-04
9.6927E-04
9.7045E-04
9.7149E-04
9.7248E-04
9.7341E-04
9.7408E-04
9.7455E-04
9.7484E-04
I.0848E-03
1.I949E-03
1.1948E-03
1.1937E-03
1.1918E-03
1.1890E-03
1.1856E-03
1.1824E-03
1.1773E-03
1.1703E-03
L2954E-03
1.4I61E-03
1.4021E-03
1.3876E-03
1.3712E-03
1.3519E-03
1.3306E-03
1.3077E-03
1.2817E-03
1.2540E-03
1.2268E-03
1.1980E-03
1.1654E-03
1.1306E-03
1.0942E-03
1.0581E-03
5.8165E-04
5.8987E-04
5.9046E-04
5.9088E-04
5.9121E-04
5.9148E-04
5.9172E-04
5.9194E-04
5.9215E-04
5.9234E-04
6.02I6E-04
6.1194E-04
6.1205E-04
6.1220E-04
6.1247E-04
6.I289E-04
6.1345E-04
6.1417E-04
6.1500E-04
6.1591E-04
6.4422E-04
6.7269E-04
6.7390E-04
6.7514E-04
6.7636E-04
6.7750E-04
6.7855E-04
6.7940E-04
6.8008E-04
6.8057E-04
7.3I59E-04
7.8253E-04
7.8243E-04
7.8163E-04
7.801 1E-04
7.7806E-04
7.7519E-04
7.7185E-04
7.6800E-04
7.6302E-04
8.0475E-04
8.4464E-04
8.3503E-04
8.2278E-04
8.0879E-04
7.9483E-04
7.8025E-04
7.6327E-04
7.4442E-04
7.2457E-04
7.0370E-04
6.8209E-04
6.5923E-04
6.3499E-04
6.0966E-04
5.8373E-04
1.0440E-03
1.0559E-03
1.0568E-03
1.0574E-03
I.0578E-03
1.0582E-03
I.0585E-03
I.0588E-03
1.0590E-03
1.0593E-03
1.0838E-03
1.1083E-03
1.1085E-03
1.1087E-03
1.1089E-03
1.1092E-03
1.1096E-03
1.1101E-03
1.1107E-03
1.1112E-03
I.1933E-03
1.2754E-03
1.2762E-03
1.2769E-03
1.2773E-03
1.2777E-03
1.2781E-03
1.2782E-03
1.2780E-03
1.2778E-03
1.4480E-03
1.6185E-03
1.6178E-03
1.6160E-03
1.6132E-03
1.6091E-03
I.6047E-03
I.6013E-03
1.5944E-03
1.5S48E-03
1.7940E-03
1.9960E-03
1.9768E-03
1.9590E-03
1.9391E-03
1.9133E-03
1.8841E-03
I.8540E-03
1.8193E-03
1.7823E-03
1.7470E-03
1.7092E-03
1.6649E-03
1.6176E-03
1.5682E-03
1.5196E-03
Illj^^
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
1.0235E-03
9.8687E-04
9.4804E-04
9.0958E-04
8.7322E-04
8.3756E-04
8.0035E-04
7.6115E-04
7.2281E-04
6.8640E-04
6.4945E-04
6.1217E-04
5.7595E-04
5.4257E-04
5.0956E-04
4.7319E-04
4.3750E-04
4.0519E-04
3.7128E-04
3.3352E-04
2.97I6E-04
2.6959E-04
2.4116E-04
2.0644E-04
1.7S94E-04
1.5265E-04
1.2527E-04
1.0676E-04
8.5772E-05
6.0957E-05
4.5885E-05
3.7977E-05
3.1379E-05
2.5908E-05
2.1411E-05
1.7769E-05
1.4874E-05
1.2615E-05
1.0893E-05
9.6370E-06
8.8043E-06
8.3736E-06
8.3687E-06
8.8616E-06
9.9894E-06
1.1654E-05
1.3561 E-05
1.5672E-05
1.7885E-05
1.9987E-05
2.1609E-05
2.1878E-05
2.0454E-05
1.3824E-05
3.2615E-06
5.5840E-04
5.3317E-04
5.0697E-04
4.7892E-04
4.5041E-04
4.2368E-04
3.9679E-04
3.7004E-04
3.4547E-04
3.2135E-04
2.9676E-04
2.735 1E-04
2.5215E-04
2.3181E-04
2.1240E-04
1.9315E-04
1.7497E-04
1.5848E-04
1.4065E-04
1.2272E-04
1.0757E-04
9.3865E-05
8.0987E-05
6.9602E-05
5.9020E-05
4.9093E-05
4.062 1E-05
3.2877E-05
2. 6 191 E-05
2.1455E-OS
1.7740E-05
1.4502E-05
1.1847E-05
9.683 1E-06
7.9292E-06
6.5218E-06
5.4089E-06
4.5452E-06
3.8927E-06
3.4191E-06
3.1029E-06
2.9314E-06
2.9153E-06
3.0854E-06
3.5016E-06
4.1326E-06
4.8602E-06
5.6714E-06
6.5307E-06
7.3592E-06
S.0207E-06
8.1823E-06
7.7131E-06
5.2909E-06
1.2482E-06
1.4734E-03
1.4229E-03
1.3690E-03
1.3175E-03
1.2703E-03
1.2228E-03
1.1722E-03
1.1177E-03
1.0627E-03
1.0109E-03
9.5857E-04
9.0445E-04
8.5078E-04
8.0164E-04
7.5250E-04
6.9739E-04
6.4294E-04
5.9358E-04
5.4287E-04
4.8611E-04
4.3045E-04
3.8935E-04
3.4680E-04
2.9364E-04
2.5268E-04
2.1400E-04
1.7350E-04
1.4717E-04
1.1699E-04
8.0763E-05
5.9373E-05
4.8716E-Q5
3.9897E-05
3.2644E-05
2.6735E-05
2.1993E-05
1.8255E-05
1.5354E-05
1.3147E-05
1.153 1 E-05
1.0445E-05
9.8540E-06
9.7716E-06
1.0268E-05
1.1486E-05
1.3301 E-05
1.5370E-05
1.7649E-05
2.0023E-05
2.2254E-05
2.3940E-05
2.4124E-05
2.2454E-05
I.5109E-05
3.5523E-06
B-5
-------
Table B-3. Attributable Mortality Risk Coefficients: Stomach (DDREF=2)(Sv1)
Age
0
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
IS
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
General
7.7487E-03
7.8476E-03
7.8548E-03
7.8599E-03
7.8638E-03
7.8669E-03
7.8697E-03
7.8722E-03
7.8745E-03
7.8764E-03
9.2363E-03
1.0596E-02
1.0598E-02
1.0600E-02
1.0603E-02
1.0607E-02
1.0613E-02
1.0619E-02
1.0626E-02
1.0635E-02
1.0464E-02
1.0293E-02
I.0300E-02
1.0307E-02
1.03I4E-02
1.0320E-02
1.0324E-02
1.0327E-02
1.0328E-02
1.0329E-02
5.9191E-03
1.5104E-03
1.5095E-03
1.5079E-03
1.5060E-03
1.5039E-03
1.50I4&03
1.4981E-03
1.4942E-03
1.4901 E-03
I.3792E-03
1.2683E-03
1.2633E-03
1.2571E-03
1.2501E-03
1.2430E-03
1.2354E-03
1.2262E-03
1.2160E-03
1.2052E-03
1.1929E-03
1.1794E-03
1.1654E-03
1.1507E-03
1.1350E-03
1.1172E-03
Males
5.0763E-03
5.1480E-03
5.1531E-03
5.1568E-03
5.1598E-03
5.1621E-03
5.1642E-03
5.1661E-03
5.1678E-03
5.1694E-O3
6.6015E-03
8.0341 E-03
8.0356E-03
8.0375E-03
8.0402E-03
8.0446E-03
8.0510E-03
8.0590E-03
8.0684E-03
8.0787E-03
8.0651E-03
8.0519E-03
8.0637E-03
8.0752E-03
8.0860E-03
8.0963E-03
8.1058E-03
8.113SE-03
8.1196E-03
8.1249E-03
4.6797E-03
1.2298E-03
1.2294E-03
1.2284E-03
1.2269E-03
1.2251E-03
I.2225E-03
1.2190E-03
I.2156E-03
1.2116E-03
1.1323E-03
1.0533E-03
1.0480E-03
1.0416E-03
1.0341E-03
I.0262E-03
1.0177E-03
1.0076E-03
9.9666E-04
9.8546E-04
9.7289E-04
9.5872E-04
9.4337E-04
9.2699E-04
9.0960E-04
8.9034E-04
Females
1.0557E-02
1.0677E-02
1.0686E-02
1.0692E-02
1.0697E-02
1.0700E-02
1.0703E-02
1.0706E-02
1.0708E-02
1.0711E-02
1.1995E-02
1.3279E-02
1.3281E-02
1.3283E-02
1.3285E-02
1.3288E-02
1.3291E-02
1.3294E-02
1.3297E-02
1.3301E-02
1.2964E-02
1.2624E-02
I.2623E-02
1.2623E-02
1.2622E-02
I.2620E-02
1.2617E-02
1.2611E-02
1.2605E-02
1.2598E-02
7.1934E-03
1.7986E-03
1.7968E-03
1.7943E-03
1.7918E-03
1.7891 E-03
1.7862E-03
1.7829E-03
I.7781E-03
1.7735E-03
1.6301E-03
1.4865E-03
1.4814E-03
1.4752E-03
1.4682E-03
1.4615E-03
1.4544E-03
1.4455E-03
1.4354E-03
1.4245E-03
1.4118E-03
1.3982E-03
1.3846E-03
1.3705E-03
1.3555E-03
1.3380E-03
Age
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
General
1.0982E-03
1.0786E-03
1.0571 E-03
1.0340E-03
1.0091 E-03
9.8265E-04
9.5452E-04
9.2406E-04
8.9098E-04
8.5707E-04
8.2314E-04
7.8797E-04
7.5242E-04
7.1577E-04
6.7534E-04
6.3206E-04
5.8892&04
5.4759E-04
5.0498E-04
4.5985E-04
4.1439E-04
3.68J8E-04
3.2359E-04
2.8427E-04
2.4708E-04
2.1205E-04
1.8156E-04
1.5259E-04
1.2810E-04
1.0836E-04
8.9934E-05
7.4304E-05
6.1291E-05
5.0522E-05
4.1688E-05
3.4545E-05
2.8874E-05
2.4452E-05
2.1085E-05
1.8628E-05
1.6996E-05
1.6144E-05
1.6115E-05
1.7047E-05
1.9201E-05
2.2386E-05
2.6031E-05
3.0063E-05
3.4288E-05
3.8294E-05
4.1379E-05
4.1871E-05
3.9125E-05
2.6434E-05
6.2328E-06
Males
8.6985E-04
8.4758E-04
8.2440E-04
8.0076E-04
7.7489E-04
7.4724E-04
7.I886E-04
6.9035E-04
6.6061E-04
6.2946E-04
5.9679E-&4
5.6194E-04
5.27I3E-04
4.9457E-04
4.6167E-04
4.2536E-04
3.8913E-04
3.5560E-04
3.2316E-04
2.9231E-04
2.6094E-04
2.2844E-04
1.9967E-04
1.7415E-04
1.4659E-04
1.1881E-04
9.8039E-05
8.2497E-05
6.7939E-05
5.5091E-05
4.4641 E-05
3.6493E-05
2.9813E-05
2.4367E-05
I.9953E-05
1.6412E-05
1.3611E-05
1.1438E-05
9.7957E-06
8.6039E-06
7.8083E-06
7.3769E-06
7.3363E-06
7.7644E-06
8.8H7E-06
1.0399E-05
1.2230E-05
1.4272E-05
I.6434E-05
1.8519E-05
2.0184E-05
2. 0591 E-05
1.9410E-05
1.33I4E-05
3.1409E-06
Females
1.3190E-03
1.3006E-03
1.2793E-03
1.2549E-03
1.2292E-03
1.2017E-03
1.1717E-03
1.I371E-03
1.0985E-03
I.0594E-03
1.02I5E-03
9.8305E-04
9.4365E-04
9.00I7E-04
8.5004E-04
7.9755E-04
7.4527E-04
6.942 1E-04
6.4026E-04
5.8112E-04
5.2228E-04
4.6341E-04
4.053 1E-04
3.5445E-04
3.0887E-04
2.6729E-04
2.2914E-04
1.9092E-04
1.5%3E-04
1.3507E-04
1.1164E-04
9.1601E-05
7.5018E-05
6. 1381 E-05
5. 0271 E-05
4.1354E-05
3.4325E-05
2.8871E-05
2.4721E-05
2.1683E-05
1.9641E-05
1.8529E-05
1.8374E-05
1.9307E-05
2.1598E-05
2.50IOE-05
2.8901 E-05
3.3186E-05
3.7650E-05
4.1845E-05
4.5014E-05
4.5360E-05
4.2220E-05
2.8409E-05
6.6794E-06
B-6
-------
Table B-4. Attributable Mortality Risk Coefficients: Colon (DDREF=2)(Sv1)
Age
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
General
2.8462E-02
2.8825E-02
2.885 1E-02
2.8870E-02
2.8884E-02
2.8896E-02
2.8906E-02
2.8915E-02
2.8923E-02
2.8930E-02
2.8936E-02
2.8939E-02
2.8943E-02
2.8948E-02
2.8956E-02
2.8969E-02
2.8985E-02
2.9005E-02
2.9027E-02
2.9049E-02
1.6991E-02
4.9I23E-03
4.9170E-03
4.9217E-03
4.9262E-03
4.9304E-03
4.9342E-03
4.937 1E-03
4.9392E-03
4.941 OE-03
6.0606E-03
7.1793E-03
7.I780E-03
7.1754E-03
7.1710E-03
7.1654E-03
7.I581E-03
7.1485E-03
7.1365E-03
7.1223E-03
4.3437E-03
1.5777E-03
1.5725E-03
I.5663E-03
I.5596E-03
1.5519E-03
1.5429E-03
I.5327E-03
1.5214E-03
1.5089E-03
1.4951E-03
1.4804E-03
1.4647E-03
1.4474E-03
1.4283E-03
1.4066E-03
Males
2.1918E-02
2.2227E-02
2.2249E-02
2.2265E-02
2.2278E-02
2.2288E-02
2.2297E-02
2.2305E-02
2.2312E-02
2.2318E-02
2.2323E-02
2.2326E-02
2.2329E-02
2.2332E-02
2.2340E-02
2.2354E-02
2.2372E-02
2.2394E-02
2.2418E-02
2.2445E-02
1.2701E-02
2.9314E-03
2.9360E-03
2.9407E-03
2.9452E-03
2.9496E-03
2.9534E-03
2.9566E-03
2.9592E-03
2.9614E-03
3.7367E-03
4.5121E-03
4.5126E-03
4.5120E-03
4.5102E-03
4.5075E-03
4.5044E-03
4.5000E-03
4.4937E-03
4.485 1E-03
2.7074&4>3
9.3810E-04
9.3480E-04
9.3079E-04
9.2643E-04
9.2145E-04
9.1546E-04
9.084 1E-04
9.007 1E-04
8.9231E-04
8.8250E-04
8.7208E-04
8.6136E-04
8.4916E-4W
8.3510E-04
8.1923E-04
Females
3.5340E-02
3.5740E-02
3.5770E-02
3.5790E-02
3.5805E-02
3.5817E-02
3.5828E-02
3.5837E-02
3.5845E-02
3.5853E-02
3.5858E-02
3.5862E-02
3.5867E-02
3.5872E-02
3.5879E-02
3.5888E-02
3.5899E-02
3.5912E-02
3.5925E-02
3.5937E-02
2.1460E-02
6.9732E-03
6.9754E-03
6.9771E-03
6.9786E-03
6.9799E-03
6.9810E-03
6.9808E-03
6.9798E-03
6.9788E-03
8.4499E-03
9.9183E-03
9.9123E-03
9.9045E-03
9.8946E-03
9.8829E-03
9.8685E-03
9.8502E-03
9.8293E-03
9.8060E-03
6.0067E-03
2.2269E-03
2.2186E-03
2.2092E-03
2.1990E-03
2.1874E-03
2.I739E-03
2.1590E-03
2.1425E-03
2.1241E-03
2.I044E-03
2.0833E-03
2.060 1E-03
2.0354E-03
2.0084E-03
1.9780E-03
Age
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97'
98
99
100
101
102
103
104
105
106
107
108
109
110
General
1.3830E-03
1.3586E-03
1.3326E-03
1.3046E-03
1.2744E-03
1.2417E-03
1.2063E-03
1.1686E-03
1.1292E-03
1.0883E-03
1.0454E-03
9.9954E-04
9.5133E-04
9.0155E-04
8.5070E-04
7.9747E-04
7.4123E-04
6.8429E-04
6.2720E-04
5.7019E-04
5.1372E-04
4.5743E-04
4.0258E-04
3.5105E-04
3.0444E-04
2.6269E-04
2.2443E-04
1.8913E-04
1.5618E-04
1.2759E-04
I.0526E-04
8.7143E-05
7.2022E-05
5.9480E-05
4.9169E-05
4.0816E-05
3.4I74E-05
2.8990E-05
2.5039E-05
2.2157E-05
2.0247E-05
1.9260E-05
1.9252E-05
2.0390E-05
2.2988E-05
2.6822E-05
3.1214E-05
3.6076E-05
4.1174E-05
4.601 7E-05
4.9758E-05
5.0381E-05
4.7105E-05
3.1839E-05
7.5123E-06
Males
8.0230E-04
7.8457E-04
7.6502E-04
7.4349E-04
7.2104E-04
6.9735E-04
6.7124E-04
6.4383E-04
6.1588E-04
5.8684E-04
5.5664E-04
5.2560E-04
4.9475E-04
4.6443E-04
4.3367E-04
4.0227E-04
3.7040E-04
3.3779E-04
3.0589E-04
2.7433E-04
2.430 iE-04
2.1394E-04
1.8577E-04
1.5859E-04
1.3410E-04
1.1245E-04
9.4085E-05
7. 803 IE-OS
6.2353E-05
4.8516E-05
3.8798E-05
3.1716E-05
2. 59 HE-OS
2.1178E-05
1.7342E-05
1.4264E-05
I.1830E-05
9.9409E-06
8.5136E-06
7.4778E-06
6.7863E-06
6.4113E-06
6.3761E-06
6.748 1 E-06
7.6583E-06
9.0383E-06
1.0630E-05
1.2404E-05
1.4283E-05
1.6095E-05
I.7542E-05
1.7896E-05
1.6869E-05
I.1572E-05
2.7298E-06
Females
1.9447E-03
1.9102E-03
I.8743E-03
1.8361E-03
1.7942E-03
1.7484E-03
1.6993E-03
1.6470E-03
I.5916E-03
1.534 1 E-03
1.4737E-03
1.4086E-03
1.3389E-03
1.2660E-03
1.19I7E-03
1.I139E-03
1.0314E-03
9.4890E-04
8.6626E-04
7.8435E-04
7.0404E-04
6.2338E-04
5.4558E-04
4.7369E-04
4.09I7E-04
3.5170E-04
2.9870E-04
2.4990E-04
2.0534E-04
I.6724E-04
I.37HE-04
1.1250E-04
9.2131E-05
7.5383E-05
6.1739E-05
5.0788E-05
4.2156E-05
3.5457E-05
3.0361E-05
2.6629E-05
2.4121E-05
2.2755E-05
2.2565E-05
2.3712E-05
2.6525E-05
3.0715E-05
3.5494E-05
4.0756E-05
4.6238E-05
5.1391E-05
5.5283E-05
5.5708E-Q5
5.1852E-05
3.4890E-05
8.2031E-06
B-7
-------
Table B-5. Attributable Mortality Risk Coefficients: Liver (DDREF=2)(Sv1)
Age
0
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
General
1.8102E-03
1.8330E-03
I.8345E-03
1.8355E-03
1.8361E-03
1.8364E-03
1.8365E-03
1.8366E-03
1.8366E-03
1.8365E-03
1.8363E-03
1.8361E-03
I.8356E-03
1.8349E-03
1.8347E-03
1.8349E-03
1.8351E-03
1.8356E-03
1.S364E-03
I.8370E-03
1.8376E-03
1.8381E-03
1.8388E-03
1.8398E-03
1.8406E-03
1.8413E-03
1.8418E-03
1.8417E-03
1.8416E-03
1.8414E-03
1.8405E-03
1.8387E-03
1.8371E-03
1.8351E-03
1.8318E-03
1.8280E-03
1.8233E-03
1.8173E-03
1.8106E-03
1.8031E-03
1.7934E-03
1.7823E-03
1.7713E-03
1.7592E-03
1.7465E-03
1.7328E-03
1.7149E-03
1.6934E-03
I.6726E-03
1.6514E-03
1.6273E-03
I.6006E-03
1.5715E-03
1.5394E-03
1.5043E-03
1.4664E-03
Males
2.0737E-03
2.1026E-03
2.1044E-03
2.1057E^)3
2.1066E-03
2.107IE-03
2.1074E-03
2.1077E-03
2.1079E-03
2.1079E-03
2.1078E-03
2.1076E-03
2.1072E-03
2.1066E-03
2.1065E-03
2.1071E-03
2.1080E-03
2.1094E-03
2.1111E-03
2.1129E-03
2.1148E-03
2.1165E-03
2.H85E-03
2.1208E-03
2.1232E-03
2.1254E-03
2.1273E-03
2.1287E-03
2.1301E-03
2.I315E-03
2.1318E-03
2.1309E-03
2.1300E-03
2.1286E-03
2.1255E-03
2.1217E-03
2.1172E-03
2.I108E-03
2.1030E-03
2.0945E-03
2.0835E-03
2.0696E-03
2.0546E-03
2.0388E-03
2.0226E-03
2.005 1E-03
1.9817E-03
1.9529E-Q3
1.9272E-03
1.9011E-03
1.8685E-03
1.8320E-03
1.7935E-03
1.7528E-03
1.7089E-03
1.6598E-03
Females
1.5333E-03
1.5505E-03
1.5515E-03
I.5523E-03
1.5528E-03
1.5528E-03
1.5527E-03
1.5527E-03
I.5527E-03
1.5524E-03
I.5521E-03
1.5519E-03
1.5511E-03
1.5504E-03
I.5503E-03
1.5502E-03
1.5498E-03
I.54%E-03
1.5496E-03
1.5493E-03
1.5488E-03
I.5484E-03
1.5483E-03
1.5482E-03
1.5478E-03
1.5473E-03
1.5468E-03
1.5455E-03
1.5441E-03
1.5429E-03
1.5411E-03
1.5387E-03
I.5366E-03
1.5343E-03
1.5312E-03
1.5276E-03
I.5231E-03
1.5178E-03
1.5128E-03
1.5067E-03
1.4985E-03
1.4907E-03
1.4842E-03
1.4763E-03
1.4676E-03
1.4583E-03
1.4467E-Q3
1.4330E-03
1.4178E-03
1.4024E-03
1.3873E-03
I.3713E-03
1.3525E-03
1.3298E-03
1.3042E-03
1.2783E-03
Age
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
no
General
1.4242E-03
1.3809E-03
1.3386E-03
I.2935E-03
1.2444E-03
1.1915E-03
1.1367E-03
I.0808E-03
1.0245E-03
9.6867E-04
9.1256E-04
8.5536E-04
7.9867E-04
7.4318E-04
6.8802E-04
6.3410E-04
5.8074E-04
5.2838E-04
4.7739E-04
4.2407E-04
3.7020E-04
3.2311E-04
2.8047E-04
2.3598E-04
1.9680E-04
1.6542E-04
1.3570E-04
1.09I5E-04
8.6504E-05
6.7033E-05
5.3135E-05
4.3664E-05
3.5828E-05
2.9383E-O5
2.4125E-05
1.9896E-05
1.6552E-05
1.3953E-05
1.1977E-05
1.0534E-05
9.5688E-06
9.0507E-06
8.9994E-06
9.4874E-06
I.0657E-05
1.2397E-05
1.4384E-05
1.6576E-05
1.8866E-05
2.1027E-05
2.2677E-05
2.2904E-05
2.1365E-05
1.4417E-05
3.3925E-06
Males
1.6039E-03
1.5468E-03
1.4910E-03
I.4321E-03
1.3687E-03
1.3011E-03
1.2291E-03
1.1576E-03
1.0882E-03
1.0172E-03
9.4599E-04
8.7353E-04
7.9946E-04
7.2727E-04
6.6314E-04
6.0885E-04
5.5296E-04
4.9614E-04
4.4443E-04
3.8773E-04
3.3248E-04
2.9001E-04
2.4943E-04
2.0574E-04
1.7063E-04
1.4546E-04
1.2017E-04
9.4649E-05
7.2443E-05
5.5537E-05
4.4304E-05
3.6218E-05
2.9588E-05
2.4183E-05
1.9803E-05
1.6288E-05
1.3509E-05
1.1352E-05
9.72I8E-06
8.5390E-06
7.7493E-06
7.3212E-06
7.2810E-06
7.7058E-06
8.7452E-06
1.0321E-05
1.2138E-05
1.4164E-05
1.6310E-05
1.8379E-05
2. 003 IE-OS
2.0435E-05
1.9263E-05
1.3214E-05
3.1172E-06
Females
1.2505E-03
1.2215E-03
1.1932E-03
1.1623E-03
1.1276E-03
1.0896E-03
1.05I5E-03
1.0108E-03
9.6708E-04
9.2552E-04
8.8325E-04
8.3967E-04
7.9799E-04
7.5645E-04
7.0836E-04
6.543 1 E-04
6.0247E-04
5.5300E-04
5.0191E-04
4.5038E-04
3.9672E-04
3.4567E-04
3.0094E-04
2.5525E-04
2.1289E-04
1.7725E-04
1.4455E-04
1.1709E-04
9.3872E-05
7.2797E-05
5.7367E-05
4.7070E-05
3.8549E-05
3.1541E-05
2.5832E-05
2.1250E-05
1.7639E-05
1.4836E-05
1.2703E-05
1.1142E-05
1.0093E-05
9.5211E-06
9.4415E-06
9.9213E-06
1.1098E-05
1.2851E-05
1.4851E-05
I.7053E-05
1.9347E-05
2.1502E-05
2.3131E-05
2.3309E-05
2.1695E-05
1.4598E-05
3.4323E-06
B-8
-------
Table B-6. Attributable Mortality Risk Coefficients: Lung (DDREF=2)(Sv1)
111^
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
1.5378E-02
1.5574E-02
1.5588E-02
1.5598E-02
1.5606E-02
1.5612E-02
1.5618E-02
I.5623E-02
I.5627E-02
1.5632E-02
1.5635E-02
1.5638E-02
1.564IE-02
1.5644E-02
1.5649E-02
1.5657E-02
1.5668E-02
1.5680E-02
1.5694E-02
1.5709E-02
8.8600E-03
1.9967E-03
1.9989E-03
2.0010E-03
2.003 1E-03
2.0049E-03
2.0064E-03
2.0073E-03
2.0078E-03
2.0076E-03
3.8972E-03
5.7828E-03
5.7742E-03
5.7626E-03
5.7478E-03
5.7278E-03
5.7024E-03
5.6710E-03
5.6341E-03
5.5919E-Q3
6.7063E-03
7.7876E-03
7.6951E-03
7.5940E-03
7.4818&O3
7.3591E-03
7.2255E-03
7.0799E-03
6.9255E-03
6.7609E-03
6.5821E-03
6.3914E-03
6.1888E-03
5.9732E-03
5.7478E-03
5.5089E-03
1.3711E-02
1.3904E-02
1.3918E-02
1.3928E-02
1.3936E-02
1.3943E-02
1.3949E-02
1.3954E-02
1.3959E-02
1.3963E-02
1.3967E-02
1.3970E-02
1.3972E-02
1.3976E-02
1.3983E-02
1.3993E-02
1.4006E-02
1.4022E-02
I.4040E-02
1.406IE-02
7.8274E-03
1.5741E-03
1.5770E-03
1.5799E-03
1.5828E-03
1.585SE-03
1.5880E-03
.1.5902E-03
1.5920E-03
I.5934E-03
3.1586E-03
4.7236E-03
4.7224E-03
4.7I96E-03
4.7139E-03
4.705 1E-03
4.6936E-03
4.6784E-03
4.6587E-03
4.6333E-03
5.3778E-03
6.1046E-03
6.0496E-03
5.9882E-03
5.9164E-03
5.8354E-03
5.7473E-03
5.6495E-03
5.5440E-03
5.4314E-03
5.3062E-03
5.1684E-03
5.0205E-03
4.8633E-03
4.6967E-03
4.5177E-03
1.7130E-02
1.7324E-02
1.7338E-02
1.7348E-02
1.7355E-02
1.7361&O2
1.7366E-02
I.7371E-02
1.7374E-02
1.7378E-02
1.7381E-02
1.7384E-02
1.7387E-02
I.7390E-02
1.7394E-02
1.7399E-02
1.7405E-02
I.7412E-02
1.7420E-02
1.7428E-02
9.9358E-03
2.4365E-03
2.4373E-03
2.4380E-03
2.4386&03
2.4390E-03
2.4387E-03
2.4378E-03
2.4364E-03
2.4340E-03
4.6566E-03
6.8706E-03
6.8532E-03
6.83I4E-03
6.806 1E-03
6.7735E-03
6.7327E-03
6.6836E-03
6.628 1E-03
6.5674E-Q3
8.0564E-03
9.4956E-03
9.3626E-03
9.2185E-03
9-0626E-03
8.8949E-03
8.7I22E-03
8.5152E-03
8.3081E-03
8.0875E-03
7.85IOE-03
7.6033E-03
7.341 9E-03
7.0639E-03
6.7757E-03
6.473 1E-03
|i;
56
57
58
59
60
6V
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
HO
:.-';; General. •
5.2592E-03
5.0060E-03
4.7467E-03
4.4848E-03
4.2256E-03
3.9627E-03
3.6972E-03
3.4376E-03
3.1837E-03
2.9352E-03
2.6991E-03
2.4693E-03
2.2409E-03
2.0272E-03
1.8290E-03
I.6419E-03
1.4664E-03
1.2999E-03
1.1452E-03
1.0036E-03
8.6877E-04
7.4572E-04
6.3645E-04
5.3912E-04
4.5756E-04
3.8590E-04
3.2069E-04
2.6547E-04
2.1968E-04
1.7825E-04
1.4369E-04
1.1878E-04
9.8023E-05
8.0836E-05
6.6730E-05
5.5320E-05
4.6257E-05
3.9190E-05
3.3807E-05
2.9879E-05
2.7271E-05
2.5913E-05
2.5875E-05
2.7380E-05
3.0846E-05
3.5970E-05
4.1835E-05
4.8323E-05
5.5123E-05
6.1574E-05
6.6546E-05
6.7347E-05
6.2940E-05
4.2529E-05
1.0029E-05
.' '. Male's •"•:, :'i ;
4.3294E-Q3
4.1345E-03
3.9309E-03
3.7199E-03
3.5058E-03
3.2876E-03
3.0626E-03
2.8380E-03
2.6188E-03
2.4018E-03
2.1888E-03
1.9818E-03
1.7790E-03
1.5855E-03
1.4058E-03
1.2384E-03
1.0817E-03
9.3493E-04
7.9949E-04
6.7712E-04
5.6701E-04
4.6809E-04
3.8249E-04
3.1120E-04
2.5264E-04
2.0502E-04
1.6548E-04
1.3369E-04
1.0790E-04
8.4830E-05
6.6958E-05
5.4737E-05
4.4718E-05
3.6549E-05
2.9929E-05
2.4617E-05
2.0416E-05
1.7156E-05
1.4693E-05
1.2905E-05
1.1712E-05
1.1065E-05
1.1004E-05
1.1646E-05
1.3217E-05
I.5598E-05
1.8345E-05
2.1407E-05
2.4650E-05
2.7777E-05
3.0274E-05
3.0884E-05
2.9113E-05
1.9971E-05
4.7112E-06
^MM.M
6.1584E-03
5.8435E-03
5.5253E-03
5.2094E-03
4.901 6E-03
4.5910E-03
4.2820E-03
3.9841E-03
3.6925E-03
3.4093E-03
3.1463E-03
2.890IE-03
2.6330E-03
2.3955E-03
2.1751E-03
1.9648E-03
1.7675E-03
1.5786E-03
1.4025E-03
I.2398E-03
1.0809E-03
9.3493E-04
8.0395E-04
6.8436E-04
5.8357E-04
4.9306E-04
4.0912E-04
3.3753E-04
2.7826E-04
2.2509E-04
1.8047E-04
L4807E-04
1.2127E-04
9.9224E-05
8.V264E-05
6.6850E-05
5.5488E-05
4.6671E-05
3.9962E-05
3.5051E-05
3.1749E-05
2.9952E-05
2.9701E-05
3.1211E-05
3.4913E-05
4.0429E-05
4.6719E-05
5.3646E-05
6.0862E-05
6.7643E-05
7.2766E-05
7.3326E-05
6.8250E-05
4.5924E-05
1.0797E-05
B-9
-------
Table B-7. Attributable Mortality Risk Coefficients: Bone (DDREF=2)(SV1)
Age
0
1
2
3
4
5
6
7
8
9
10
II
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
General
1.1344E-04
1.1480E-04
1.1482E-04
1.1480E-04
1.1476E-04
1.1470E-04
1.1464E-04
1.1456E-04
1.1448E-04
I.1439E-04
I.1428E-04
1.1417E-04
1.1404E-04
1.1392E-04
1.1380E-04
1.1370E-04
1.I360E-04
1.1351E-04
1.1343E-04
1.I335E-04
L1326E-04
1.1317E-04
1.1307E-04
1.1296E-04
1.1284E-04
1.1269E-04
1.1252E-04
I.I232E-04
1.1209E-04
1.1182E-04
1.H53E-04
1.1120E-04
1.1083E-04
1.I041E-04
I.0996E-04
1.0946E-04
1.0892E-04
1.0833E-04
1.0769E-04
1.0699E-04
1.0624E-04
1.0543E-04
1.0457E-04
1.0365E-04
I.0266E-04
1.0161E-04
1.0049E-04
9.9303E-05
9.8042E-05
9.6713E-05
9.5312E-05
9.3837E-05
9.2283E-05
9.0646E-05
8.8926E-05
8.7122E-05
Males
1.I305E-04
1.I452E-04
1.1451E-04
1.1446E-04
1.1439E-04
1.1430E-04
I.1419E-04
1.1408E-04
1.1395E-04
1.1381E-04
1.1365E-04
1.1348E-04
1.1330E-04
1.1312E-04
1.I295E-04
1.1280E-04
1.1266E-04
1.1255E-04
I.I244E-04
1.1233E-04
1.1223E-04
1.1213E-04
1.1203E-04
1.1191E-04
1.1178E-04
1.1162E-04
1.1142E-04
1.1118E-04
1.1091E-04
1.1059E-04
1.1023E-04
1.0982E-04
I.0936E-04
1.0884E-04
1.0827E-04
1.0764E-04
I.0695E-04
1.0619E-04
1.0537E-04
I.0448E-04
1.0352E-04
1.0248E-04
1.0I37E-04
1.0019E-04
9.8930E-05
9.7587E-05
9.6160E-05
9.4649E-05
9.3059E-05
9.1391E-05
8.9647E-05
8.7824E-05
8.5920E-05
8.3936E-05
8.1876E-05
7.9744E-05
Females
1.1385E-04
1.1509E-04
1.1513E-04
I.1515E-04
1.1514E-04
1.1513E-04
I.1510E-04
1.1507E-04
1.1504E-04
1.1499E-04
1.1494E-04
1.1489E-04
1.1483E-04
1.1476E-04
1.1470E-04
1.1464E-04
1.1458E-04
1.1452E-04
1.1447E-04
1.1440E-04
1.1433E-04
1.1425E-04
1.1415E-04
1.1405E-04
1.1393E-04
1.1380E-Q4
1.1365E-04
1.I349E-04
1.1330E-04
1.1309E-04
1.1286E-04
1.1261E-04
1.1233E-04
1.1202E-04
1.1169E-04
1.1133E-04
1.1093E-04
1.1050E-04
1.1004E-04
1.0954E-04
1.0901E-04
1.0843E-04
1.0781E-04
1.07I5E-04
1.0644E-04
1.0567E-04
1.0485E-04
1.0397E-04
1.0303E-04
1.0202E-04
1.0095E-04
9.9796E-05
9.8563E-05
9.7240E-05
9.5821E-05
9.4299E-05
Age
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
10!
102
103
104
105
106
107
108
109
110
General
8.5230E-05
8.3247E-05
8.1176E-05
7.9021 E-05
7.6788E-05
7.4485E-05
7.2121E-05
6.9702E-05
6.7234E-05
6.472 IE-OS
6.2168E-05
5.9583E-05
5.6979E-05
5.4372E-05
5.1779E-05
4.92I4E-05
4.6684E-05
4.4193E-05
4.1743E-05
3.9335E-05
3.6971E-05
3.4660E-05
3.241 3E-05
3.0241E-05
2.8156E-05
2.6I69E-05
2.4285E-05
2.2503E-05
2.0817E-05
1.9223E-05
1.7727E-05
1.6336E-05
1.5034E-05
1.3807E-05
I.2649E-05
1.1576E-05
1.0604E-05
9.7364E-06
8.9704E-06
8.30I8E-06
7.7265E-06
7.2308E-06
6.8091E-06
6.4594E-06
6.1829E-06
5.9866E-06
5.8837E-06
5.9000E-06
6.0779E-06
6.4870E-06
7.239SE-06
8.5149E-06
1.0626E-05
1.3582E-05
1.72 11 E-05
Males •
7.7540E-05
7.5264E-05
7.2924E-05
7.0528E-05
6.8087E«5
6.5615E-05
6.31I8E-05
6.061 IE-OS
5.8100E-05
5.5592E-05
5.3089E-05
5.0600E-05
4.8133E-05
4.5702E-05
4.3322E-05
4.I001E-05
3.8748E-05
3.6558E-05
3.4427E-05
3.2350E-05
3. 0331 E-05
2.8377E-05
2.6492E-05
2.4678E-05
2.2942E-05
2.1293E-05
1.9741E-05
1.8284E-05
1.6914E-05
1.5621E-05
I.4410E-05
1.3285E-05
1.2236E-05
1.1248E-O5
1.0314E-05
9.4371E-06
8.6319E-06
7.9119E-06
7.2871E-06
6.7554E-06
6.3063E-06
5.9188E-06
5.5876E-06
5.3098E-06
5.0860E-06
4.0203E-06
4.8227E-06
4.8I24E-06
4.9237E-06
5.2I33E-06
5.7766E-06
6.7694E-06
8.4725E-06
1.0900E-05
1.3887E-05
Females
9.2668E-05
9.091 9E-05
8.905 IE-OS
8.7065E-05
8.4960E-05
8.2742E-05
8.0416E-05
7.7988E-O5
7.5460E-05
7.2837E-05
7.0125E-05
6.7337E-05
6.4488E-05
6.1600E-05
5.8694E-05
5.5788E-05
5.2894E-05
5.0024E-05
4.7187E-05
4.4391E-05
4.1639E-05
3.8943E-05
3.6319E-05
3.3786E-05
3.1363E-05
2.9058E-05
2.6874E-05
2.48IOE-05
2.2862E-05
2.1029E-05
1.93I7E-05
1.7732E-O5
1.6255E-05
1.4869E-05
1.3572E-05
I.2379E-05
1.1308E-05
1.0356E-05
9.5124E-06
8.7729E-06
8.1353E-06
7.5877E-06
7.1233E-06
6.7393E-06
6.4360E-06
6.2200E-06
6.1043E-06
6.1150E-06
6.2953E-06
6.7I57E-06
7.4908E-06
8.8011E-06
I.0964E-05
1.3985E-05
I.7692E-05
B-10
-------
Table B-8. Attributable Mortality Risk Coefficients: Skin (DDREF=2)(Sv1)
3-
0
i
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
:; general
2.I462E-04
2.1402E-04
2.I087E-04
2.0766E-04
2.044 1E-04
2.0115E-04
1.9787E-04
1.9460E-04
I.9131E-04
1.8802E-04
1.8472E-04
1.8142E-04
1.7813E-04
1.7484E-04
1.7158E-04
1.6835E-04
1.6515E-04
1.6197E-04
1.5881E-04
1.5566E-04
1.5252E-04
1.4938E-04
1.4626E-04
1.4314E-04
1.4002E-04
1.3690E-04
1.3376E-04
1.3063E-04
1.2749E-04
I.2435E-04
1.2121E-04
1.I807E-04
1.1493E-04
1.1179E-04
1.0866E-04
1.0554E-04
1.0243E-04
9.9335E-05
9.6255E-05
9.3192E-05
9.0148E-05
8.7125E-05
8.4126E-05
8.I154E-05
7.8210E-05
7.5294E-05
7.2408E-05
6.9555E-05
6.6738E-05
6.3959E-05
6.I220E-05
5.8520E-05
5.5861 E-05
5.3244E-05
5. 0671 E-05
4.8145E-05
•. Male's ''-1 :.:.':
2.0238E-04
2.0190E-04
1.9875E-04
1.9555E-04
1.9232E-04
I.8906E-04
1.8580E-04
1.8253E-04
1.7926E-04
1.7598E-04
1.7269E-04
1.6940E-04
1.6612E-04
1.6285E-04
1.5962E-04
1.5643E-04
1.5328E-04
1.5016E-04
1.4707E-04
1.4399E-04
1.4094E-04
1.3790E-04
1.3487E-04
1.3185E-04
1.2883E-04
1.2579E-04
1.2275E-04
1.1969E-04
1.1663E-04
1.1356E-04
1.1049E-04
1.0742E-04
1.0434E-04
I.0127E-04
9.8197E-05
9.5136E-05
9.2086E-05
8.9051E-05
8.6031E-05
8. 3031 E-05
8.0051 E-05
7.7096E-05
7.4169E-05
7.I272E-05
6.8409E-05
6.5578E-05
6.2784E-05
6.0029E-05
5.7317E-05
5.4650E-05
5.2032E-05
4.9463E-05
4.6941 E-05
4.4471 E-05
4.2054E-05
3.%94E-05
-iiil^^^
2.2749E-04
2.2672E-04
2.2356E-04
2.2034E-04
2.1708E-04
2.1381E-04
2.1052E-04
2.0723E-04
2.0393E-04
2.0063E-04
1.9732E-04
1.9401E-04
1.9070E-04
1.8740E-04
1.8411E-04
1.8083E-04
1.7756E-04
1.7431E-04
1.7106E-04
1.6782E-04
1.6458E-04
1.6133E-04
1.58IOE-04
1.5486E-04
1.5162E-04
1.4838E-04
I.4515E-04
1.4191E-04
1.3868E-04
1.3545E-04
1.3222E-04
I.2900E-04
1.2578E-04
1.2257E-04
1.1937E-04
1.16I8E-04
1.1299E-04
1.0983E-04
1.0667E-04
1.0353E-04
1.0041E-04
9.7303E-05
9.4217E-05
9.1152E-05
8.8108E-05
8.5087E-05
8.2088E-05
7.9113E-05
7.6165E-05
7.3247E-05
7.0356E-05
6.7496E-05
6.4666E-05
6.1866E-05
5.9099E-05
5.6366E-05
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
4.5666E-05
4.3234E-05
4.0851 E-05
3.8520E-05
3.6244E-05
3.4026E-05
3.1868E-05
2.9772E-05
2.7737E-05
2.5764E-05
2.3852E-05
2.2002E-05
2.0216E-05
1.8498E-05
1.6853E-05
1.5284E-05
1.3793E-05
1.2383E-05
1.1054E-05
9.8082E-06
8.6463E-06
7.5716E-06
6.5860E-06
5.690 1E-06
4.8823E-06
4.1601E-06
3.5204E-06
2.9593E-06
2.47I9E-06
2.0527E-06
1.6971E-06
1.3996E-06
1.1524E-06
9.4829E-07
7.8116E-07
6.4626E-07
5.3932E-07
4.5603E-07
3.9264E-07
3.4637E-07
3.1555E-07
2.993 1E-07
2.9839E-07
3.1529E-07
3.5481E-07
4.1336E-07
4.8033E-07
5.5434E-07
6.3179E-07
7.0514E-07
7.6147E-07
7.7005E-07
7.1916E-07
4.8569E-07
1.1444E-07
3.7391E-05
3.5146E-05
3.2961 E-05
3.0838E-05
2.8781 E-05
2.6793E-05
2.4876E-05
2.3032E-05
2.1262E-05
1.9564E-05
1.7938E-05
1.6384E-05
I.4903E-05
1.3498E-05
1.2170E-05
1.0921E-05
9.7517E-06
8.6618E-06
7.6500E-06
6.7149E-06
5.8562E-06
5.0743E-06
4.3683E-06
3.7355E-06
3.1726E-06
2.6761 E-06
2.2420E-06
1.8660E-06
1.5430E-06
1.2686E-06
1.0388E-06
8.4921E-07
6.9378E-07
5.6704E-07
4.6433E-07
3.8192E-07
3.I675E-07
2.6617E-07
2.2795E-07
2.0022E-07
I.8170E-07
1.7166E-07
1.7072E-07
1.8068E-07
2.0505E-07
2.4200E-07
2.8461E-07
3.3212E-07
3.8244E-07
4.3095E-07
4.6969E-07
4.791 5E-07
4.5168E-07
3.0983E-07
7.3091E-08
5.3668E-05
5.1006E-05
4.8381 E-05
4.5795E-05
4.3253E-05
4.0757E-05
3.8310E-05
3.5914E-05
3.3569E-05
3.1276E-05
2.9035E-05
2.6850E-05
2.4725E-05
2.2667E-05
2.0682E-05
1.8777E-05
1.6956E-05
1.5225E-05
1.3587E-05
1.2047E-05
1.0608E-05
9.2735E-06
8.0487E-06
6.9356E-06
5.9335E-06
5.0393E-06
4.2487E-06
3.5572E-06
2.9586E-06
2.4459E-06
2.0126E-06
1.6514E-06
1.3524E-06
1.1066E-06
9.0628E-07
7.4553E-07
6.1882E-07
5.2049E-07
4.4567E-07
3.9090E-07
3.5408E-07
3.3403E-07
3.3124E-07
3.4807E-07
3.8937E-07
4.5087E-07
5.2I02E-07
5.9828E-07
6.7875E-07
7.5438E-07
8.1151E-07
8.I775E-07
7.6115E-07
5.1215E-07
1.2042E-07
B-11
-------
Table B-9. Attributable Mortality Risk Coefficients: Breast (DDREF=1)
-------
Table B-10. Attributable Mortality Risk Coefficients: Ovary (DDREF=2)(Sv1)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
3.1184E-03
3.1581E-03
3.1608E-03
3.1627E-03
3.1640E-03
3.1650E-03
3.1657E-03
3.1660E-03
3.1662E-03
3.1664E-03
2.8319E-03
2.4973E-03
2.497 1E-03
2.4969E-03
2.497 1E-03
2.4976E-03
2.4984E-03
2.4998E-03
2.5016E-03
2.5032E-03
2.3172E-03
2.1311E-03
2.1327E-03
2.1342E-03
2.1353E-03
2.I358E-03
2.1359E-03
2.1357E-03
2.1348E-03
2.1329E-03
1.9912E-03
1.8489E-03
1.8443E-03
I.8378E-03
1.8307E-03
1.8225E-03
1.8120E-03
1.8010E-03
1.7881E-03
1.7720E-03
1.6050E-03
I.4386E-03
1.4192E-03
1.3985E-03
1.3772E-03
1.3550E-03
1.3315E-03
1.3075E-03
1.2822E-03
1.2541E-03
1.2254E-03
1.I960E-03
1.1632E-03
1.1289E-03
I.0947E-03
1.0590E-03
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
6.3958E-03
6.4680E-03
6.473 1E-03
6.4764E-03
6.4787E-03
6.4802E-03
6.4811E-03
6.4814E-03
6.48I4E-03
6.4816E-03
5.7966E-03
5.1116E-03
5.1111E-03
5.1106E-03
5.I104E-03
5.1103E-03
5.1105E-03
5.1115E-03
5.1130E-03
5.II37E-03
4.7311E-03
4.3484E-03
4.3486E-03
4.3487E-03
4.3476E-03
4.3456E-03
4.3428E-03
4.3396E-03
4.3349E-03
4.3285E-03
4.0384E-03
3.7477E-03
3.736IE-03
3.7211E-03
3.7046E-03
3.6858E-03
3.6626E-03
3.6383E-03
3.6101E-03
3.5753E-03
3.2361E-03
2.8987E-03
2.8574E-03
2.8133E-03
2.7680E-03
2.7207E-03
2.6707E-03
2.6194E-03
2.5653E-03
2.5055E-03
2.4441E-03
2.3811E-03
2.3113E-03
2.2384E-03
2.I654E-03
2.0892E-03
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
1.0220E-03
9.8438E-04
9.4664E-04
9.0924E-04
8.6993E-04
8.2879E-04
7.8799E-04
7.4820E-04
7.0873E-04
6.6724E-04
6.2454E-04
5.8219E-04
5.3901E-04
4.9832E-04
4.5996E-04
4.I995E-04
3.7951E-Q4
3.3998E-04
3.0069E-04
2.6237E-04
2.2820E-04
1.9637E-04
1.6401E-04
1.3537E-04
1.1090E-04
8.8793E-05
7.1377E-05
5.9322E-05
5.0242E-05
4.2130E-05
3.5044E-05
2.9184E-05
2.4256E-05
2.0I39E-05
1.6734E-05
1.3960E-05
1.1744E-05
1.0008E-05
8.6827E-06
7.7168E-06
7.0815E-06
6.7636E-06
6.7858E-06
7.2094E-06
8.I485E-06
9.5273E-06
1.1110E-05
1.2865E-05
1.4712E-05
1.6472E-05
1.7842E-05
1.8095E-05
1.6944E-05
1.1466E-05
2.7100E-06
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
O.OOOOE+00
2.0I04E-03
1.9304E-03
1.8501E-03
1.7704&03
1.6870E-03
I.6001E-03
I.514IE-03
1.4302E-03
1.3471E-03
1.2604E-03
1.1719E-03
I.0846E-03
9.9653E-04
9.1374E-04
8.3602E-04
7.561 5E-04
6.7650E-04
5.9961E-04
5.2442E-04
4.5229E-04
3.8863E-04
3.3020E-04
2.7218E-04
2.2163E-04
1.7909E-04
1.4140E-04
1.I204E-04
9.1764E-05
7.6569E-05
6.3255E-05
5.1837E-05
4.2533E-05
3.4833E-05
2.8501 E-05
2.3342E-05
1.9202E-05
1.5938E-05
1.3406E-05
1.1479E-05
1.0068E-05
9.1197E-06
8.6034E-06
8.5314E-06
8.9650E-06
1.0029E-05
1.1613E-05
1.3420E-05
1.5409E-05
I.7482E-05
1.9430E-05
2. 0901 E-05
2.1062E-05
1.9604E-05
1.3I91E-05
3.1014E-06
B-13
-------
Table B-11. Attributable Mortality Risk Coefficients: Bladder (DDREF=2)(SV1)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
3.0187E-03
3.0572E-03
3.0601E-03
3.0620E-03
3.0635E-03
3.0647E-03
3.0659E-03
3.0669E-03
3.0678E-03
3.0686RO3
2.9815E-03
2.8943E-03
2.8949E-03
2.8956E-03
2.8966E-03
2.8980E-03
2.9000E-03
2.9024E-03
2.905 1E-03
2.9081E-03
2.8680E-03
2.8280E-03
2.83I4E-03
2.8350E-03
2.8385E-03
2.8421E-03
2.8455E-03
2.8489E-03
2.8520E-03
2.8548E-03
2.8795E-03
2.9043E-03
2.9065E-03
2.9083E-03
2.9105E-03
2.9128E-03
2.9144E-03
2.9155E-03
2.9163E-03
2.9164E-03
2.7771E-03
2.6382E-03
2.6373E-03
2.6350E-03
2.6317E-03
2.6284E-03
2.6252E-03
2.6204E-03
2.6122E-03
2.6032E-03
2.5935E-03
2.5797E-03
2.5629E-03
2.5446E-03
2.5244E-03
2.5006E-03
4.2171E-03
4.2766E-03
4.2809E-03
4.2840E-03
4.2864E-03
4.2883E-O3
4.2902E-03
4.2919E-03
4.2933E-03
4.2947E-03
4.1932E-03
4.0916E-03
4.0924E-03
4.0935E-03
4.0954E-03
4.0982E-03
4.1021E-03
4.1069E-03
4.1126E-03
4.1188E-03
3.9703E-03
3.8218E-03
3.8289E-03
3.8363E-03
3.8439E-03
3.8514E-03
3.8588E-03
3.8660E-03
3.8727E-03
3.8789E-03
3.8499E-03
3.8206E-03
3.8256E-03
3.8300E-03
3.8352E-03
3.84IOE-03
3.8452E-03
3.8485E-03
3.8518E-03
3.8542E-03
3.6898E-03
3.5248E-03
3.5251E-03
3.5240E-03
3.520SE-03
3.5174E-03
3.5143E-03
3.5096E-03
3.5003E-03
3.4893E-03
3.4783E-03
3.4621 E-03
3.4406E-03
3.4175E-03
3.3940E-03
3.3643E-03
1.7593E-03
1.7792E-03
1.7807E-03
1.7817E-03
1.7824&O3
1.7830E-03
I.7836&03
1.7841E-03
1.7845E-03
1.7849E43
1.7130E-03
1.6410E-03
1.6413E-03
1.6416E-03
1.6420E-03
1.6425E-03
1.643IE-03
1.6439E-03
1.6447E-03
1.6455E-03
I.7197E-03
1.7940E-03
1.7950E-03
1.7960E-03
1.7969E-03
1.7977E-03
1.7985E-03
I.7993E-03
1.8001E-03
1.8007E-03
1.8819E-03
1.9633E-03
1.9636E-03
1.9639E-03
1.9641E-03
1.9638E-03
1.9638E-03
1.9637E-03
1.9632E-03
1.9620E-03
1.8496E-03
1.7385E-03
1.7376E-03
1.7356E-03
1.7337E-03
1.7323E-03
1.7311E-03
1.7284E-03
1.7236E-03
1.7190E-03
1.7136E-03
1.7053E-03
1.6967E-03
1.6868E-03
1.6739E-03
1.6603E-03
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
2.471 1E-03
2.4384E-03
2.4042E-03
2.3647E-03
2.3196E-03
.2.26S8E-03
2.2139E-O3
2.1565E-03
2.0929E-03
2.0236E-03
1.9507E-03
1.8727E-03
1.7905E-03
1.7062E-03
1.6176E-03
1.5235E-03
1.4249E-03
1.3242E-03
1.2215E-03
1.1126E-03
1.0048E-03
9.0397E-04
8.0406E-04
7.0664E-04
6.1850E-04
5.4140E-04
4.7088E-04
4.0685E-04
3.5016E-04
3.0281E-04
2.5767E-04
2.1051E-04
1.7174E-04
1.4005E-04
1.1436E-04
9.3797E-05
7.7615E-05
6.508 1E-05
5.5572E-05
4.8619E-05
4.3935E-05
4.1346E-05
4.0917E-05
4.2958E-05
4.8094E-05
5.5790E-05
6.4554E-05
7.4192E-05
8.4217E-05
9.3626E-05
1.0073E-04
1.0149E-04
9.4469E-05
6.3645E-05
1.4938E-05
3.3240E-03
3.2798E-03
3.2353E-03
3.1835E-03
3.1218E-03
3.0481E-03
2.9688E-03
2.8872E-03
2.7938E-03
2.6932E-03
2.5925E-03
2.4861E-03
2.3702E-03
2.2510E-03
2.1289E-03
1.9964E-03
I.8605E-03
1.7332E-03
1.6001E-03
1.4458E-03
1.2932E-03
I.1524E-03
1.0128E-03
8.8480E-04
7.7423E-04
6.8054E-04
5.9354E-04
5.0596E-04
4.2700E-04
3.6427E-04
3.0847E-04
2.5216E-04
2.0601E-04
1.6838E-04
1.3788E-04
1.1341E-04
9.4054E-05
7.9035E-05
6.7688E-05
5.9453E-05
5.3955E-05
5.0974E-05
5.0694E-05
5.3651E-05
6.0888E-05
7.1859E-05
8.4512E-05
9.8618E-05
1.1356E-04
1.2797E-04
1.3947E-04
1.4228E-04
1.3412E-04
9.2001&05
2.1704E-05
1.6461E-03
1.6298E-03
1.6111E-03
1.5893E-03
1.5661&03
1.5436E-03
1.5182E-03
1.4904E-03
1.4616E-03
1.4283E-03
1.3882E-03
1.3433'E-OS
1.2985E-03
1.2520E-O3
1.1996E-03
1.1449E-03
1.0840E-03
1.0119E-03
9.3983EW
8.7147E-04
8.0207E-04
7.3468E-04
6.6637E-04
5.9310E-04
5.2275E-04
4.589JE-04
4.0100E-04
3.5266E-04
3.0989E-04
2.7200E-04
2.3333E-04
1.9145E-04
1.5679E-04
1.2829E-04
1.0507E-04
8.6434E-05
7.1743E-05
6.0343E-05
5.1670E-05
4.5319E-05
4.1051E-05
3.8726E-05
3.S402E-05
4.0354E-05
4.5141E-05
5.2272E-05
6.0405E-05
6.9362E-05
7.8691E-05
8.7460E-05
9.4083E-05
9.4807E-05
8.8244E-05
5.9377E-05
1.3960E-05
B-14
-------
Table B-12. Attributable Mortality Risk Coefficients: Kidney (DDREF=2)(Sv1)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
6.7552E-04
6.8402E-04
6.8455E-04
6.S489E-04
6.8512E-04
6.8528E-04
6.8542E-W
6.8551E-04
6.8562E-04
6.857IE-04
6.8574E-04
6.8570E-04
6.8569E-04
6.8569E-04
6.8571E-04
6.8583E-04
6.8609E-04
6.8644E-04
6.8683E-04
6.8730E-04
6.8783E-04
6.8835E-04
6.8882E-04
6.8921E-04
6.8952E-04
6.8974E-04
6.8992E-04
6.90IOE-04
6.9002E-04
6.8960E-04
6.8907E-04
6.8843E-04
6.8747E-04
6.8608E-04
6.8413E-04
6.8190E-04
6.7923E-04
6.7602E-04
6.7249E-04
6.6804E-04
6.6270E-04
6.5724E-04
6.5I04E-04
6.4394E-04
6.3610E-04
6.2736E-04
6.1820E-04
6.0833E-04
5.9770E-04
5.8625E-04
5.7294E-04
5.5879E-04
5.4523E-04
5.3112E-04
5.I602E-04
5.0032E-04
8.2322E-04
8.3475E-04
8.3550E-04
8.3605E-04
8.3643E-04
8.3667E-04
8.3688EXM
8.3710E-04
8.3732E-04
8.3753E-04
8.3763E-04
8.3764E-04
8.3766E-04
8.3769E4W
8.3783E-04
8.3819E-04
8.3879E-04
8.3951E-04
8.4033E-04
8.4129E-04
8.4238E-04
8.4357E-04
8.4475E-04
8.4594E-04
8.4704E-04
8.4790E-04
8.4863E-04
8.4929E-04
8.4976E-04
8.498 1E-04
8.4954E-04
8.4896E-04
8.4791&04
8.4622E-04
8.4370E-04
8.4077E-04
8.3740E-04
8.3342E-04
S.2888E-04
8.2289E-04
8.1543E-04
8.077IE-04
7.9884E-04
7.8896E-04
7.7856E-04
7.6683E-04
7.5450E-04
7.4I31E-04
7.271 3E-04
7.1174E-04
6.9347E-04
6.7454E-04
6.5695E-04
6.3784E-04
6.1674E-04
5.9580E-04
5.2029E-04
5.2604E-04
5.2635E-04
5.2651E-04
5.2660E-04
5.267 1E-04
5.2678E-04
5.2678E-04
5.2677&O4
5.2675E-O4
5.2672E-04
5.2665E-04
5.2660E-04
5.2658E-04
5.2652E-04
5.2644E-04
5.2645E-04
S.2652&44
5.2659E-04
5.2671E-04
5.2683E-04
5.2685E-04
5.2680E-04
5.2659E-04
5.2632E-04
5.2609E-04
5.2593E-04
5.2582E-04
5.2539E-04
5.2468E-04
5.2408E-04
5.2357E-04
5.2290E-04
5.2198E-04
5.2080E-04
5.1947E-04
5.1769E-04
5.1545E-04
5.1314E-04
5.1045&O4
5.0748E-04
5.0452E-04
5.0126E-04
4.9723E-04
4.9223E-04
4.8680E-04
4.8113E-04
4.7490E-04
4.6818E-04
4.6104E-04
4.5307E-04
4.4409E-04
4.3496E-04
4.2624E4W
4.1751E-04
4.0744E-04
||g^
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
4.8417E-04
4.6750E-04
4.4997E-04
4.3222E-04
4.1426E-04
3.9591E-04
3.7634E-04
3.554SE-04
3.3509E-04
3.1507E-04
2.9524E-04
2.7457E-04
2.5361E-04
2.3357E-04
2.1339E-04
1.9441E-04
1.7727E-04
1.5947E-04
1.4005E-04
1.2151E-04
1.0540E-04
9.0927E-05
7.7733E-05
6.5296E-05
5.4699E-05
4.6882E-OS
3.9825E-05
3.2761E-05
2.5715E-05
1.8924E-05
1.4273E-05
I.1608E-05
9.4284E-06
7.655 IE-06
6.2236E-06
5.0826E-06
4.1877E-06
3.4964E-06
2.9726E-06
2.5895E-06
2.3298E-06
2.IS32E-06
2.1519E-06
2.2512E-06
2.5131E-06
2.9083E-06
3.3571E-06
3.8492E-06
4.3592E-06
4.8353E-06
5.1907E-06
5.2193E-06
4.8485E-06
3.2618E-06
7.6377E-07
5.7529E-04
5.5435E-04
5.3260E-04
5.I009E-04
4.8628E-04
4.6278E-04
4.3889E-04
4.1295E-04
3.8787E-04
3.6387E-04
3.3925E-04
3.1358E-04
2.8805E-04
2.6351E-04
2.3913E-04
2.1751E-04
2.0000E-04
1.8027E-04
1.5641E-04
L3444E-04
1.1565E-04
9.8634E-05
8.3089E-05
6.9749E-05
5.8957E-05
5.0472E-05
4.3445E-05
3.5340E-05
2.8499E-05
2.4726E-05
2.I021E-05
1.7184E-05
1.4039E-05
1.1474E-05
9.3960E-06
7.7283E-06
6.4096E-06
5.3861E-06
4.6I28E-06
4.0516E-06
3.6769E-06
3.4737E-06
3.4546E-06
3.6562E-06
4.1494E-06
4.8970E-06
5.7593E-06
6.7206E-06
7.7388E-06
8.7206E-06
9.5045E-06
9.6960E-06
9.1400E-06
6.2697E-06
1.4791E-06
3.9604E-04
3.8404E-04
3.7II1E-04
3.5848E-04
3.4661E-04
3.3369E-04
3.1869E-04
3.0310E-04
2.8756E-04
2.7I68E-04
2.5667E-04
2.4091 E-04
2.2438E-04
2.0861E-04
1.9235E-04
1.7593E-04
1.5948E-04
1.4359E-04
I.2788E-04
1.I216E-04
9.8193E-05
8.5675E-05
7.4200E-05
6.2458E-05
5.208 1E-05
4.4755E-05
3.7762E-05
3.I351E-05
2.4256E-05
1.6015E-05
LI039E-05
9.0574E-06
7.4178E-06
6.0693E-06
4.9707E-06
4.0891E-06
3.3941E-06
2.8548E-06
2.4444E-06
2.1440E-06
1.9420E-06
1.8321E-06
1.8168E-06
I.9091E-06
2.1356E-06
2.4729E-06
2.8577E-06
3.2814E-06
3.7228E-06
4.1376E-06
4.4510E-06
4.4852E-06
4.I747E-06
2.8091E-06
6.6045E-07
B-15
-------
Table B-13. Attributable Mortality Risk Coefficients: Thyroid (DDREF=2)(Sv'1)
Age
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
General
8.6903E-04
8.6775E-04
8.5617E-04
8.4435E-04
8.3239E-04
8.2033E-04
8.0825E-04
7.9613E-04
7.8398E-04
7.7180E-04
7.5958E-04
7.4734E-04
7.3511E-04
7.2292E-04
7.1082E-04
6.9883E-04
6.8695E-04
6.7517E-04
6.6346E-04
6.5180E-04
4.801 5E-04
3.1431E-04
3.0854E-04
3.0277E-04
2.9700E-04
2.9122E-04
2.8542E-04
2.796 1 E-04
2.7379E-04
2.6796E-04
2.6213E-04
2.5630E-04
2.5046E-04
2.4462E-04
2.3879E-04
2.3297E-04
2.2716E-04
2.2138E-04
2.1562E-04
2.0988E-04
2.0417E-04
1.9849E-04
I.9284E-04
1.8724E-04
1.8I68E-04
1.7617E-04
1.7070E-04
1.6528E-04
1.599IE-Q4
1.5461E-04
1.4937E-04
1.4420E-04
1.3908E-04
1.3402E-04
1.2903E-04
1.2411E-04
Males
5.4325E-04
5.4262E-04
5.3485E-04
5.2692E-04
5.1891E-04
5.I083E-04
5.0273E-04
4.9461E-04
4.8646E-04
4.7829E-04
4.7010E-04
4.6188E-04
4.5367E-04
4.4550E-04
4.3742E-04
4.2946E-04
4.2159E-04
4.1382E-04
4.0612E-04
3.9848E-04
2.9317E-04
1.9168E-04
1.8792E-04
1.8417E-04
1.8042E-04
1.7666E-04
1.7288E-04
1.6909E-04
1.6528E-04
1.6147E-Q4
1.5765E-04
1.5382E-04
1.4998E-04
1.4615E-04
1.4231E-04
1.3848E-04
1.3466E-04
1.3086E-04
1.2706E-04
1.2329E-04
1.1954E-04
1.1581E-04
I.1210E-04
1.0843E-04
1.0480E-04
1.0119E-04
9.7626E-05
9.4099E-05
9.0618E-05
8.7187E-05
8.3807E-05
8.0479E-05
7.7198E-05
7.3969E-05
7.0793E-05
6.7675E-05
Females
1.2114E-03
1.2085E-03
1.I929E-03
1.1769E-03
1.1608E-03
1.1445E-03
1.1282E-03
1.1119E-03
1.0955E-03
1.0791E-03
1.0626E-03
1.0462E-03
1.0297E-03
1.0133E-03
9.9693E-04
9.8062E-04
9.6439E-04
9.4822E-04
9.3210E-04
9:1599E-04
6.7493E-04
4.419 1E-04
4.3387E-04
4.2583E-04
4.1778E-04
4.0974E-04
4.0170E-04
3.9366E-04
3.8562E-04
3.7759E-04
3.6956E-04
3.6154E-04
3.5352E-04
3.4552E-04
3.3754E-04
3.2957E-04
3.2163E-04
3.1372E-04
3.0584E-04
2.9799E-04
2.9018E-04
2.8240E-04
2.7466E-04
2.6697E-04
2.5933E-04
2.5173E-04
2.4419E-04
2.3669E-04
2.2926E-04
2.2189E-04
2.I458E-04
2.0734E-04
2.0016E-04
I.9304E-04
1.8599E-04
1.7901 E-04
Age
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
General
1.1925E-04
1.1446E-04
I.0974E-04
1.0509E-04
1.0053E-04
9.6044E-Q5
9.1649E-05
8.7340E-05
8.3114E-05
7.8967E-05
7.4895E-05
7.0900E-05
6.6985E-05
6.3159E-05
5.9427E-05
5.5792E-05
5.2255E-05
4.8810E-05
4.5454E-05
4.2187E-05
3.9013E-05
3.5944E-05
3.2994E-05
3.0175E-05
2.7499E-05
2.4976E-05
2.261 IE-OS
2.0406E-05
1.8353E-05
1.6443E-05
1.4677E-05
1.3060E-05
1.1584E-05
1.0241E-05
9.0288E-06
7.9528E-06
7.0I80E-06
6.2I73E-06
5.5387E-06
4.9698E-06
4.5008E-06
4.1189E-06
3.8187E-06
3.6001E-06
3.4690E-06
3.4402E-06
3.5404E-06
3.8I58E-06
4.3417E-06
5.2391E-06
6.5180E-06
8.0574E-06
9.8545E-06
1.1858E-05
1.3921E-05
Males
6.4613E-05
6.1607E-05
5.8661E-05
5.5777E-05
5.2960E-05
5.0213E-05
4.7539E-05
4.4938E-05
4.2409E-05
3.9952E-05
3.7564E-05
3.5246E-05
3.3001E-05
3.0832E-05
2.8744E-05
2.6737E-05
2.4812E-05
2.2964E-05
2.1188E-05
1.9482E-05
1.7848E-05
1.6292E-05
1.4817E-05
1.3427E-05
1.2124E-05
1.091 1 E-05
9.7912E-06
8.7627E-06
7.8188E-06
6.9517E-06
6.1584E-06
5.4384E-06
4.7858E-06
4.1968E-06
3.6700E-06
3.2064E-06
2.8064E-06
2.4678E-06
2.1864E-06
I.9553E-06
1.7672E-06
1.6134E-06
1.4909E-06
1.3990E-06
1.3395E-06
1.3176E-06
1.3440E-06
1.437IE-06
1.6288E-06
1.9712E-06
2.4706E-06
3.0735E-06
3.7787E-06
4.5670E-06
5.3818E-06
Females
1.7210E-04
1.6525E-04
1.5849E-04
1.5180E-04
1.4520E-04
1.3870E-04
1.3230E-04
1.2599E-04
1.1978E-04
I.1365E-04
1.076 1 E-04
1.0167E-04
9.5832E-05
9.0108E-05
8.4512E-05
7.9053E-05
7.3730E-05
6.8548E-05
6.3509E-05
5.8622E-05
5.3893E-05
4.9339E-05
4.4982E-05
4.0847E-05
3.6952E-05
3.3308E-05
2.9915E-05
2.6773E-05
2.3873E-05
2.1202E-05
1.8759E-05
1.6547E-05
1.4549E-05
1.2751E-05
1.H45E-05
9.7353E-06
8.5223E-06
7.4904E-06
6.6183E-06
5.8883E-06
5.2877E-06
4.8004E-06
4.4175E-06
4.1361E-06
3.9604E-06
3.9048E-06
3.9970E-06
4.2861E-06
4.8525E-06
5.8259E-06
7.2120E-06
8.8746E-06
1.0808E-05
1.2955E-05
1.5154E-05
B-16
-------
Table B-14. Attributable Mortality Risk Coefficients: Leukemia (DDREF=2)(SV1)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
7.3754E-03
7.5543E-03
7.5322E-03
7.3855E-03
7.2153E-03
7.0626E-03
7.0I77E-03
7.1385E-03
7.3594E-03
7.601 3E-03
5.1868E-03
2.6202E-03
2.6167E-03
2.6227E-03
2.6511E-03
2.7014E-03
2.7751E-03
2.8646E-03
2.9696E-03
3.0916E-03
3.6964E-03
4.3532E-03
4.5633E-03
4.8008E-03
5.0618E-03
5.3462E-03
5.6490E-03
5.9750E-03
6.3289E-03
6.7054E-03
5.8302E-03
4.8255E-03
5.1086E-03
5.4032E-03
5.7074E-03
6.0190E-03
6.3358E-03
6.6526E-03
6.9654E-03
7.2690E-03
6.6280E-03
5.8978E-03
6.0712E-03
6.2188E-03
6.3322E-03
6.4063E-03
6.4424E-03
6.4377E-03
6.39I2E-03
6.3043E-03
6.1779E-03
6.0157E-03
5.8232E-03
5.6061E-03
5.3723E-03
5.1271E-03
S.1542E-03
8.4145E-03
8.3847E-03
8.I778E-03
7.9377E-03
7.7290E-03
7.6516E-03
7.8131E-03
8.1275E-03
8.4690E-03
5.9127E-03
3.1642E-03
3.147SE-03
3.1365E-03
3.1571E-03
3.2116E-03
3.2891E-03
3.3746E-03
3.4739E-03
3.5988E-03
4.3470E-03
5.1567E-03
5.3834E-03
5.6382E-03
5.9257E-03
6.2469E-03
6.5925E-03
6.9702E-03
7.3862E-03
7.8327E-03
7.0990E-03
6.242 1E-03
6.6162E-03
7.0077E-03
7.4098E-03
7.8212E-03
8.2394E-03
8.6561E-03
9.0692E-03
9.4734E-03
7.9955E-03
6.3524E-03
6.5441E-03
6.7064E-03
6.8274E-03
6.9043E-03
6.9379E-03
6.9246E-03
6.S652E-03
6.7638E-03
6.6207E-03
6.4411E-03
6.2317E-03
5.9992E-03
5.7482E-03
5.4870E-03
6.5570E-03
6.6527E-03
6.6388E-03
6.5553E-03
6.4586E-03
6.3645E-03
6.3539E-G3
6.4320E-03
6.5550E-03
6.6927E-03
4.4268E-03
2.0507E-03
2.Q608E-03
2.0848E-03
2.1216E-03
2.1676E-03
2.2377E-03
2.3318E-03
2.4432E-03
2.5627E-03
3.0185E-03
3.5172E-03
3.7111E-03
3.9319E-03
4.1666E-03
4.4144E-03
4.6742E-03
4.948IE-03
5.2391E-03
5.5449&03
4.5257E-Q3
3.3706E-03
3.5620E-03
3.7591 E-03
3.9649E-03
4.1764E-03
4.3916E-03
4.6089E-03
4.8219E-03
5.0256E-03
5.2382E-03
5.4364E-03
5.5921E-03
5.7255E-03
5.8321E-03
5.9043E-03
5.9441E-03
5.9492&O3
5.9168E-03
5.8459E-03
5.7375E-03
5.5942E-03
5.4200E-03
5.2199E-03
5.0047E-03
4.7770E-03
Iffllf^^^^ j|
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
4.8792E-03
4.6392E-03
4.4160E-03
4.2050E-03
4.015 1E-03
3.8534E-03
3.7148E-03
3.6129E-03
3.5409E-03
3.4858E-03
3.4492E-03
3.4240E-03
3.4056E-03
3.3912E-03
3.3750E-03
3.3592E^)3
3.3431E-03
3.3267E-03
3.3023E-03
3.2643E-03
3.2061E-03
3.1402E-03
3.0562E-03
2.9359E-03
2.7990E-03
2.65QIE-Q3
2A992E-03
2.3569E-O3
2.2142E-03
2.0345E-O3
1.8439E-O3
1.6721E-03
1.5052E-03
1.3568E-03
1.2136E-03
1.0610E-03
9.2363E-04
8.1474E-04
7.3632E-04
6.6847E-04
6.1035E-04
5.6044E-04
5.1794E-04
4.8239E-04
4.5366E-04
4.3218E-04
4.1914E-04
4.1701E-04
4.3020E-04
4.6614E-04
5.3666E-04
6.5789E-04
8.4424E-04
1.0752E-03
1.3532E-03
5.2294E-03
4.9822E-03
4.7585E-03
4.5498E-03
4.361 4E-03
4.2072E-03
4.0835E-03
3.9962E-03
3.9342E-03
3.8905E-03
3.8656E-03
3.8495E-03
3.8361E-03
3.8265E-03
3.8151E-03
3.7933E-03
3.7634E-03
3.7467E-03
3.7334E-03
3.6959E-03
3.6374E-03
3.5836E-03
3.5172E-03
3.4043E-03
3.2576E-03
3.1027E-03
2.9421E-03
2.8013E-03
2.6630E-03
2.4899E-03
2.2964E-03
2.1020E-03
1.9844E-03
I.8779E-03
1.7790E-03
1.59I6E-03
1.4026E-03
1.3200E-03
1.2044E-03
1.1060E-03
1.0229E-03
9.5126E-04
8.8997E-04
8.3842E-04
7.9665E-04
7.6553E-O4
7.4731E-04
7.465 1E-04
7.7I43E-04
8.3628E-04
9.6439E-04
1.1888E-03
1.5405E-03
1.9791E-03
2.5103E-03
4.5404E-03
4.3096E-03
4.0892E-03
3.8784E-03
3.6899E-03
3.5242E-03
3.3750E-03
3.2636E-03
3.1867E-03
3.1259E-03
3.0842E-03
3.0569E-03
3.0401E-03
3.0284E-03
3.0152E-03
3.0117E-03
3.0143E-03
3.0059E-03
2.9816E-03
2.9519E-03
2.9030E-03
2.8379E-03
2.7522E-03
2.6374E-03
2.5171E-03
2.3820E-03
2.2469E-03
2.1139E-03
1.9790E-03
1.8061E-03
1.6270E-03
1.4755E-03
1.2962E-03
1.1404E-03
9.9031E-04
8.6179E-04
7.5253E-04
6.4320E-04
5.8559E-04
5.35I5E-04
4.9160E-04
4.5413E-04
4.2224E-04
3.9570E-04
3.7452E-04
3.5922E-04
3.5091E-04
3.5186E-04
3.6594E-04
3.9967E-04
4.6331E-04
5.7084E-04
7.3492E-04
9.3915E-04
1.1860E-03
B-17
-------
Table B-15. Attributable Mortality Risk Coefficients: Residual (DDREF=2)(Sv1)
Age
0
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
General
2.7008E-02
2.7348E-02
2.7368E-02
2.7381E-02
2.7388E-02
2.7390E-02
2.7392E-02
2.7392E-02
2.7392E-02
2.7391E-02
2.7460E-02
2.7527E-02
2.752QE02
2.7514E-02
2.7508E-02
2.75Q5E-02
2.7504E-02
2.7506E-02
2.7512E4J2
2.7519E-02
1.8081E-02
8.6374E-03
8.6394E-03
8.6412E-03
8.6423E-03
8.6424E-03
8.6412E-03
8.638 1E-03
8.6330E-03
S.6266E-03
8.6654E-03
8.7023E-03
8.6897E-03
8.6741E-03
8.6553E-03
8.6339E-03
8.6I05E-03
8.5838E-03
8.5531E-03
8.5177E-03
8.6306E-03
8.7368E-03
8.6834E-03
8.6248E-03
8.5605E-03
8.4885E-03
8.4103E-03
8.3258E-03
8.2346E-03
8.1367E-03
8.0314E-03
7.9176E-03
7.7937E-03
7.6584E-03
7.5122E-03
7.3589E-03
Males
3.0296E-02
3.0718E-02
3.0745E-02
3.0761E-02
3.0771E-02
3.0775E-02
3.QT77&O2
3.0779E-02
3.0780E-02
3.0779E-02
3.0827E-02
3.0872E-02
3.0862E-02
3.0854&02
3.0849E-02
3.0849E-4J2
3.0855E-02
3.0866E-02
3.0884E-02
3.0907E-02
1.9225E-02
7.5250E-03
7.5319E-03
7.5387E-03
7.5456&03
7.5518E-03
7,5569E-03
7.5603E-O3
7.56I5E-03
7.5615E-03
7.6005E-03
7.63S2E-03
7.6333E-03
7.6252E-03
7.6141 E-03
7.6009E-03
7.5859&03
7.5680E-03
7.5465E-03
7.5206E-03
7.6887E-03
7.8504E-03
7.8085E-03
7.7629E-03
7.7118E-03
7.6517E-03
7.5861 E-03
7.5165E-03
7.4403E-03
7.3582E-03
7.2712E-03
7.1753E-03
7.0694E-03
6.9553E-03
6.8304E-03
6.6962E-03
Females
2.3553E-02
2.38I5E-02
2.3830E-02
2.3839E^)2
2.3844E-02
2.3845E-02
2.3846E-02
2.3846E-02
2.3845E-02
2.3844E-02
2.3935E-02
2.4026E-02
2.4022E-02
2.4018E-02
2.4012E-02
2.4006E-02
2.4001E-02
2.3996E-02
2.3991E-Q2
2.3986E-02
I.6889E-02
9.7948E-03
9.7902E-03
9.7850E-03
9.778SE-Q3
9.7707E-03
9.7615E-03
9.7504E-03
9.7373E-03
9.7230E-03
9.7603E-Q3
9.7951 E-03
9.7734E-03
9.7489E-03
9.72IOE-03
9.6901E-03
9.6569E-03
9.6201E-03
9.5788E-03
9.5323E-03
9.5879E-03
9.6363E-03
9.5699E-03
9.4968E-03
9.4176E-03
9.3319E-Q3
9.2392E-03
9.1377E-O3
9.0295E-03
8.9136E-03
8.7874E-03
8.6532E-03
8.5085E-03
8.3493E-03
8.1790E-03
8.0037E-03
Age
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
General
7.1979E-03
7.0256E-03
6.8448E-03
6.6555E-03
6.4570&03
6.2485E-03
6.0288E-03
5.80Q8E-03
5.5654E-03
5.3234E-03
5.0743E-Q3
4.8156E-03
4.5491E-03
4.2778E-03
4.0044E^)3
3.7264E-03
3.4418E-03
3.1563E-03
2.8696E-03
2.5868E-03
2.3145E-03
2.0502E-03
I.7960E-03
1.5597E-03
1.3485E-03
1.1583E-03
9.8432E-04
8.2820E-04
6.9394E-04
5.81I9E-04
4.8156E-04
3.9553E-04
3.2440E-04
2.6592E-04
2.1824E-04
1.7990E-04
L4960E-04
1.2605E-04
1.0816E-04
9.5090E-05
8.6342E-05
8.I634E-05
8.H41E-05
8.5514E-05
9.6033E-05
1.1169E-04
1.2956E-04
1.4927E-04
1.6986E-04
1.8928E-04
2.0410E-04
2.0610E-04
1.9223E-04
1.2970E-04
3.0S13E-05
Males
6.5535E-03
6.3996E-03
6.2360E-03
6.0654E-03
5.8884EX)3
5.70I4E-03
5.5003E-03
5.28&9E-03
5.0706E-03
4.8454E-03
4.6144E-Q3
4.376 IE-03
4.I312E-03
3.8835E-03
3.6335E-03
3.3787E-03
3.1234E-03
2.8673E-03
2.5989E-03
2.3351E-03
2.0896E-03
1.8471E-03
1.6113E-03
1.3955&03
1.2040E-03
1.0355E-03
8.8144E-04
7.3853E-04
6.1456E-04
5.0864E-04
4.1595E-04
3.4003E-04
2.7779E-04
2.2705E-04
1.8592E^>4
1.5292E-04
1.2683E-04
1.0658E-04
9.1273E-05
8.0169E-05
7.2755E-05
6.8735E-05
6.8358E-05
7.2346E-05
8.2104E-05
9.6898E-05
I.1396E-04
1.3298E-04
1.5313E-04
1.7256E-04
1.8807E-04
1.9186E-04
1.8085E-04
1.2406E-04
2.9266E-05
Females
7.821 IE-03
7.6273E-03
7.4259E-03
7.2145E-03
6.9910E-03
6.7577E-03
6.5158E-03
6.2673E-03
6.011 IE-03
5.7483E-03
5.4774E-03
5.1949E-03
4.9037E^)3
4.6065E-03
4.3077E-03
4.0048E-03
3.6910E-03
3.3770E-03
3.0710E-03
2.7689E-03
2.4726E-03
2.1886E-03
1.9178E-03
1.6644E-03
1.4373&
-------
Table B-16. Attributable Mortality Risk Coefficients: All Cancers (Sv1)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
1.0764E-01
1.0908E-01
1.0913E-01
1.0903E-01
1.0888E-OI
1.0874E-OI
1.0871E-01
1.0884E-01
1.0906E-01
1.0931E-01
1.0791E-01
1.0636E-01
1.0634E-01
1.0634E-01
1.0637E-01
I.0643E-01
1.0653E-01
1.0666E-01
1.0681E-01
1.0699E-01
7.5513E-02
4.40S4E-02
4.4279E-02
4.4529E-02
4.4798E-02
4.5087E-02
4.5388E-02
4.5702E-02
4.6035E-02
4.6383E-02
4.41HE-02
4.1699E-02
4.I9I8E-02
4.2135E-02
4.2346E-02
4.2549E-02
4.2740E-02
4.2914E-02
4.3061E-02
4.3171E-02
3.9144E-02
3.5033E-02
3.4966E-02
3.4852E-02
3.4679E-02
3.4439E-02
3.4134E-02
3.3759E-02
3.3315E-02
3.2806E-02
3.2227E-02
3.1580E-02
3.0866E-02
3.0091E-02
2.9268E-02
2.8400E-02
8.7708E-02
8.9075E-02
8.9109E-02
8.8943E-02
8.8729E-02
8.8535E-02
8.8468E-02
8.8637E-02
8.8956E-02
8.9299E-02
8.8128E-02
8.6759E-02
8.6728E-02
8.6708E-02
8.673 1E-02
8.6807E-02
8.6922E-02
8.7062E-02
8.7229E-02
8.7434E-02
6.0283E-02
3.3135E-02
3.3393E-02
3.3679E-02
3.3997E-02
3.4346E-02
3.4717E-02
3.5114E-02
3.5544E-02
3.6000E-02
3.4216E-02
3.2300E-02
3.2664E-02
3.3036E-02
3.3408E-02
3.3783E-02
3.4154E-02
3.4512E-02
3.4854E-02
3.5169E-02
3.2598E-02
2.9841E-02
2.9886E-02
2.9884E-02
2.9819E-02
2.9688E-02
2.9492E-02
2.9222E-02
2.8887E-02
2.8491E-02
2.8023E-02
2.7484E-02
2.6887E-02
2.6239E-02
2.5544E-02
2.4801E-02
1.2859E-01
1.3004E-01
1.30I1E-01
1.3007E-01
1.3000E-01
1.2991E-01
1.2991E-01
1.3000E-01
I.3012E-01
1.3025E-01
1.2862E-01
1.2688E-01
I.2688E-OI
1.2689E-01
1.2692E-01
1.2696E-01
1.2704E-01
1.2714E-01
1.2725E-01
1.2738E-01
9.1377E-02
5.5415E-02
5.5589E-02
5.5786E-02
S.S990E-02
5.6200E-02
5.6414&02
5.6627E-02
5.6846&02
5.7071E-02
5.4285E-02
5.1350E-02
5J412E-02
5.1459E-02
5.1495E-02
5.1512E-02
5.1509E-02
5.1485E-02
5.1424E-02
5.13I4E-02
4.5796E-02
4.0301 E-02
4.0114E-02
3.9878E-02
3.9587E-02
3.9229E-02
3.8804E-02
3.8311E-02
3.7747E-02
3.7112E-02
3.6409E-02
3.5638E-02
3.4793E-02
3.3876E-02
3.2910E-02
3.1900E-02
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
2.7496E-02
2.6577E-02
2.5653E-02
2.4717E-02
2.3783E-02
2.2849E-02
2.1911E-02
2.0998E-02
2.0103E-02
1.9217E-02
1.8347E-02
1.7476E-02
1.6598E-02
1.5738E-02
1.4882E-02
1.4020E-02
1.3158E-02
1.2307E-02
1.I454E-02
1.0592E-02
9.7376E-03
8.9212E-03
8.1199E-03
7.3219E-03
6.5855E-03
5.9019E-03
5.2617E-03
4.6885E-03
4.1665E-03
3.6545E-03
3.1832E-03
2.7772E-03
2.4158E-03
2.1069E-03
1.8323E-03
1.5737E-03
1.3520E-03
I.1775E-03
1.0489E-03
9.4427E-04
8.6138E-04
7.9795E-04
7.5372E-04
7.3006E-04
7.3044E-04
7.5257E-04
7.8961E-04
8.4307E-04
9.1478E-04
1.0067E-03
1.1211E-03
1.2512E-03
1.4030E-03
1.4640E-03
1.4699E-03
2.4025E-02
2.3235E-02
2.2445E-02
2.1641E-02
2.0829E-02
2.00I9&02
1.9206E-02
1.8414E-02
1.7637E-02
1.6865E-02
1.6105E-02
1.5344E-02
1.4574E-02
1.3818E-02
1.3078E-02
1.2333E-02
U590E-02
1.0879E-02
1.0166E-02
9.4240E-03
8.7009E-03
8.0258E-03
7.3684E-03
6.7155E-03
6.0960E-03
5.5349&03
5.0107E-03
4.53I8E-03
4.0962E-03
3.6768E-03
3.2759E-03
2.9046E-03
2.64I8E-03
2.4168E-03
2.2216E-03
1.9568E-03
I.7065E-03
I.5761E-03
1.4242E-03
I.29%E-03
I.1987E-03
1.1172E-03
1.0546E-03
1.0119E-03
9.9236E-04
9.9515E-04
1.0162E-03
1.0593E-03
1.1310E-03
1.2413E-03
1.4062E-03
1.6409E-03
1.9697E-03
2.2806E-03
2.5971E-03
3.0853E-02
2.9789E-02
2.8714E-02
2.763 1E-02
2.6558E-02
2.5483E-02
2.4405E-02
2.3353E-02
2.2324E-02
2.1308E-02
2.0312E-02
1.9315E-02
I.8316E-02
I.7338E-02
1.6358E-02
1.5371E-02
1.4385E-02
1.3397E-02
1.2412E-02
1.1438E-02
1.0466E-02
9.5314E-03
8.6156E-03
7.7083E-03
6.8864E-03
6.1193&03
5.4047E-03
4.7742E-03
4.2033E-03
3.6433&03
3.1387E-03
2.7189E-03
2.3173E-03
1.9782E-03
1.6786E-03
1.4298E-03
L2254E-03
1.0421E-03
9.2804E-04
8.3602&O4
7.6428E-04
7.1110&04
6.763 1E-04
6.6143E-04
6.7000E-04
6.9947E-04
7.4250E-04
8.003 IE-04
8.7406E-04
9.6456E-04
1.0722E-03
1.1873E-03
1.3140E-03
I.3411E-03
1.3070E-03
B-19
-------
Table B-17. Attributable Mortality Risk Coefficients: Radon Daughter Inhalation (WL*1)
: Age
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
General
2.4098E-04
2.4405E-04
2.4427E-04
2.4443E-04
2.4456E-04
2.4466E-04
2.4475E-04
2.4484E-04
2.4492E-04
2.4499E-04
2.4506E-04
2.4512E-04
2.4518E-04
2.4526E-04
2.4537E-04
2.4553E-04
2.4573E-04
2.4599E-04
2.4630E4W
2.4667E-04
2.4710E-04
2.4760E-04
2.4818E-04
2.4888E-04
2.4970E-04
2.5067E-04
2.5180E-04
2.5310E-04
2.5454E-04
2.5620E-04
2.5813E-04
2.6033E-04
2.6280E-04
2.6555E-04
2.6857E-04
2.7185E-04
2.7542E-04
2.7918E-04
2.83IOE-04
2.8727E-04
2.9114E-04
2.9430E-04
2.9699E-04
2.993 1E-04
3.0115E-04
3.0273E-04
3.0381E-04
3.0439E-04
3.0457E-04
3.0385E-04
3.0135E-04
2.9575E-04
2.8770E-04
2.7878E-04
2.6890E-04
2.5740E-04
Males
3.4421E-04
3.4907E-04
3.4942E-04
3.4967E-04
3.4988E-04
3.5005E-04
3.5020E-04
3.5034E-04
3.5048E-04
3.5060E-04
3.5070E-04
3.5079E-04
3.5089E-04
3.5J01E-04
3.5121E-04
3.5150E-04
3.5188E-04
3.5235E-04
3.5293E-04
3.5360E-04
3.5438E-04
3.5525E-04
3.5626E-04
3.5746E-04
3.5880E-04
3.6032E-04
3.6211E-04
3.6408E-04
3.6620E-04
3.6865E-04
3.7144E-04
3.7459E-04
3.7809E-04
3.8199E-04
3.8645E-04
3.9137E-04
3.9661E-04
4.0224E-04
4.0824E-04
4.1468E-04
4.2092E-04
4.2633E-04
4.3128E-04
4.3575E-04
4.3939E-04
4.4274E-04
4.457 1E-04
4.4815E-04
4.5003E-04
4.5052E-04
4.4835E-04
4.4163E-04
4.3125E-04
4.I956E-04
4.0658E-04
3.9110E-04
m*Mim
1.3248E-04
1.3397E-04
1.3408E-04
1.3416E-04
I.3422E-04
1.3426E-04
1.3430E-04
1.3435E-04
1.3439E-04
1.3442E-04
1.3445E-04
1.3448E-04
1.3451E-04
1.3455E-04
1.3460E-04
I.3467E-04
1.3475E-04
1.3486E-04
1.3500E-04
1.3515E-04
1.3534E-04
1.3558E-04
1.3588E-04
I.3622E-04
1.3666E-04
1.3721E-04
1.3782E-04
1.3857E-04
1.3945E-04
1.4044E-04
1.4163E-04
1.4299E-04
1.4454E-04
1.4622E-04
1.479IE-04
1.4965E-04
1.5164E-04
1.5363E-04
1.5560E-04
1.5761E-04
1.5923E-04
1.6029E-04
1.6089E-04
1.6126E-04
1.6154E-04
1.6159E-04
1.6107E-04
1.6013E-04
1.5898E-04
1.5747E-04
I.55I1E-04
1.5113E-04
1.4595E-04
1.4035E-04
L3416E-04
1.2723E-04
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
2.4441E-04
2.3012E-04
2.1434E-04
1.9709E-04
1.8183E-04
1.7327E-04
1.6843E-04
I.6310E-04
1.5719E-04
1.5086E-04
1.4400E-04
1.3653E-04
1.2885E-04
1.2109E-04
1.1315E-04
1.0527E-04
9.7380E-05
8.9305E-05
8.1437E-05
7.3924E-05
6.6694E-05
5.9778E-05
5.3107E-05
4.6829E-05
4.1092E-05
3.5720E-05
3.0764E-05
2.6382E-05
2.2566E-05
1.9371E-05
1.6623E-05
1.4161E-05
1.2078E-05
1.0325E-05
8.6571E-06
7.2639E-06
6.3003E-06
5.4847E-06
4.7993E-06
4.2266E-06
3.7545E-06
3.3694E-06
3.0632E-06
2.8325E-06
2.6795E-06
2.6142E-06
2.6574E-06
2.8418E-06
3.2337E-06
3.9142E-06
4.8445E-06
5.9411E-06
7.2096E-06
8.6092E-06
1.0033E-05
3.7312E-04
3.5310E-04
3.3090E-04
3.06I8E-04
2.8433E-04
2.7279E-O4
2.6690E-04
2.6009E-04
2.5228E-04
2.4364E-04
2.3405E-04
2.233 IE-04
2.H98E-04
2.0045E-04
I.8842E-04
1.7609E-04
1.6365E-04
1.5083E-04
1.3801E-04
1.2564E-04
I.1362E-04
I.0194E-04
9.0569E-05
7.9718E-05
6.9681E-05
6.0363E-05
5.1670E-05
4.3935E-05
3.7330E-05
3.1747E-05
2.7072E-05
2.3041 E-05
1.9686E-05
1.6850E-05
1.4085E-05
1.1853E-05
I.0369E-05
9.1084E-06
8.0564E-06
7.1868E-06
6.4744E-06
5.8894E-06
5.4214E-06
5.0675E-06
4.8357E-06
4.7472E-06
4.8450E-06
5.1983E-06
5.9407E-06
7.2570E-06
9.1111E-06
1.1327E-05
1.3918E-05
1.6812E-05
1.9800E-05
1.I983E-04
1.11S1E-04
1.0299E-04
9.3633E-05
8.5427E-05
8.0486E-05
7.7525E-05
7.4503E-05
7.1352E-05
6.8I89&05
6.4867E-05
6.1435E-05
5.8097E-05
5.4742E-05
5.1410E-05
4.8380E-05
4.5347E-05
4.2153E-05
3.9185E-05
3.6349E-05
3.3569E-05
3.0923E-05
2.8296E-05
2.5781E-05
2.3437E-05
2.1058E-05
1.8801 E-05
1.6741 E-05
1.4798E-05
1.3141E-05
1.1597E-05
1.0085E-05
8.7500E-06
7.6081E-06
6.5087E-06
5.5373E-06
4.8450E-06
4.2532E-06
3.7498E-06
3.3247E-06
2.9720E-06
2.6846E-06
2.4575E-06
2.2894E-06
2.1835E-06
2.1490E-06
2.2046E-06
2.3783E-06
2.7271E-06
3.3180E-06
4.1182E-06
5.0643E-06
6.1652E-06
7.3858E-06
8.6351E-06
' Lung cancer mortality risk based on relative risk model, using BEIR IV (NAS91) model and K-factor (K=0.7).
Assumes single exposure at given age, Te, to 0.242 WLM. DDREF = 1.
B-20
-------
Appendix C
PRE-1994 EPA Radiogenic
Cancer Risk Models and Slope Factors
C-1
-------
[This page is blank intentionally.]
C-2
-------
CONTENTS
Section Pa9e
C.I RADIOGENIC CANCER FROM LOW-LET RADIATION C-5
C.I.I Organ Risks c~6
C.2 RADIOGENIC CANCER RISK FROM ALPHA-PARTICLE EMITTERS C-9
C.2.1 General Approach C-9
C.2.2 Radon Decay Products c~9
C.3 EXAMPLE CALCULATIONS: EPA RADIONUCLIDE
SLOPE FACTORS (1989 - 1992) C-12
C.3.1 General Information C-12
C.3.2 Illustrative Examples C-12
C.4 INTERIM 1992 REVISIONS IN DOSE AND RISK MODELS C-20
C.5 REFERENCES C-22
C-3
-------
TABLES
Table Page
C-l Mortality risk coefficients for (pre-1993) EPA constrained risk model (BEIR III) C-8
C-2 Site-specific mortality risk per unit dose (l.OE-6 per rad) for
combined leukemia-bone and constrained relative risk model C-10
C-3 Site-specific incidence risk per unit dose (1 .OE-6 per rad) for
combined leukemia-bone and constrained relative risk model C-l 1
C-4 Reference life table data used for EPA risk estimates prior to 1994
(1970 decennial life table for U.S. population - male and female combined) C-14
C-5 Attributable Cancer Risk from Uniform Low-LET Radiation
(chronic constant dose rate to all organs) : C-15
C-6 Derivation of Attributable Cancer Risk Resulting from Chronic Exposure to
Gamma Radiation from Cs-137+D Ground Contamination (1 pCi/g, 0,037 Bq/g) C-16
C-7 Derivation of Attributable Cancer Risk Resultin
from Chronic Inhalation of Pu-238 [1 pCi/y (0.037 Bq/y) constant intake rate] C-18
C-8 Derivation of Attributable Cancer Risk Resulting
from Chronic Ingestion of Sr-90 (1 pCi/y constant intake rate) C-l9
C-9 Cancer Mortality Risk (Original and Revised Values)
from Lifetime Ingestion of 22fiRa or 228Ra in Drinking Water C-21
C-10 Cancer Mortality Risk (Previous and Revised Values)
from Lifetime Ingestion of Uranium C-22
C-4
-------
Appendix C
PRE-1994 EPA Radiogenic Cancer Risk Models and Slope Factors
Appendix C presents a summary of the methodology previously used by EPA for estimating radiogenic cancer
risk. This approach was used for development of the radionuclide slope factors prior to 1994. In 1994, EPA
adopted a revised methodology for estimating radiogenic cancer risk and developing radionuclide slope factors
(EPA94), as described in the main body of the text.
The models and assumptions used by EPA for estimating radiogenic cancer risk from exposure to low-LET
and high-LET radiation are summarized in Sections C. 1 and C.2, respectively. Additional information on these
risk models may be found in Reference (EPA89). Simplified numerical examples of the methods used to
derive radionuclide slope factors are presented in Section C.3. Interim revisions to the dose and risk
calculations adopted in 1992 are described in Section C.4.
C.1 RADIOGENIC CANCER FROM LOW-LET RADIATION
From 1984 to 1992, EPA's estimates of cancer risks from low-LET radiation were based largely on the
National Academy of Sciences BEIR III report (NAS80). These estimates of radiation risk were based on a
presumed linear dose response function; a relative risk model with a lifetime expression period was assigned
for all cancer sites except for leukemia and bone cancer, where an absolute risk model with a 25-ye'ar
expression period was used. These risk estimates were used in the development of radionuclide slope factors
prior to 1993.
More recently, important new data have become available, especially revised dosimetry and further
epidemiological follow-up on the Japanese atomic bomb survivors. EPA has recently adopted a revised
methodology for estimating radiogenic cancer risks (EPA94) to incorporate this new information. In addition,
the revised approach utilizes more recent vital statistics for the 1980 U.S. population, in place of the 1970 U.S.
vital statistics used previously. The revised methodology is summarized in Chapter 3.
For development of slope factors prior to 1992, EPA used a life table analysis to estimate the number of
radiogenic cancers in an exposed population of 100,000 persons. This analysis considered not only death due
to radiogenic cancer, but also the probabilities of other competing causes of death which were much larger and
varied considerably with age (Bu81, Co78). For ages 0 to 110, the risk of death due to all causes was
calculated by applying the 1970 mortality data from the National Center for Health Statistics (NCHS75) to a
cohort of 100,000 persons. Age-dependent risk coefficients from the BEIR III report were used in the life table
analysis. For relative risk estimates, EPA used age-specific cancer mortality data also provided by NCHS
(NCHS73). The EPA computer program used for the life table analysis was furnished to the BEIR III
C-5
-------
Committee by EPA and used by the Committee to prepare its risk estimates. Therefore, the population base
and calculations should be essentially the same in both the BEIR III and EPA analyses.
Both absolute and relative risk models were considered to project the observed risks of most solid radiogenic
cancers beyond the period of current observation. The range of estimated radiogenic cancers resulting from
the choice of a particular projection model and its internal assumptions was about a factor of 3. The relative
risk model was adopted as the better projection model for solid cancers, whereas the absolute risk model was
selected for projecting radiogenic risk from leukemia and bone cancer. Previously, EPA had used an average
of the risks calculated by the absolute and relative risk projection models (EPA84).
To estimate the radiogenic risk resulting from leukemia and bone cancer, EPA used an absolute risk model,
a minimum latency period of 2 years, and a 25-year expression period. To estimate the radiogenic risk
resulting from other cancers, EPA used a relative risk projection model, a 10-year minimum latency period,
and the remaining balance of an exposed person's lifetime as the expression period.
BEIR III also presented estimates of excess soft tissue cancer incidence risk coefficients for specific sites, as
a function of age at exposure (NAS80 Table V-14). By summing the site-specific risks, it then arrived at an
estimate for the whole-body risk of cancer incidence (other than leukemia and bone cancer) (NAS80 Table V-
30). Finally, by using the weighted incidence:mortality ratios (NAS80 Table V-15), the estimates of cancer
incidence (other than leukemia and bone cancer) were expressed in terms of mortality to yield (for lifetime
exposure) a risk estimate of about 242 and 776 cancer fatalities per million person-rad, depending on whether
an absolute or a relative risk projection model, respectively, was used to estimate lifetime risk. These values
were about 1.7 and 2.1 times their counterparts for the BEIR IlfL^Lmodel and 4.2 and 5.2 times the LQ^L
values. These models all presumed a uniform dose to all tissues at risk in the body. In practice, such uniform
whole-body exposures seldom occur, particularly for ingested or inhaled radioactivity.
C.I.I Organ Risks
Environmental exposures to radioactive materials often result in nonuniform radiation doses to body organs
and tissues. In particular, depending on the chemical and physical characteristics of the radioactive material,
inhalation and ingestion may result in a nonuniform distribution of radioactive materials within the body so
that some organ systems receive much higher doses than others. For example, since iodine isotopes
concentrate preferentially in the thyroid gland, the dose to this organ can be orders of magnitude larger than
the average dose to the body.
To determine the probability that fatal cancer occurs at a particular site, EPA performed life table analyses for
each cancer type using the information on cancer incidence and mortality in BEIR III (NAS80). BEIR III
published incidence risk coefficients (NAS80 Table V-14) and mortality to incidence ratios (NAS80 Table V-
15). These data were used in the development of EPA's risk coefficients, as described below, with the
C-6
-------
exception of the mortality to incidence ratios for thyroid and lung cancer. Since not all forms of thyroid cancer
can be induced by radiation and since, for those that are, a more reasonable mortality to incidence ratio would
be 0.1 (NRC85), EPA used that value in its calculations. Lung cancer incidence and mortality showed an
increasing trend between 1970 and 1980. Since incidence leads mortality, an unconnected mortality to
incidence ratio gives a low estimate of the fraction of those persons who, having been diagnosed with lung
cancer, will die of that disease. Therefore, a mortality to incidence ratio of 0.94, based on long-term survival
studies by the National Cancer Institute for lung cancer was used.
Risk coefficients for a site-specific relative risk model were calculated as follows:
1. Mortality risk coefficients for an absolute risk model were calculated using the site-specific incidence risk
coefficients from BEIR III (NAS80, Table V-14) and mortality:incidence ratios (NAS80, Table V-15,
except for thyroid and lung).
2. Following the procedure used in BEIR III, absolute risks at an absorbed dose rate of 1 mrad/y were
calculated for each cancer site for males and females in each age group. A 10-year minimum latency and
a 20-year plateau, i.e., a 30-year follow-up, was used for these calculations.
3. The relative risk coefficients (rad"1) for each age group providing the same 30-year projected risk were then
calculated. Following the BEIR III convention, the values calculated for ages 10-19 were used for ages
0-9. For consistency, EPA used this convention for all cancers including lung and breast, for which the
BEIR III absolute risk coefficients are zero in the first decade. For calculating thyroid risks, the relevant
age-specific mortality rate was considered to be one-tenth of the corresponding incidence rate (NRC85).
A mortality to incidence ratio of 0.94, based on long-term survival studies by the National Cancer Institute
for lung cancer (J. Horn, private communication), was used. For leukemia and bone cancer, the incidence
and mortality risks were considered to be equal, as in BEIR III.
4. Male and female risks for lifetime expression of risk at 1 mrad/y were then calculated and cpmbined to
obtain estimates for the general population. EPA used the National Center for Health Statistics 1970 Life
Table and mortality data (NCHS73,75) for these calculations. Male and female cohort estimates were
combined based on a male:female sex ratio at birth of 1.0511, consistent with the expected lifetimes at
birth for the 1970 male, female, and general cohort life tables.
5. The low-LET risk coefficient for bone was obtained by dividing the value for alpha particles (high-LET)
in BEIR III (NAS80, Table A-27) by an RBE of 8 to obtain a low-LET value of 1.25 x 10'7 per rad-year.
The risk coefficients for leukemia were obtained by subtracting the risk coefficients for bone from the risk
coefficients for leukemia and bone from BEIR III (NAS80 Table V-17). EPA followed the BEIR III
Committee's practice of using the absolute risk model projections for leukemia and bone cancer with the
relative risk projection for all other cancers. Since the expression period for leukemia and bone cancer
is 27 years, there is no difference between the number of cancers projected for a 30-year and a lifetime
follow-up period.
6. Ingested iodine-131 has been reported to be only one-tenth as effective as x-rays or gamma rays in
inducing thyroid cancer (NCRP85). BEIR III reported estimates of factors of 10-80 times reduction for
ingested iodine-131 compared to x-rays and noted the estimates were derived primarily from animal
experiments (NAS80). However, one study in rats reported that iodine-131 was just as effective as x-rays
C-7
-------
in inducing thyroid cancer, leading a review group to select one-third as the minimum ratio of iodine-131
to x-ray effects that is compatible with both old and new data (NRC85). For this analysis, EPA employed
a thyroid cancer risk coefficient for internal exposures to iodine-131 and iodine-129 which is one-third
that used for gamma rays or beta radiations from other radionuclides.
7. It is generally accepted that the risk estimates for individual cancer sites are less certain than is the risk
estimate for all sites combined. Thus, the lifetime risks calculated for the BEIR III linear model were used
as a constraint on the sum of the individual site estimates. The relative risk coefficient for each site was
calculated by multiplying the coefficient for the unconstrained model for each sex by the quotient of the
average risk for all age groups for the BEIR HI linear, unconstrained site-specific model. The constrained
risk coefficients are about one-half of the unconstrained values.
The resulting risk coefficients are presented in Table C-l.
Table C-1. Mortality risk coefficients for (pre-1993) EPA constrained risk model (BEIR III)
Cancer ; .:•:•-?-
:" Type ; ; -t-:-':'
Male:
Leukemia
Bone
Thyroid
Breast
Lung
Esophagus
Stomach
Intestine
Liver
Pancreas
Urinary
Lymphoma
Other
Female:
Leukemia
Bone
Thyroid
Breast
Lung
Esophagus
Stomach
Intestine
Liver
Pancreas
Urinary
Lymphoma
Other
MOuei --'- "'":'.
• " T\"iJe^:: :^'
A
A
R
R
R
R
R
R
R
R
R
R
R
A
A
R
R
R
R
R
R
R
R
R
R
R
3.852
0.125
52.74
0
2.99
6.15
11.71
3.35
120.37
7.81
4.14
4.41
1.12
2.417
0.125
35.30
10.52
6.36
13.30
14.15
2.63
142.77
11.81
8.10
6.28
0.53
1.724
0.125
52.74
0
2.99
6.15
11.71
3.35
120.37
7.81
4.14
4.41
1.12
1.067
0.125
35.30
10.52
6.36
13.30
14.15
2.63
142.77
11.81
8.10
6.28
0.50
2.471
0.125
38.00
0
2.15
1.44
4.20
1.28
25.19
2.49
1.38
1.28
1.02
1.541
0.125
35.96
2.80
6.27
3.90
7.08
1.06
46.62
3.61
3.41
1.60
0.47
1.796
0.125
28.63
0
1.34
0.71
1.76
0.48
7.23
1.12
0.59
0.42
0.44
1.112
0.125
34.81
1.52
6.10
2.31
3.19
0.45
16.29
1.50
1.63
0.50
0.24
4.194
0.125
22.43
0
1.18
1.15
1.70
0.46
4.24
1.37
0.39
0.21
0.47
2.635
0.125
29.53
1.02
6.12
3.17
2.60
0.42
7.80
1.59
0.96
0.25
0.27
1.00
1.00
0.10
-
0.94
1.00
0.75
0.52
1.00
0.91
0.37
0.73
0.65
1.00
1.00
0.10
0.39
0.94
1.00
0.78
0.55
1.00
0.90
0.46
0.75
0.50 -
Notes:
Risk model type
Absolute (A)
Relative (R)
Coefficient units
10-6(rad/y)-'[10-t(Gy/y)-1]
Lethality fractions (mortality:incidence ratios) are from BEIR II! (NAS80).
C-8
-------
Table C-2 shows the average mortality risks per unit absorbed dose for the combined leukemia/bone and
constrained relative risk models. Values are presented for males, females, and the general population (male
and female combined) for age-averaged individuals exposed in five age groups. The risk, in general, decreases
with increasing age at exposure. For a constant, uniform absorbed dose rate to all organs and tissues, about
60 percent of the risk is conferred by the exposures in the first 20 years of life.
The mortality to incidence ratios presented in Table C-l were used to convert the mortality risk estimates in
Table C-2 to incidence risk estimates. For leukemia and bone cancer, the incidence risks are considered to be
equal as in BEIR III (NAS80). The resultant incidence risks are shown in Table C-3.
C.2 RADIOGENIC CANCER RISK FROM ALPHA-PARTICLE EMITTERS
C.2.1 General Approach
EPA evaluated the risk to specific body organs by applying an RBE of 8 for alpha radiations to the risk
estimates for low dose rate, low-LET radiations; the RBE value for leukemia only was revised to 1.117 in
1992. As in the case of low-LET radiations, EPA risk estimates for high-LET radiations were based on a linear
dose response function. For bone cancer and leukemia, EPA used the absolute risk projection model described
in the previous section. For other cancers, relative risk projections were used.
Lifetime risk estimates for alpha doses, as a function of age, sex, and cancer site, were obtained by multiplying
the appropriate entries in Table C-2 and C-3 by a factor of 8. The whole-body risks from lifetime exposure
ofthe general population were then calculated to be3.1 X 10'Vrad (mortality) and 5.0 X 10"3/rad (incidence).
C.2.2 Radon Decay Products
For estimating risks from radon decay products, EPA employed an epidemiological approach, based on human
epidemiological data. When radon-222, a radioactive noble gas, decays, a number of short half-life
radionuclides (principally polonium-218, lead-214, bismuth-214, and polonium-214) are formed. These decay
products, commonly referred to as "progeny" or "daughters," readily attach to inhalable aerosol particles in air.
When inhaled, the radon progeny are deposited on the surfaces ofthe larger bronchi ofthe lung. Since two
of these radionuclides decay by alpha-particle emission, the bronchial epithelium is irradiated by high-LET
radiation. A wealth of data indicate that a range of exposures to the bronchial epithelium of underground
miners causes an increase in bronchial lung cancer, both in smoking and in nonsmoking miners, and in some
members ofthe general public.
The epidemiological approach to estimation of radon risks makes maximal use of the extensive human
epidemiological data and avoids uncertainties associated with estimating the bronchial dose delivered by the
inhaled radon progeny and selection of an appropriate RBE value. On this basis, EPA employed a central risk
estimate for excess radon exposure of 360 fatal lung cancers/106 working level months (WLM) and an
uncertainty range of 140-720 fatal lung cancers/106 WLM (EPA89).
C-9
-------
Table C-2. Site-specific mortality risk per unit dose (1.0E-6 per rad) for
combined leukemia-bone and constrained relative risk model
Site
Male
Leukemia
Bone
Thyroid
Breast
Lung
Esophagus
Stomach
Intestine
Liver
Pancreas
Urinary
Lymphoma
Other
Total
Female
Leukemia
Bone
Thyroid
Breast
Lung
Esophagus
Stomach
Intestine
Liver
Pancreas
Urinary
Lymphoma
Other
Total
General
Leukemia
Bone
Thyroid
Breast
Lung
Esophagus
Stomach
Intestine
Liver
Pancreas
Urinary
Lymphoma
Other
Total
0-9
94.68
3.07
8.25
0.00
145.90
25.57
110.95
53.49
168.01
74.36
40.73
33.43
37.48
796.43
59.93
3.10
15.85
309.33
78.57
21.47
102.64
57.14
115.94
103.00
46.40
45.71
27.69
986.78
77.69
3.09
12.22
151.21
112.98
23.56
106.89
55.28
142.55
88.36
43.50
39.44
32.69
889.49
10-19
41.86
3.04
8.25
0.00
146.95
25.76
111.72
53.83
168.24
74.90
40.99
33.28
37.23
746.05
26.35
3.09
14.54
310.52
78.89
21.57
103.05
57.38
115.25
103.48
46.54
45.66
27.65
955.96
34.26
3.06
11.33
52.03
113.63
23.71
107.48
55.57
142.30
88.89
43.71
39.34
32.54
847.84
20-34
58.46
2.96
5.08
0.00
107.22
6.13
40.63
20.89
35.40
24.21
13.85
9.62
33.72
358.15
37.39
3.03
11.46
81.01
77.09
6.32
51.49
23.07
36.97
31.71
19.64
11.54
24.48
415.21
48.06
2.99
8.23
39.95
92.34
62.22
45.98
21.96
36.17
27.90
16.70
10.56
29.16
386.21
35-50
37.52
2.61
2.69
0.00
61.40
2.82
16.4
7.60
9.48
10.34
5.79
2.88
13.09
172.65
25.27
2.84
7.46
36.93
64.70
3.46
22.39
9.57
11.95
12.70
9.08
3.35
11.27
220.95
31.39
2.72
5.07
18.40
63.00
3.14
19.37
8.58
10.71
11.51
7.43
3.11
12.18
196.60
50 +
48.64
1.45
0.80
0.00
22.55
2.03
9.36
4.30
2.50
6.55
2.22
0.71
6.93
108.06
35.27
1.67
2.24
10.30
24.96
2.26
10.73
5.01
2.80
7.11
3.06
0.79
5.80
112.01
41.20
1.58
1.61
5.75
23.91
2.16
10.13
4.70
2.67
6.87
2.69
0.76
6.30
110.32
All
54.19
2.47
4.32
0.00
84.21
9.91
6 . 95
22.78
58.87
30.78
16.60
12.49
22 .66
366.25
35.86
2.53
8.42
107.63
56.72
8.33
45.00
23.08
40.74
38.15
18.80
15.13
16.20
416.59
44.76
2.50
6.43
55.36
70.07
9.09
45.95
2.94
49.55
34.57
17.73
13.85
19.34
392.14
C-10
-------
Table C-3. Site-specific incidence risk per unit dose (1.0E-6 per rad) for
combined leukemia-bone and constrained relative risk model
Age at Exposure
Site
Male
Leukemia
Bone
Thyroid
Breast
Lung
Esophagus
Stomach
Intestine
Liver
Pancreas
Urinary
Lymphoma
Other
Total
Female
Leukemia
Bone
Thyroid
Breast
Lung
Esophagus
Stomach
Intestine
Liver
Pancreas
Urinary
Lymphoma
Other
Total
General
Leukemia
Bone
Thyroid
Breast
Lung
Esophagus
Stomach
Intestine
Liver
Pancreas
Urinary
Lymphoma
Other
Total
0-9
94.68
3.07
87.59
0.00
155.21
25.57
147.94
102.87
168.01
81.71
110.08
45.80
57.66
1080.20
59.93
3.10
158.45
793.16
83.59
21.47
131.59
103.90
115.94
114.44
100.88
60.95
55.38
1802.80
77.69
3.09
122.24
387.78
120.19
23.56
139.95
103.38
142.55
97.71
105.58
53.21
56.55
1433.50
10-19
41.86
3.04
82.52
0.00
156.33
25.76
148.97
103.52
168.24
82.31
110.79
45.58
57.27
1026.20
26.35
3.09
145.42
796.20
83.93
21.57
132.11
104.34
115.25
114.98
101.16
60.88
55.30
1760.60
34.26
3.06
113.32
389.82
120.88
23.71
140.71
103.92
142.30
98.30
106.08
53.07
56.31
1385.70
20-34
58.46
2.96
50.84
0.00
114.07
6.13
54.18
40.16
35.40
26.60
37.44
13.17
51.88
491.27
37.39
3.03
114.59
207.73
82.01
6.32
66.01
41.94
36.97
35.23
42.70
15.38
48.97
738.28
48.06
2.99
82.26
102.42
98.24
6.22
60.00
41.03
36.17
30.85
40.02
1426
50.43
612.96
IT ~ — — r. . .
35-50
37.52
2.61
26.92
0.00
65.31
2.82
21.87
14.63
9.48
11.37
15.65
3.94
20.15
232.28
25.27
2.84
74.60
94.69
68.83
3.46
28.69
17.40
11.95
14.11
19.74
4.47
22.54
388.58
31.39
2.72
50.66
47.18
67.02
3.14
25.25
16.00
10.71
12.73
17.68
4.20
21.33
310.01
50
48.64
1.45
8.04
0.00
23.99
2.03
12.48
8.28
2.50
7.20
6.01
.98
10.65
132.25
35.27
1.67
22.38
26.40
26.56
2.26
13.75
9.11
2.80
7.91
6.66
1.06
11.61
167.42
41.20
1.58
16.05
14.74
25.43
2.16
13.20
8.74
2.67
7.60
6.37
1.02
11.19
151.96
All
54.19
2.47
43.23
0.00
89.58
9.91
62.61
43.81
58.87
33.83
44.87
17.12
34.86
495.35
35.86
2.53
84.16
275.97
60.34
8.33
57.70
41.96
40.74
42.39
40.88
20.18
32.40
743.44
44.76
2.50
64.28
141.95
74.54
9.09
60.08
42.86
49.55
38.23
42.28
18.69
33.60
622.96
C-11
-------
C.3 EXAMPLE CALCULATIONS: EPA RADIONUCLIDE SLOPE FACTORS (1989 -1992)
C.3.1 General Information
From 1989 to 1991, EPA radionuclide slope factors were derived using the following information:
• Organ-specific dose rates over the lifetime of the exposed population were derived from (1) the
RADRISK computer code (Du80) for inhalation and ingestion exposures, assuming constant annual
intake of activity; and (2) the DOSFACTER (Ko81) and DFSOIL (SJ84) computer codes for external
exposures to radionuclides in soil. (See Appendix A for additional information on the methods and
assumptions used to estimate dose rates.)
• Age- and sex-specific cancer incidence risks, assuming equal and constant dose rates in each body
organ, were derived from the NAS BEIR III study (NAS80), as summarized in Table C-3. As shown
in Table C-3, estimates of the lifetime cancer incidence risks per unit dose for thirteen cancer sites
(leukemia, bone sarcoma, thyroid, breast, lung, esophagus, stomach, intestine, liver, pancreas, urinary,
lymphoma, and other) and five age intervals (0-9 y, 10-19 y, 20-34 y, 35-49 y, and 50+ y) were
considered.
• Vital statistics for the 1970 U.S. population (NCHS73) and the CAIRO computer code (Co78) were
used to account for competing risks and estimate the projected years of life remaining at various ages
in the reference population. Table C-4 presents the 1970 life table data used for these calculations.
The Tx column in Table C-4 displays the expected total collective person-years of life remaining for
the survivors of an initial cohort of 100,000 persons, initially liveborn at age zero, who are still alive
at a given age, from birth to 110 years. This cohort also represents a stationary population of diverse
ages from zero to 110 years, with the mortality statistics of the 1970 U.S. population.
Integration of these data is complicated by the different time periods considered in each. The risk factors are
for five age intervals: 0-9 y, 10-19 y, 20-34 y, 35-50 y, and 50+ y. RADRISK computes dose rates for the
midpoints of nine time intervals following the beginning of exposure (times 1, 3,6,12,20,30,42, 56, and 87
y). The Life Table data are provided for each age in the cohort from 0 to 110 y. These data are integrated by
averaging over the age intervals of the risk data, where the data are weighted by the survivors' collective
person-years of life remaining at any age, or by the fraction of the time spent by survivors in the smaller age
intervals. This averaging process is illustrated in the following section.
C.3.2 Illustrative Examples
The examples presented here are designed to illustrate the principal features of the method for different
radionuclides, body organs and endpoints (cancer sites), and pathways of exposure. These examples consider
the following radionuclides and exposure pathways: uniform low-LET radiation, exposure to external gamma
rays due to Cs-137 in soil, inhalation of Pu-238, and ingestion of Sr-90. The Pu-238 example illustrates how
high- and low-LET radiation dose rates and risks are combined to obtain the slope factor.
Because of the large number of calculations involved, the derivation of a slope factor is tedious and computer
codes are used to compile and organize the data and calculations that are required. Nevertheless, the purpose
here is to present the basic elements of the derivation using a few examples to illustrate the principal
considerations.
C .3.2.1 Example A: Risk Estimate for Uniform Low-LET Radiation. Example A considers chronic exposure
to low-level low-LET radiation, where it is assumed that each member of the exposed population receives a
uniform, constant dose rate of 1 mrad/y (10'5 Gy/y) to all body organs. For purposes of this and the following
C-12
-------
examples, the cohort survivors' life expectancy data from Table C-4 have been aggregated over the age
intervals for the risk model as shown in Table C-l (i.e., 0-9 y, 10-19 y, 20-34 y, 35-49 y, and 50+ y). These
five intervals are denoted as "Risk Intervals" to distinguish them from other age intervals used in the
calculations. [Note that somewhat different risk intervals are used under EPA's revised methodology, as
discussed in the main text.]
The data in the columns labelled Tx in Table C-4 express the collective expected person-years of life remaining
in the survivors of an initial cohort of 100,000 persons, initially Hveborn at age zero, who are still alive at a
given age. For example, at age 0, the 100,000 persons in the cohort have a collective remaining life
expectancy of 7,075,647 person-y. (A person aged 0 is living in his/her first year.) From this information, the
collective person-y lived by the survivors within each Risk Interval can be computed from a successive
subtraction of adjacent life expectancies. These results, which will be used in the following analyses, are
summarized below.
Rfek Interval
fr)
0-9
10-19
20-34
35-49
50+
Person-y Uved by Cohort Survivors
In Risk Interval
9.780E+5
9.71 9E+5
14.346E+5
1 3.841 E+5
23.070E+5
It should be noted that, when normalized by the length of the respective risk interval, the person-y lived by the
cohort survivors decreases monotonically. This accounts for the fact that some deaths are expected to occur
from causes other than radiation exposure at each age. This consideration becomes more important at later
ages, since the baseline mortality rates generally increase with age. Accounting in this way assures that the
radiation-induced excess cancer incidence risk is calculated for only the surviving population at any age.
Table C-4 indicates the initial collective person-y of life expected for the cohort to be 70.756 x 105 person-y.
Dividing by the initial size of the cohort, i.e., 100,000, provides the average (expected) lifetime of an
individual in the cohort. Thus, individuals born in the reference population are expected to live an average
of 70.756 years.
The cohort life expectancy data in Table C-4 may be used in conjunction with the age-specific attributable
cancer incidence risk per unit dose from Table C-3, to estimate the total lifetime attributable cancer incidence
risk resulting from uniform low-LET irradiation, assuming chronic equal dose rates to each body organ, as
illustrated in Table C-5.
C-13
-------
Table C-4. Reference life table data used for EPA risk estimates prior to 1994
(1970 decennial life table for U.S. population - male and female combined)
Age A !, T,
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
0.0200200000
0.0012449230
0.0008582290
0.0006953530
0.0005730420
0.0005017000
0.0004712200
0.0004304470
0.0003793670
0.0003487390
0.0003078190
0.0002976500
0.0003490720
0.0004621690
0.0006267850
0.0008225290
0.0010084280
0.0011639520
0.0012787460
0.0013423370
0.0014061790
0.0014702840
0.0015139260
0.0015266070
0.0015081390
0.0014687500
0.0014396140
0.0014103490
0.0014437260
0.0014772440
0.0015633690
0.0016288700
0.0017157350
0.0018346690
0.0019436760
0.0020850530
0.0022485020
0.0024449100
0.0026640240
0.0028955160
0.0031503820
0.0033968270
0.0037104150
0.0040381950
0.0044350240
0.0048369310
0.0052883350
0.0057355890
0.0062457010
0.0067761420
0.0073843460
0.0080394040
0.0087552080
0.0095695430
0.0104293840
0.0113735170
100000.0000000000
97998.0000000000
97876.0000358460
97792.0000142112
97724.0000536253
97668.0000971866
97619.0000615378
97573.0000363288
97531.0000311822
97493.9999882933
97460.0000282314
97429.9999884827
97400.9999489862
97366.9999871319
97321.9999781149
97261.0000083586
97181.0000152827
97082.9999737993
96970.0000218138
96846.0000221659
96716.0000530341
96580.0000447955
96438.0000160097
96292.0000203974
96144.9999791223
95999.9999549988
95858.9999550648
95720.9999967035
95585.9999800792
95447.9999866719
95307.0000013796
95157.9999920945
95002.9999806473
94840.0000084755
94666.0000005000
94481.9999682830
94284.9999908031
94072.9999797538
93842.9999613733
93592.9999572442
93321.9999283800
93027.9999796016
92711.9999575149
92367.9999621925
91994.9999665852
91586.9999338533
9 1143. 9999346763
90661.9999297817
90141.9999602665
89578.9999809726
88971.9999568835
88314.9999248899
87604.9999612337
86837.9999647331
86006.9999900366
85109.9999604525
7075647.4998189092
6976648.4998189092
6878711.4998009864
6780877.4997759578
6683119.4997420397
6585423.4996666338
6487779.9995872716
6390183.9995383383
6292631.9995045830
6195119.4994948453
6097642.4994865831
6000197.4994782261
5902781.9995094917
5805397.9995414328
5708053.4995588094
5610761.9995655727
5513540.9995537521
5416408.9995592113
5319382.4995614048
5222474.4995394151
5125693.4995018153
5029045.4994529006
4932536.4994224980
4836171.4994042946
4739952.9994045349
4643880.4994374744
4547950.9994824426
4452160.9995065585
4356507.4995181672
4260990.4995347918
4165612.9995407662
4070380.4995440294
3975299.9995576586
3880378.4995630973
3785625.4995586097
3691051.4995742184
3596667,9995946754
3502488.9996093970
3408530.9996388336
3314812.9996795249
3221355.4997367130
3128180.4997827224
3035310.4998141644
2942770.4998543109
2850588.9998899221
2758797.9999397029
2667432.5000054382
2576529.5000732094
2486127.5001281854
2396267.0001575660
2306991.5001886380
2218348.0002477514
2130388.0003046896
2043166.5003417062
1956744.0003643215
1871185.5003890770
Age ^
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
0.0123481730
0.0134170850
0.0145143190
0.0157058340
0.0169497920
0.0182908890
0.0197391560
0.0213328730
0.0230609390
0.0249398750
0.0269892640
0.0291885240
0.0315150780
0.0340055480
0.0366062210
0.0394373270
0.0426603900
0.0464370910
0.0507610340
0.0555074940
0.0606015420
0.0659622230
0.0715430180
0.0773957380
0.0839450190
0.0912044050
0.0989276600
0.1069553060
0.1154920040
0.1255978570
0.1374576090
0.1497875580
0.1616319830
0.1728647690
0.1850059160
0.1988913820
0.2136738060
0.2285774150
0.2433460080
0.2577171570
0.2693423600
0.2806088680
0.2897884080
0.2979274610.
0.3081180810
0.3146666670
0.3190661480
0.3314285710
0.3333333330
0.3333333330
0.3461538460
0.3529411760
0.3636363640
0.3571428570
0.0000000000
1*
84141.9999290323
83102.9999573426
81987.9999431600
80797.9999578130
79528.9999829435
78180.9999752646
76750.9999828080
75236.0000209914
73630.9999875156
71932.9999882945
70138.9999602114
68245.9999735893
66253.9999654562
64165.9999887328
61983.9999961480
59714.9999938250
57360.0000122635
54913.0000413403
52363.0000613376
49705.0000348820
46946.0000436758
44101.0000502970
41192.0000504563
38245.0000493905
35285.0000457579
32323.0000465017
29375.0000594456
26469.0000410648
23638.0000421587
20908.0000467377
18282.0000467115
15769.0000325527
13407.0000255747
11240.0000253600
9297.0000174161
7577.0000131421
6070.0000091142
4773.0000047467
3682.0000018667
2785.9999999565
2068.0000005657
1510.9999999333
1087.0000004040
772.0000007910
542.0000006633
375.0000005569
257.0000002567
175.0000001388
117.0000001678
78.0000001509
52.0000001266
34.0000000908
22.0000000747
14.00000003%
0.0000000000
T.
1786559.5004443347
1702937.0005011472
1620391.5005508962
1538998.5006004099
1458835;00063003I8
1379980.0006509279
1302514.0006718917
1226520.5006699921
1152087.0006657387
1079305.0006778338
1008269.0007035810
939076.5007366807
871826.5007671580
806616.5007900635
743541.5007976232
682692.0008026367
624154.5007995925
568018.0007727906
514380.0007214517
463346.0006733418
415020.5006340629
369497.0005870765
326850.5005366999
287132.0004867765
250367.0004392023
216563.0003930725
185714.0003400988
157792.0002898437
132738.5002482320
110465.5002037838
90870.5001570592
73845.0001174271
59257.0000883634
46933.5000628961
36665.0000415080
28228.0000262289
21404.5000151008
15983.0000081703
11755.5000048635
8521.5000039519
6094.5000036908
4305.0000034413
3006.0000032726
2076.5000026751
1419.5000019480
961.0000013379
645.0000009311
429.0000007334
283.0000005801
185.5000004208
120.5000002820
77.5000001734
49.5000000906
31.5000000335
20.0000000000
tqx-reference probability of death at age x. lx=number of members of initial cohort surviving to age x. Tx=years of life remaining to the survivors at age x
C-14
-------
Table C-5. Attributable Cancer Risk from Uniform Low-LET Radiation
(chronic constant dose rate to all organs)
Risfc Interval
-.' -"-.M'v*\ ':...'.
0-9
10-19
20-34
35-49
50+
t^R^f^S
-^i&ti$k%&
0.001
0.001
0.001
0.001
0.001
; - : : V'^ur^i^jp.;EXpCSUr^;:i;l;l
'. ::"; : : /•:••; ?:.;:::--KEJu(aiidiri li&^'isiS
^^m^s^^MM
9.780E+5
9.71 9E+5
14.346E+5
1 3.841 E+5
23.Q70E+5
70.756E+5
1443.5E-6
1385.7E-6
612.9E-6
310.0E-6
151.9E-6
1.41
1.35
0.88
0.43
0.35
4.42
Average individual risk = 4.42 attributable cancers/(70.756E+5 p-y x 0.001 rad/y)
= 6.2E-4 attributable cancers/rad
Within each risk interval, risk is computed as the product of the pertinent dose rate, expected duration of
exposure of the cohort survivors, and lifetime risk factor at the age being considered. The cancers projected
for each risk interval are summed to estimate the total number of attributable cancers projected in the lifetime
of the survivors of the cohort (4.42 cancers).
Hence, a chronic dose rate of 1 mrad/y (10~5 Gy) in each body organ results in an expected lifetime sum-total
collective dose of 0.001 rad/y x 70.756E+5 person-y = 7075.6 person-rad (7.0756E+5 person-Gy) in each
organ for members of the cohort. This collective dose is expected to induce a total of 4.42 attributable cancers
during the lifetime of the initial population of 100,000 persons. Thus, the average individual's risk at age zero
due to the radiation exposure is estimated to be 4.42/100,000 - 4.42E-5 attributable cancers per person under
the assumed exposure conditions (chronic dose rate of 1 mrad/y in all body organs). For comparison, the
current baseline cancer incidence risk from all causes is about 0.3.
The estimated lifetime cancer incidence risk per unit lifetime dose is the expected number of attributable
cancers in the cohort survivors divided by the projected total lifetime collective dose, or 4.42 attributable
cancers/7075.6 person-rad = 6.2E-4 per person-rad (6.2E-6 Gy"1).
This illustration is simplistic in that it assumes identical dose rates in all body organs at all times. In many
exposure situations, this is not the case, especially for internal exposures. In these cases, the dose rates at
various ages must be appropriately averaged in the discrete risk intervals, as illustrated in the following
examples.
C.3.2.2 Example B: External Exposure to Cs-137+D in Soil. Example B considers the case of chronic
exposure to gamma radiation from Cs-13 7 in soil contaminated at a uniform level of 1 pCi of Cs-137 per gram
of soil (1 pCi/g or 0.037 Bq/g). Cs-137 is a pure beta-emitter, which decays to Ba-137m with a half-life of
approximately 30 years and a branching fraction of 0.946—i.e., 94.6% of all Cs-137 atoms decay to produce
Ba-137m. For this example, Cs-137 is assumed to be in equilibrium with its radioactive decay product Ba-
137m, i.e., the soil is also assumed to contain a uniform concentration of 0.946 pCi/g of Ba-137m per gram
C-15
-------
H'g;. mis is a case where inclusion of the radioactive decay products is
extremely important in estimating radiation risk, since the external pathway dose from this decay series is
entirely from Ba-137m. The inclusion of radioactive decay products in radionuclide slope factors is indicated
as"Cs-137+D".
Although Cs-137 decays with a half-life of 30 years, the slope factor derivation assumes exposure to a constant
and uniform soil contamination level, and constant dose rates in the various body organs. The decrease in
radionuclide concentrations over time (i.e., by radioactive decay and also any physical removal processes)
should be accounted for in pathway modeling used in conjunction with the slope factors to estimate risk.
Conceptually, this can be accommodated by calculating the exposure-time integral in the appropriate units
(e.g., pCi-y/g) and multiplying by the slope factor to obtain the lifetime risk.
In this example, however, it is assumed that the ground contamination level is constant and uniform. Thus,
the dose rates in each body organ will also be constant over the lifetime of the exposed population. However,
since some body organs are shielded by other body organs, each organ can be subjected to a slightly different,
but constant, dose rate. Since the dose rates in this example are constant over the life of the cohort, averaging
dose rates over the five risk intervals is unnecessary. Table C-6 shows the necessary data and calculations for
estimating attributable cancer risk for this example. The first column lists the risk intervals. The second lists
the organ dose rate for each risk interval.
Table C-6. Derivation of Attributable Cancer Risk Resulting from Chronic Exposure to
Gamma Radiation from Cs-137+D Ground Contamination (1 pCi/g, 0.037 Bq/g)
. Risk InteivMi
>;:;£>:
'$^M$f$ii$$$i&$$i&$
|liy||||ii^^lii;.;||
li;|liiiiSH;;|i||l!ll.!
^^fl^^S^^^l^^
IlillBKii^illP;
lllilli^Si^iiiulllI
0-9
10-19
20-34
35-49
50+
3.54E-3
3.54E-3
3.54E-3
3.54E-3
3.54E-3
9.780E+5
9.71 9E+5
14.346E+5
1 3.841 E+5
23.070E+5
70.756E+5
387.78E-6
389.82E-6
102.42E-6
47.18E-6
14.74E-6
1.34
1.34
0.52
0.23
0.12
3.56
:-:;.:.>. ^^^.^^^^^^^^^M^^^^MJ^^i^^^^f^^MM^^?^^^^^^}^^^^^^
0-9
10-19
20-34
35-49
50+
2.92E-3
2.92E-3
2.92E-3
2.92E-3
2.92E-3
9.780E+5
9.719E+5
14.346E+5
13.841 E+5
23.070E+5
70.756E+5
120.19E-6
120.88E-6
98.24E-6
67.02E-6
25.44E-6
0.34
0.34
0.41
0.27
0.17
1.54
. " -: : ":C/ V" :-: :vl^;:ilill^lflwilii^£lS|8 ^SS^^MX^Mi:
Lifetime attributable cancers in cohort = 14.15
Slope Factor = 14.15 attributable cancers/(70.756E+5 person-y x 1 pC /g)
= 2E-6 attributable cancers per pCi-y/g
C-16
-------
The third column lists the collective years of life lived by survivors in each risk interval. The fourth column
lists the pertinent risk factors from Table C-3. The last column is the predicted attributable cancers in each
age interval, calculated as the product of the pertinent dose rate, collective exposure duration, and risk factor.
This calculation is repeated for each risk interval and for each of the 13 cancer sites considered.
The slope factor is then computed as the projected number of attributable cancers in the cohort divided by the
total exposure of the cohort. "At the assumed constant soil contamination level of 1 pCi/g (0.037 Bq/g), the
expected number of attributable cancers in the cohort survivors is approximately 14 cancers. The collective
exposure duration of the cohort is 70.756E+5 person-years. Thus, the slope factor may be calculated as
SF = 14 attributable cancers/(70.756E+5 person-y x 1 pCi/g)
= 2.0E-6 attributable cancers per pCi-y/g.
C.3.2.3 Example C: Inhalation of Pu-238. Example C considers the case of chronic inhalation of Pu-238 at
a constant rate of 1 pCi/y (0.037 Bq/y). In the calculation of ingestion and inhalation slope factors, it is
assumed that survivors in the cohort chronically ingest or inhale a constant amount of activity of a given
radionuclide each year (e.g., 1 pCi/y) throughout each survivor's lifetime. Unlike the cases considered above,
where the dose rates in body organs remained constant over time, in this example dose rates in body organs
are not constant as survivors age, and average dose rates in each risk interval must be calculated.
For this example, it is assumed that the chemical form of the particles carrying the Pu-238 is insoluble in body
fluids, i.e., the clearance time of the particles from the lung is very long (i.e., ICRP lung clearance class "Y";
see Appendix A). In this case, the dose rate to body organs increases rapidly during the first few years of
exposure, and then plateaus assymtoptically. For the purpose of this calculation, this means that dose rates will
vary significantly over the risk interval 0-9 y, and then become relatively constant for subsequent intervals.
Thus, an average dose rate for the 0-9 y interval must be calculated, taking into account the cohort survival.
This is done by calculating the fraction of the time spent by survivors in the age groups within this risk interval.
For the 0-9 y risk interval, three age groups are considered: 0-2,2-4, and 4-10. Dose rates in the middle of
these age intervals, at 1, 3 and 6 y of age, are used to estimate the average dose rate in the 0-9 y interval.
Similarly, a weighted average of the dose rate to each organ of interest is computed for each of the five risk
intervals.
Since Pu-238 is an alpha-emitter and weak photon emitter, both high- and low-LET dose rates must be
considered. The high-LET dose rates are adjusted for the greater relative biological effectiveness (RBE) of
the alpha particles in inducing lung cancer, relative to beta and gamma radiation. Prior to 1992, EPA's risk
estimates assumed an RBE of eight for estimating risks from alpha particles for all cancer sites. [In the
development of radionuclide slope factors published in 1992, the high-LET RBE for leukemia was reduced
from 8 to 1.117. EPA's revised methodology has adopted an RBE value of 20 for all cancer sites except
leukemia, for which an RBE of 1 is assigned and breast which is assigned an RBE of 10.]
The weighted average dose rates for each organ of interest are combined with the corresponding life table data
from Table C-4 and the age-specific radiogenic cancer risk values from Table C-3 to estimate the number of
radiation-induced excess cancers in the survivors in each risk interval, as illustrated in Table C-7. Under the
assumed exposure conditions, the expected number of attributable cancers in the cohort survivors is
approximately 0.3 cancers. Since this attributable cancer risk arises in an initial cohort of 100,000 persons,
the lifetime risk to an average individual initially in the cohort is 0.3/100,000, or 3.0E-6, or three chances in
C-17
-------
Table C-7. Derivation of Attributable Cancer Risk Resultin
from Chronic Inhalation of Pu-238 [1 pCi/y (0.037 Bq/y) constant intake rate]
;::":>::i^^l:MSiil:s
:l!:;.;:N:Sllb^el!^i[e1lsl£':^
;1;|| |f !ittifci!iP!l:
|;|pi|i^
li!liiftiei^^fefelia^^?S^
'^J^^M^Bf-
^^:^Gmce^:\ - .:
:,'••
0-9
10-19
20-34
35-49
50+
4.31 E-5
5.32E-5
5.33E-5
5.34E-5
5.35E-5
9.780E+5
9.71 9E+5
14.346E+5
1 3.841 E+5
23.070E+5
70.756E+5
8x120.19E-6
8 x 120.88E-6
8x 98.24E-6
8x 67.02E-6
8x 25.44E-6
4.05E-2
5.00E-2
6.01 E-2
3.96E-2
2.51 E-2
2.15E-1
^^^^^^^^^^^^^^^^^^^^^^^^^^^^S^^^^^^^^^^^^^^^^^M.^^'^-^^
0-9
10-19
20-34
35-49
50+
9.07E-8
1.12E-7
1.12E-7
1.12E-7
1.12E-7
9.780E+5
9.71 9E+5
14.346E+5
13.841 E+5
23.070E+5
70.756E+5
120.19E-6
120.88E-6
98.24E-6
67.02E-6
25.44E-6
1.07E-5
1.32E-5
1.58E-5
1.04E-5
6.57E-6
5.67E-5
;.o£i:?^ :'Vv'":"-,':
Lifetime attributable cancers in cohort = 0.3
Slope Factor = 0.3 attributable cancers/(70.756E+5 person-y x 1 pCi/y)
= 3.9E-8 attributable cancers/pCi inhaled
a million, in this example. This attributable cancer risk may be divided by the total exposure (intake) of the
cohort to estimate the radionuclide slope factor for inhalation of Pu-238 (Class Y) as follows:
SF = 0.3 attributable cancers / (70.756E+5 person-y x 1 pCi/y)
= 3.9E-8 attributable cancers/pCi inhaled
C.3.2.4 Example D: Ingestion of Sr-90. Example D considers the case of chronic ingestion of Sr-90 at a
constant rate of 1 pCi/y over a lifetime. It is assumed here that the chemical form of the Sr-90 is soluble in
the gastrointestinal tract, with a Gl-tract-to-blood absorption fraction (fj) of 0.3. Since strontium accumulates
preferentially in the skeletal tissues, the dose rates to these tissues exceed those for other body organs;
therefore, this example focuses on attributable risk of bone sarcoma and leukemia (red bone marrow). The
annual dose rates computed by RADRISK for these tissues increase with time, due to the accumulation of Sr-
90 in these tissues—i.e., the deposition and retention of Sr-90 in bone surfaces and red bone marrow greatly
exceeds its biological and radiological removal rate.
C-18
-------
Since the dose rates to bone surface and red marrow are not constant, average dose rates in each of the five risk
intervals are calculated. For each cancer site, the dose rate within each risk interval is calculated as a weighted
average based on the fraction of time spent by survivors in each age group within this risk interval.
Attributable cancer risk for this case is calculated as shown in Table C-8. In each risk interval, the average
dose rates are multiplied by the person-years of life expected for survivors in the time intervals over which
Table C-8. Derivation of Attributable Cancer Risk Resulting
from Chronic Ingestion of Sr-90 (1 pCi/y constant intake rate)
Risk Interval
Dose Rate
(rattfy)
Effective
Dutate &*-y)
Inteivai Risk Factor
(ratf1)
Attributable
Cancers
Leukemia
0-9
10-19
20-34
35-49
50+
2.96E-7
5.60E-7
6.28E-7
6.49E-7
6.51 E-7
9.78E+5
9.71 9E+5
14.346E+5
1 3.841 E+5
23.070E+5
70.756.E+5
77.69E-6
34.26E-6
48.06E-6
31.39E-6
41.20E-6
2.25E-5
1.86E-5
4.33E-5
2.82E-5
6.19E-5
1.75E-4
0-9
10-19
20-34
35-49
50+
4.89E-7
1.04E-6
1.27E-6
1.42E-6
1.47E-6
9.78E+5
9.71 9E+5
14.346E+5
13.841 E+5
23.070E+5
70.756E+5
3.09E-6
3.06E-6
2.99E-6
2.72E-6
1.58E-6
1.48E-6
3.09E-6
5.44E-6
5.35E-6
5.36E-6
2.07E-5
[ ete, for each of Hie 13 cancer sites 3
Lifetime attributable cancers in cohort = 2.3E-4
Slope Factor = 2.3E-4 attributable cancere/(70.756E+5 person-y x 1 pCi/y)
= 3.3E-11 attributable cancer/pCi ingested
the dose rate factors apply, to obtain the collective dose in the interval. These doses are multiplied by the
attributable cancer incidence risk per unit dose, obtained from Table C-3, to estimate the committed risk for
the interval. The sum of these products is divided by the total lifetime intake of the cohort, 70.756E+5 pCi,
to obtain the slope factor. Under the assumed exposure conditions, the expected number of attributable cancers
in the cohort survivors is approximately 2E-4 cancers; this represents an individual risk of approximately 2E-
4/1E+5, or 2E-9, or two chances in a billion, in this example. This attributable cancer risk may be divided by
the total exposure (intake) of the cohort to estimate the radionuclide slope factor for ingestion of Sr-90 as
C-19
-------
SF = 2.3E-4 attributable cancers / (70.756E+5 person-y x 1 pCi/y)
= 3.3E-11 pCi'1 ingested.
Note that this example considers ingestion of Sr-90 only. In the modified case where Sr-90 is assumed to be
in equilibrium with its radioactive daughter, Y-90, estimates of dose and risk are approximately 10% higher.
While RADRISK explicitly accounts for ingrowth of radioactive decay products following intake, it does not
address intake of multiple radionuclides.
C.4 INTERIM 1992 REVISIONS IN DOSE AND RISK MODELS
In 1992, radiological slope factors for inhalation and ingestion were revised consistent with recommendations
of the EPA Science Advisory Board (SAB) for the regulation of radionuclides in drinking water. These
changes included a reduction in the GI absorption factor (fj) for uranium radionuclides from 0.2 to 0.05,
incorporation of sinus carcinomas in the Ra-226 risk, an adjustment in the doses and resultant risks of bone
cancer and leukemia risks for Ra-228, a reduction in the leukemia risk from alpha radiation, and a recalculation
of the urinary system cancer risk based on the dose to both the kidney and the urinary bladder.
The changes to the radium risk estimates reflect three distinct corrections. First, the Agency's high-LET risk
calculated for leukemia was found to be high when compared to epidemiological studies of leukemia incidence
among radium dial painters exposed to Ra-226 and Ra-228, patients injected with Ra-224, and Thorotrast
patients. The epidemiological data for leukemia from the high-LET absorbed dose from alpha particles
indicate an average risk of approximately 5 x 10"5 rad"1, which is only 11.7% higher than the value for low-LET
risk. In order to correct this discrepancy, the high-LET leukemia risks calculated by RADRISK for all
radionuclides have been multiplied by a factor of 0.1396 to bring them in line with the bone marrow dyscrasia
observed in Ra-224, Ra-226 and Thorotrast patients. This corresponds to a reduction in the alpha particle
quality factor from 8 to 1.117 for leukemia.
Second, the SAB pointed out that neither the RADRISK model nor the ICRP publication 3 0 model from which
it was derived includes a calculation of the paranasal sinus and mastoid carcinomas that apparently result from
trapped Rn-222 gas produced by the decay of Ra-226. A contribution from these cancers was included by
assuming that their risk is equal to that of bone sarcoma and then adding this value to the total risk for an intake
of Ra-226.
Third, it was discovered that, contrary to ICRP and NRPB dosimetric estimates showing that Ra-228 may yield
a dose to bone 1.5 to 2.8 times higher than Ra-226, RADRISK calculates a lower risk of bone sarcoma from
Ra-228 than from Ra-226. This discrepancy was due to the choice of assumptions regarding the biokinetic
model for radioactive decay products—i.e., the RADRISK calculations assumed that each radioactive decay
product would be distributed and retained in body tissues according to the characteristics of that element,
whereas ICRP estimates assumed that all progeny would follow the biokinetic model of the parent
radionuclide. A multiplicative correction factor was used to make the relationship of these doses consistent
with those calculated for Ra-226 and Ra-228 by the ICRP publication 30 model and the NRPB model from
which both were derived.
The effect of the above changes was to lower the Ra-226 total mortality risk by 7% and increase the mortality
risk for Ra-228 by 0.3%, as indicated in Table C-9.
C-20
-------
Table C-9. Cancer Mortality Risk (Original and Revised Values)
from Lifetime Ingestton of ^Ra or 228Ra in Drinking Water
, ;--i;
Previous RADRISK values:
Bone sarcoma
Leukemia
All other
Total
1.85E-5
3.10E-5
4.40E-5
9.35E-5
8.53E-6
1.69E-5
4.48E-5
7.02E-5
Revised values:
Bone sarcoma
Sinus carcinoma
Leukemia
All other
Total
1.85E-5
1.85E-5
5.94E-6
4.39E-5
8.68E-5
1.90E-5
-
1.01E-5
4.48E-5
7.39E-5
Previously, the urinary system cancer risk was calculated on the basis of the dose to the kidney, even when the
dose calculated for the bladder was much lower. As a result, urinary cancer risks were appreciably over-
estimated for certain radionuclides, particularly uranium. To correct this problem, the risk estimates were
adjusted as follows:
adjusted mortality risk/original mortality risk - (l+C)/2.
adjusted incidence risk/original incidence risk = (H-2Q/3,
where C is the ratio of the bladder dose rate to the kidney dose rate. The corrections presumed: 1)
approximately equal excess relative risk per unit dose for kidney and bladder; 2) roughly equal baseline cancer
mortality rates for the two sites; and 3) an incidence rate for the bladder that is twice that for the kidney. In
the revised methodology, cancer risks to bladder and kidneys are calculated separately, so this adjustment is
not needed.
The adjusted leukemia, urinary and total risks for some selected uranium nuclides are listed in Table C-10.
For the uranium isotopes, the revised ingestion risks were reduced by a factor of 7 due to a lowering of the GI
absorption factor, fls from 0.2 to 0.05, and a reduction in leukemia and urinary cancer risk estimates. The
effect of these revisions on corresponding risk estimates for inhalation exposures are much smaller.
C-21
-------
Table C-10. Cancer Mortality Risk (Previous and Revised Values)
from Lifetime Ingestion of Uranium
Risk (Oeaths/MCi)
**u
^u
234g
KSy
238U
Previous RADRISK values (f, = 0.2):
Leukemia
Urinary
Total
4.27E-5
9.97E-5
1.90E-4
1.42E-5
4.34E-5
7.55E-5
1.42E-5
4.36E-5
7.48E-5
1.52E-5
4.00E-5
7.32E-5
1.93E-5
3.90E-5
7.40E-5
Revised values (f, = 0.05)
Leukemia
Urinary
Total
1.64E-6
1.25E-5
2.70E-5
5.02E-7
5.48E-6
1.12E-5
5.24E-7
5.41 E-6
1.11E-5
9.98E-7
5.03E-6
1.15E-5
2.30E-6
4.91 E-6
1.19E-5
C.5 REFERENCES
Bu81 Hunger, B., Cook, J.R. and M.K. Barrick, "Life Table Methodology for Evaluating Radiation
Risk: An Application Based on Occupational Exposure", Health Phys. 40 (4):439-455, 1981.
Co78 J.R. Cook, B.M. Bunger, and M.K. Barrick, A Computer Code for Cohort Analysis of
Increased Risks of Death (CAIRO). EPA 520/4-78-012, U.S. EPA, June 1978.
Du80 Dunning, D.E. Jr., R.W. Leggett, and M.G. Yalcintas, A Combined Methodology for
Estimating Dose Rates and Health Effects from Exposure to Radioactive Pollutants.
ORNI/TM-7105, Oak Ridge National Laboratory, Oak Ridge, TN, 1980.
EPA84 Environmental Protection Agency, Radionuclides: Background Information Document for
Final Rules. Volume I. EPA Report 520/1-84-022-1, US EPA, Office of Radiation Programs.
EPA89 Environmental Protection Agency, Risk Assessment Guidance for Superfund Volume 1
Human Health Evaluation Manual (Part A\ Interim Final, EPA/540/1-89/002, USEPA,
Washington, 1989.
EPA94 Environmental Protection Agency, Estimating Radiogenic Cancer Risks. J.S. Puskin and C.B.
Nelson, Office of Radiation and Indoor Air, EPA 402-R-93-076, June 1994.
Ko81 Kocher, D.C., Dose Rate Conversion Factors for External Exposure to Photons and Electrons.
NUREG/CR-1918, ORNL/NUREG-79, Oak Ridge National Laboratory, Oak Ridge, TN,
1981.
NAS80 National Academy of Sciences - National Research Council, The Effects on Populations of
Exposure to Low Levels of Ionizing Radiation. Committee on the Biological Effects of
Ionizing Radiation, (BEIR III), Washington, D.C., 1980.
NCHS73 National Center for Health Statistics, Public Use Tape, Vital Statistics - Mortality Cause of
Death Summary - 1970, PB80-133333, Washington, D.C., 1973.
NCHS75 National Center for Health Statistics, U.S. Decennial Life Tables for 1969-71. 1(1\ DHEW
Publication No. (HRA) 75-1150, U.S. Public Health Service, Rockville, Maryland, 1975.
C-22
-------
NCRP85 National Council on Radiation Protection and Measurements, Induction of Thvroid Cancer bv
Ionizing Radiation, NCRP Report No. 80, Washington, D.C., 1985,
NRC85 Nuclear Regulatory Commission, Health Effects Model for Nuclear Power Plant Accident
Consequence Analysis. NUREG/CR-4214. U.S. Nuclear Regulatory Commission,
Washington, DC, 1985.
SJ84 Sjoreen, A.L., D.C. Kocher, G.G. Killough, and C.W. Miller, MLSOIL and DFSOIL -
Computer Codes to Estimate Effective Ground Surface Concentrations for Dose
Computations. ORNL-5974, Oak Ridge National Laboratory, Oak Ridge, TN, 1984.
C-23
-------
-------
Appendix D
Calculational Methods for
Radiogenic Cancer Risk Estimates
D-l
-------
[This page is blank intentionally.]
D-2
-------
CONTENT
Section Page
D.I INTRODUCTION D-5
D.2 RISK MODEL FORMULATION D-6
D.3 RISKMODELS D-7
D.3.1 Risk model coefficients D-7
D.3.2 Time since exposure response function D-7
D.3.3 Age at expression function D-8
D.4 RISK CALCULATIONS D-8
D.4.1 Basic quantities D-8
D.4.2 Attributable lifetime risk coefficient D-10
D.4.3 Attributable lifetime loss coefficient D-10
D.4.4 Age-averaged coefficients D-l 1
DAS Sex-averaged coefficients D-l 1
D.4.6 Continuity considerations D-13
D.4.7 Cancer type and dose location associations D-13
0.4.8 Cancer incidence calculations D-l5
D.5 BASELINE FORCE OF MORTALITY CALCULATIONS D-15
D.6 RADIONUCLIDE RISK COEFFICIENTS D-16
D.6.1 Radiogenic Risk from Internal Exposure D-16
D.6.2 Radiogenic Risk from External Exposure D-18
D.7 RADIONUCLIDE SLOPE FACTOR CALCULATION D-18
0.8 REFERENCES D-19
D-3
-------
TABLES
Table
D-1 Target organs and tissues used by EPA for calculation of cancer risk
Page
D-14
D-4
-------
Appendix D
Calculations! Methods for Radiogenic Cancer Risk Estimates1
D.1 INTRODUCTION
A radiogenic cancer risk model defines the relationship between radiation dose and the subsequent force of
mortality (or morbidity) attributable to that dose. As such, the model provides the basis for calculating a time
(or age) varying rate coefficient in a death or disease process model. [General methods for structuring and
solving the differential equations representing such stochastic processes can be found elsewhere (Ch80).]
Thus, to calculate risks, the radiogenic risk model and other relevant quantities must be incorporated into a
suitable calculational procedure.
The risk calculations discussed in this section are for attributable risk. In this context, attributable risk is
defined as the likelihood of death from (or development of) cancer that, according to the risk model, is caused
by a radiation exposure. By way of comparison, the excess risk calculated in BEIR V (NAS90, Va89)
excludes the fraction of the attributable risk that represents deaths or cases among persons who would be
expected to die from (or to develop) cancer at a later age even if they had not been exposed.
The use of the attributable risk-per-unit-dose coefficients calculated here is limited to the asymptotic case, i.e.,
these coefficients can only be used for applications where the survival function is not significantly affected by
the doses being assessed. When this is not the case, risks must be calculated explicitly for the specific doses
under consideration.
Male and female survival data used in these calculations (up to an age of 110 y) are taken from the U.S.
Decennial Life Tables for 1979-1981 (NCHS85). These data were used to calculate a combined life table for
a male:female live birth ratio of 1.051. U.S. mortality data were extracted from 1979-1981 Vital Statistics
Mortality Data, Detail Tapes (NCHS82,83, 84). Deaths in these data files are classified according to the 9th
edition of the International Classification of Disease (ICD) codes (PHS80).
Radiogenic risk calculations require integrating functions of the risk model and vital statistics. The vital
statistics are discrete data, typically tabulated at one or five year intervals. Radiogenic risk models are usually
defined for several different age intervals and are inherently discontinuous. Previously, such risk model
calculations were implemented by adapting actuarial methods developed for life table calculations, e.g., the
CAIRD program (Co78) which is incorporated into the RADRISK code (Du80). The method used here is to
fit a cubic spline to discrete data and then to calculate interpolated values, derivatives, and integrals directly
1 The mathematical presentation in this section is adapted from Estimating Radiogenic Cancer Risks
(EPA94), and is reproduced here for the convenience of the reader.
D-5
-------
from the spline coefficients (de78, Fr82). This method admits almost any form of risk model and eliminates
most of the ad hoc approaches that were necessary with CAIRD. This revised calculational approach is
implemented in the CRDARTAB computer code (SJ94).
D.2 RISK MODEL FORMULATION
As noted in Section 2.2.3, there are two basic types of radiogenic cancer risk projection models: absolute risk
and relative risk. An absolute risk model presumes that the age-specific excess force of mortality (or
morbidity) due to a radiation dose is independent of cancer mortality or incidence rates in the population. It
can be written as
(D-l)
where
e(x,xe) — the excess force of mortality (or morbidity) (y"! Gy"1) at age x due to a dose at age xe
(x>xe),
tx(xj = the absolute risk coefficient (y"1 Gy"1), is a function of age at exposure, xe,
£(t,xj - the time since exposure (/ = x-x ) response function, can also be a function of x , and
y(x) = the age at expression response function.
The radiogenic risk models for bone, skin, and thyroid cancer in the current EPA methodology are all absolute
risk modeJs. In the previous methodology (i.e., for development of radionuclide slope factors prior to 1994),
absolute risk models were used for leukemia and bone cancer only.
A relative risk model presumes that the age-specific excess force of mortality (or morbidity) due to a radiation
dose is the product of an exposure-age-specific relative risk coefficient and baseline cancer mortality or
incidence rates in the population. The model can be written as
where
(D-2)
TI(X,XC) = the relative risk (Gy"1) at age x due to a dose at age xc (x > xe),
p(xj = the relative risk coefficient (Gy"1), is a function of age at exposure, xa
ffaxj = the time since exposure (t=x-x^ response function, may also be a function of x0 and
y(x) = the age at expression response function.
The radiogenic risk models for esophagus, stomach, colon, liver, lung, breast, ovary, bladder, kidney, leukemia,
and residual cancer sites in the current EPA methodology are all relative risk models. In the pre-1994
methodology, relative risk models were used for all solid cancers considered (i.e., thyroid, breast, lung,
esophagus, stomach, intestine, liver, pancreas, urinary, lymphoma, and residua! cancer sites).
D-6
-------
D.3 RISK MODELS
D.3.1 Risk model coefficients
Risk coefficients for the mortality risk models used in EPA's recently adopted methodology are shown in Table
3-1 of the main text. Absolute risk models are used for bone, skin, and thyroid cancers. Relative risk models
are used for all other cancers. Corresponding risk coefficients for estimating attributable cancer incidence risk
may be obtained by adjusting the mortality values by the appropriate lethality fraction for the cancer site of
interest (see Table 3-1).
Risk coefficients for the pre-1994 methodology risk models are presented in Appendix C. Absolute risk
models were used for leukemia and bone cancers, and relative risk models were used for all other cancer sites.
Corresponding risk coefficients for estimating excess cancer incidence risk may be obtained by adjusting the
mortality values by the appropriate lethality fraction shown in Table C-l for the cancer site of interest.
D.3.2 Time since exposure response function
The time since exposure (TSE) response function for all cancers except bone, thyroid, and leukemia has a 10
y minimal latency period and a lifetime plateau, i.e.,
C(0 = 0, t<\0
= i,
For bone cancer, a 2 y minimal latency period and a 25 y plateau period are assigned, i.e.,
ttO = 0, t<2
= 1, 2
-------
For leukemia, the TSE function developed by the NIH Working Group for the Radioepidemiology Tables
(N1H85) is used. The Working Group fitted lognormal response functions for time since exposure greater than
a minimal latency of 2 years to A-bomb survivor data for both chronic granulocytic leukemia (CGL) and acute
leukemia (AL). These response functions can be expressed as follows:
t<2
2
-------
D.4 RISK CALCULATIONS
D.4.1 Basic quantities
• S(x), the survival function, is the fraction of live born individuals expected to survive to age x.
S(Q)=1, and decreases monotonically for increasing values of*. S(x) is obtained by fitting a cubic
spline to the decennial life table values to provide a continuous function of x.
* fi is the expected lifespan at birth (age 0).
• S(x) is the life expectancy (expected lifetime remaining) (years) for an individual who has attained
age x. It is given by
— Ts(u)du .
(D-9)
ja(x) is the force of mortality or hazard rate (y ') at age x. Without a subscript, it is usually the total
rate from all causes. A subscript is used (unless it is clear by context) to indicate a specific cause, i.e.,
all i
S(x) is directly dependent on ft(x) since
i(«)AO . (D-ll)
When the baseline force of mortality n0(x) is incremented by pfc), S(x) becomes
S(x) = exp
= 50(x) Sfx) ,
where
D-9
-------
and
For sufficiently small values ofpfc), S,{x) approaches a value of 1 for all values of x, i.e., SB(x) and S(x) are
essentially the same. For most environmental radiation risk assessment cases of practical interest, the
increment of risk due to radiation satisfies this condition.
D.4.2 Attributable lifetime risk coefficient
The age-specific attributable lifetime risk (ALR) coefficient, r(x), is the risk per unit dose of a subsequent
cancer death (Gy"1) due to radiation received at age x. For an absolute risk model, the asymptotic ALR
coefficient is
Similarly, for a relative risk model,
These age-specific coefficients are principally used to calculate age-averaged coefficients and risks from
radionucJide intakes or exposures.
D.4.3 Attributable lifetime loss coefficient
The attributable lifetime loss (ALL) coefficient e(x), at age x, is the expected lifetime loss per unit dose (y Gy'1)
for a radiation dose at age x. For an absolute risk model, the asymptotic ALL coefficient is
D-10
-------
For a relative risk model,
efx) = -^-f'r\f.u)}ijiu)S(u)S0(u)du . (D-18)
SQ(x)J*
D.4.4 Age-averaged coefficients
The lifetime age-averaged risk and life loss coefficients are
r(x)S(x)dx
r =
f~S(x)d
Jo
and
(D-20)
f~S(x)d
JO
respectively. Since the age distribution of a stationary population is proportional to S(x), the stationary-
population weighted average values are identical to the lifetime age-averaged ones. When the coefficients are
averaged over a specific age interval, e.g., for assessing childhood or occupational exposures, the limits of
integration in both the numerators and the denominators of these expressions are changed accordingly.
D.4.5 Sex-averaged coefficients
Since radiogenic cancer risk models are generally sex-specific, the resulting risk coefficients must be averaged
for use in assessing risk to a combined population. This is accomplished by presuming a male:female sex ratio
for live births of 1.051. Since S(x) is sex-specific, the sex ratio is a function of age. The combined (sex-
averaged) survival function is
D-11
-------
1.051
where the subscripts m,f, and c refer to the male, female, and combined values respectively.
Similarly, the expected combined lifetime is
1.051 8 + §f
§_ = 5 / .
(D-22)
2.051
Tlie combined age-specific force of mortality must reflect the age-specific contribution of each sex. Hence,
1.051 S(x)u. (x) + S.
c
1.051 Sm(x)+ Sfx)
Combined age-specific ALR and ALL coefficients are
1.051
and
,.051
respectively. Combined age averaged ALR and ALL values must reflect the expected lifetime over the age
interval. The lifetime average combined ALR and ALL coefficients are
i.osi § + e,
m f
and
D-12
(D-26)
-------
e =
1.051 § e + §f ef
mm f f
1.051 8 + 8f
(D-27)
D.4.6 Continuity considerations
While the integration of a smoothly varying function using a spline is straightforward, the radiogenic cancer
models are inherently discontinuous. For example, the time since exposure function for most solid cancers
typically has a value of zero for times since exposure that are less than the 10 y minimal latency and a value
of one for times equal to or greater than the minimal latency. Suppose that the function to be integrated (the
integrand) is fitted at one year increments. For the Revised Methodology models, the function will change
abruptly from a value of zero for times since exposure less than 10 y to a generally smoothly varying function
of time for times equal to or greater than 10 years. However fitting a spline to the integrand provides a
continuous transition from the value at 9 y to the value at 10 y. If the integral is evaluated on the basis of these
spline coefficients, it will include an unintended contribution from this interval.
One way to solve the problem is to integrate functions in piece-wise continuous intervals. This method is
exact and would work well for the simple example considered above. In general, however, the value of the
integrand at each discontinuity depends on the interval of integration; the method becomes unwieldy for
situations with many discontinuities. An alternative method for situations where the function is reasonably
smooth on either side of a discontinuity is to replace the value of the function at the discontinuity with the
average of the values immediately above and below it. For the case above, the value of the time since exposure
response function at 10 y is changed from 1 to (0+1)/2=0.5. The reduced excess in the integral between 9 and
10 y is then compensated for by a comparable reduction in the 10 to 11 year interval. This discontinuity
smoothing method was used to calculate the risks and lifetime losses for use in the development of
radionuclide slope factors.
D.4.7 Cancer type and dose location associations
The dose locations associated with each cancer type are shown in Table D-l. When more than one dose
location is shown in the table, risks are calculated for a weighted mean of the doses at these locations using
the weights shown in the table. The residual cancer category represents a composite of primary and secondary
cancers that are not otherwise considered in the model. The dose location associated with these cancers, the
pancreas, was chosen to be generally representative of soft tissues; the pancreas is not considered the origin
of all these neoplasms.
D-13
-------
Table D-1. Target organs and tissues used by EPA for calculation of cancer risk
Cancer Site
EPA Revised
Esophagus
Stomach
Colon
Liver
Lung
Bone
Skin
Breast
Ovary
Bladder
Kidney
Thyroid
Leukemia
Residual
Dose Tissue (target organ)
Methodology
Thymus
Stomach wall
Upper large intestine wall
Lower large intestine wall
Liver
Tracheo-bronchial region
Pulmonary region
Bone surface
Skin (dermis)
Female breast
Ovary
Urinary bladder wall
Kidney
Thyroid
Red bone marrow
Pancreas
Weighting
Factor
1.0
1.0
0.5
0.5
1.0
0.8
0.2
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
EPA Pre-1994 Methodology
Leukemia
Bone
Thyroid
Breast
Lung
Esophagus '
Stomach
Intestine
Liver
Pancreas
Urinary 2
Lymphoma '
Other
Red bone marrow
Bone surface
Thyroid
Breast
Pulmonary region
-
Stomach wall
Small intestine wall
Upper large intestine wall
Lower large intestine wall
Liver
Pancreas
Kidney2
Urinary bladder wall
-
Pancreas
1.0
1.0
1.0
1.0
1.0
-
1.0
0.2
0.4
0.4
1.0
1.0
0.5
0.5
-
1.0
1 Included in "Other".
2 Prior to 1992, urinary cancer risk was calculated based on the kidney dose rates only, even when
the dose to bladder was much lower, which led to overestimates of urinary cancer risk for certain
radionuclides.
D-14
-------
D.4.8 Cancer incidence calculations
While the calculational methodology outlined above could be used with incidence models and force of
morbidity data, the method used for the Revised Methodology is to divide the mortality risk coefficient by
a corresponding lethality factor, k, shown in Table 3-4. An exception is made for skin; only mortality is
considered for calculating skin cancer incidence, i.e., k is considered to be 1. The lifetime loss coefficient
is not recalculated for incidence.
D.5 BASELINE FORCE OF MORTALITY CALCULATIONS
Age-specific mortality rates (force of mortality) were calculated at one year intervals using U.S. mortality data
for the period 1979-1981 (NCHS82, 83, 84). These calculations assume that the fraction of the recorded
deaths in each age group due to a given cause, e.g., a specific ICD code, is the same as the probability of death
in that age interval for a birth cohort with the corresponding age-specific death rate. In summary,
Let: n, be the number of deaths due to all causes between ages jcw and x,,
ntj be the number of deaths due to causey between ages *,-_, and *„
mt be the probability in a birth cohort of dying from all causes between ages x,., and xh
mi} be the probability in a birth cohort of dying from causey between ages xw and x,.
Then, given the age-specific forces of mortality, ft(x) and p/x), and the survival function, S(x),
m. = r^(x)S(x)dx = S(xn}~ S(x) , (D-28)
and
(D-29)
m =
(For M), xh n^ nlp m, and m^are all equal to 0 as well.) Let M(x) be the probability in a birth cohort of dying
from causey by age xh i.e.,
D-15
-------
(D-30)
k 0
Differentiating the expression for M/x) with respect to x,
Solving for the force of mortality,
Hence, point estimates afp/x) can be calculated by fitting a spline to M/x), calculating its derivative with
respect to x from the spline coefficients, and dividing the derivative by the value of the survival function at x,
D.6 RADIONUCLIDE RISK COEFFICIENTS
D.6 A Radiogenic Risk from Internal Exposure
D.6.1.3 Age-specific radionuclide risk calculations. The age-specific cancer risk attributable to a unit intake
of a radionuclide (Bq1) is calculated from the absorbed dose rate due to a unit intake of activity and the age-
specific risk per unit dose coefficient. The calculation is specific for each cancer and associated absorbed dose
site in the risk model. The complete calculation may involve the sum of contributions from more than one
tissue (see Table D-l) and from both low- and higfcLET absorbed doses. (Except for leukemia, the Revised
Methodology radiogenic cancer risk relative biological effectiveness (RBE) for a high-LET absorbed dose from
alpha radiation is 20 times that for a low dose, low dose rate.low-LET absorbed dose; for leukemia, the alpha
dose RBE is I. Previously the EPA methodology assigned a RBE of 8 to the high-LET absorbed dose from
alpha radiation for all cancers; in 1992, the high-LET RBE for leukemia was revised from 8 to 1.117.) Each
risk contribution is calculated as follows:
(D-33)
^ '
where
D-16
-------
rjxj = the cancer risk coefficient (Bq'1) for a unit intake of activity at age xh
d(x) = the absorbed dose rate (Gy y1) at the site at age x due to a unit intake of activity at
agex"'' i , .
r(x) = the cancer risk due to a unit absorbed dose (Gy1) at the site at age x, and
S(x) = the survival function at age x.
The integration is terminated at 110 years due to the characteristics of the survival function, i.e., no member
of the exposed population is assumed to live more than 110 years.
D.6.1.2 Sex-averaged risk coefficient. Age-specific male and female risk coefficients are combined by
calculating a weighted mean:
- m
1.051 S(x)+ S
where
ra(x) = the combined cancer risk coefficient (Bq'1) for a unit intake of activity at age xh
1.051 - the presumed sex ratio at birth (male:female),
r^jfy = the male risk per unit activity at age xt,
rfa(x) = the female risk per unit activity at age *„
SJxJ = the male survival function at age xh and
S/xj = the female survival function at age x(.
This formulation weights each sex-specific risk coefficient by the proportion of that sex in a stationary
combined population at the desired age of intake.
D.6.1.3 Lifetime average radionuclide risk coefficient. The lifetime average risk coefficient (Bq-i) for a unit
lifetime intake of a radionuclide at a constant intake rate is calculated from the age-specific value by the
equation:
r - .
-------
1.051 r 8 + r, 8,
ma m fa f
1.051* +Sf
m f
D.6.2 Radiogenic Risk from External Exposure
Risk coefficients for external radiation exposure pathway are calculated in a manner analogous to that
presented for internal exposure pathways in Section D.6.I. External exposure risks are calculated based on
the absorbed dose rate attributable to a chronic exposure to a unit concentration of the radionuclide of interest
uniformly distributed in contaminated soil, rather than the unit intake considered for internal exposures. The
calculation is specific for each cancer and associated absorbed dose site in the risk model, and may involve
the sum of contributions from more than one tissue. For the external exposure pathway, only low-LET
absorbed doses are considered.
The lifetime average risk coefficient [(Bq/g)'1] for a lifetime exposure to a unit concentration of a radionuclide
uniformly distributed in soil is calculated from the age-specific value by the equation:
r =
(D-37)
where
ra (Bq~l) - the average lifetime risk per unit concentration of activity in soil, and
§ = the expected lifetime at age 0, as defined above.
Sex-averaged risk coefficients are calculated in the same manner as for internal exposure pathways, based on
a male:female ratio of 1 .05 1 .
D.7 RADIONUCLIDE SLOPE FACTOR CALCULATION
For each radionuclide and exposure pathway, the slope factor, SF, is computed as the summation of the
individual cancer risks, Fa, described above:
Sf = E re , (D_38)
where
(Bq~') - the average lifetime risk per unit intake of activity (for internal exposures) or per unit
radionuclide concentration in soil (for external exposure) for cancer site a,
D-18
-------
SF = (Bq-1 for internal exposure pathways, (B<^g) for external exposure) is the
radionuclide slope factor for the given radionudide and exposure pathway of interest,
and the summation is performed over all cancer sites.
D.8 REFERENCES
Ch80 Chiang, C.L., An Introduction to Stochastic Processes and Their Applications. Robert E. Krieger
Publishing Company, Inc., Huntington, NY, 1980.
Co78 J.R. Cook, B.M. Bunger, and M.K. Barrick, A Computer Code for Cohort Analysis of Increased
Risks of Death (CAIRD1. EPA 520/4-78-012, U.S. EPA, June 1978.
de78 de Boor, C., A Practical Guide to Splines. Applied Mathematical Sciences Vol. 27, Springer-
Verlag, New York, NY, 1978.
Du80 Dunning, D.E. Jr., Leggett, R.W., and Yalcintas, M.G., A Combined Methodology for Estimating
Dose Rates and Health Effects from Exposure to Radioactive Pollutants. ORNL/TM-7105, 1980.
EPA94 Environmental Protection Agency, Estimating Radiogenic Cancer Risks. J.S. Puskin and C.B.
Nelson, Office of Radiation and Indoor Air, EPA 402-R-93-076, June 1994.
Fr82 Fritsch, F.N. and J. Butland, A Method for Constructing Local Monotone Piecewise Cubic
Interpolants. UCRL-87559, Lawrence Livermore National Laboratory, April 1982.
NAS90 National Academy of Sciences - National Research Council, Health Effects of Exposure to Low
Levels of Ionizing Radiation - BEIR V. National Academy Press, Washington, DC, 1990.
NCHS82 National Center for Health Statistics, Vital Statistics Mortality Data. Detail. 1979. PB82-132340,
U.S. Department of Health and Human Services, Public Health Service, National Center for Health
Statistics, Hyattsville, MD, 1982.
NCHS83 National Center for Health Statistics, Vital Statistics Mortality Data. Detail. 1980. PB83-261545,
U.S. Department of Health and Human Services, Public Health Service, National Center for Health
Statistics, Hyattsville, MD, 1983.
NCHS84 National Center for Health Statistics, Vital Statistics Mortality Data. Detail. 1981. PB84-213008,
U.S. Department of Health and Human Services, Public Health Service, National Center for Health
Statistics, Hyattsville, MD, 1984.
NCHS85 National Center for Health Statistics, U.S. Decennial Life Tables for 1979-1981. Vol. 1 No. 1,
United States Life Tables. (PHS) 85-1150-1, U.S. Department of Health and Human Services,
Public Health Service, National Center for Health Statistics, Hyattsville, MD, August 1985.
NIH85 National Institutes of Health, Report of the National Institutes of Health Ad Hoc Working Group
toDeve]opRadioepidemiologicalTables.NlHPublicationNo.85-2748,U.S.GovernmentPrinting
Office, Washington, DC 20402, p 92, 1985.
D-19
-------
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