OFFICE OF WATER
EPA-822-R-96-0Q5
UNCERTAINTY ANALYSIS OF RISKS ASSOCIATED WITH
EXPOSURE TO RADON IN DRINKING WATER
Prepared hy
U.S. Environmental Protection Agency
Office of Science and Technology
Office of Radiation and Indoor Air
Office of Policy, Planning and Evaluation .
March 1995
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DISCLAIMER
The original darft of this document, dated January 1993, has been officially reviewed by the Radiation
Advisory Commmittee (RAC) of the Science Advisory Board and EPA offices. This is the revised version
based on the comments from RAC and EPA offices.
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CONTRIBUTORS
The U.S. Environmental Protection Agency (EPA) Office of Science and Technology (OST) in the Office
of Water was responsible for the preparation of this document. The overall direction of product efforts
was provided by Margaret Stasikowski and Jennifer Orme-Zavaleta, the Director and Associate Director
of Health & Eccological Criteria Division of Office of Science and Technology.
The documentt was compiled by Roy F. Weston, Inc and Life Systems, Inc., working as a subcontractor
to Wade Miller Associates, under EPA Contract No. 68-C3-0342.
Project Manager: Ms. Lisa Almodovar, U.S. EPA
Office of Water
Task Manager: Dr. Nancy Chiu, U.S. EPA
Office of Science and Technology
Authors: Dr. Timothy Barry, U.S. EPA
Office of Policy, Planning and Evaluation
Dr. William J. Brattin,
Roy F. Weston, Inc.
Dr. Nancy Chiu, U.S. EPA
Office of Science and Technology
Dr. Jerry Puskin, U.S. EPA
Office of Radiation and Indoor Air
The following individuals have contributed to the document by providing technical review or assistance:
Jan Auerbach
Andrew Braun
Mike Conlon
Fanny Ennever
Jonas Geduldig
Helen Jacob
Arnold Kuzmack
Henry Kahn
Bruce Mintz
Jeffrey Mosher
Christopher Nelson
Neal Nelson
Marc Parrotta
Kathleen Stralka
Jim Cogliano
Karen Hammerstrom
Ron Mosley
James Repace
Andrew Ulsamer
Paul White
EPA, Office of Groundwater and Drinking Water
Life Systems, Inc.
EPA, Office of Groundwater and Drinking Water
Life Systems, Inc.
EPA, Office of Radiation and Indoor Air
EPA, Office of Science and Technology
EPA, Office of Science and Technology
EPA, Office of Science and Technology
EPA, Office of Science and Technology
Wade Miller Associates
EPA, Office of Radiation and Indoor Air
EPA, Office of Radiation and Indoor Air
EPA, Office of Groundwater and Drinking Water
Science Applications International Corporation
EPA, Office of Health and Environmental Assessment
EPA, Office of Health and Environmental Assessment
EPA, Air and Energy Engineering Research ilaboratory
EPA, Office of Health and Environmental Assessment
EPA, Office of Science, Planning, and Regulatory Evaluation
EPA, Office of Health and Environmental Assessment
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TABLE OF CONTENTS
PAGE
DISCLAIMER j
LIST OF FIGURES v
LIST OF TABLES vi
EXECUTIVE SUMMARY ES-I
1.0 INTRODUCTION i-1
1.1 Background l-i
1.1.1 Proposed Rule for Radionuclides in Drinking Water 1-1
1.1.2 Recommendations from the Science Advisory Board 1-2
1.1.3 Chafee Amendment 1-3
1.2 Quantitative Uncertainty Analysis Report 1-3
2.0 METHODS FOR QUANTIFYING UNCERTAINTY 2-1
2.1 Inhalation of Radon Gas 2-1
2.1.1 Estimate in the Proposed Rule 2-1
2.1.2 Revisions Since the Proposed Rule 2-2
2.2 Inhalation of Radon Progeny " 2-3
2.2.1 Estimate in the Proposed Rule 2-3
2.2.2 Revisions Since the Proposed Rule 2-5
2.3 Ingestion of Radon in Drinking Water 2-5
2.3.1 Risk Estimate in the Proposed Rule 2-5
2.3.2 Revisions Since Proposed Rule 2-8
2.4 Summary: Comparison of Fatal Cancer Risk Estimates in the Proposed
Rule and Estimates Derived with Revised Methodologies 2-15
2.4.1 Fatal Cancer Risk Estimates in the Proposed Rule 2-15
2.4.2 Fatal Cancer Risk Estimation by Revised Methodology 2-15
continued-
i»i.
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Table of Contents - continued
JE&QE
3.0 . METHODS FOR CHARACTERIZING AND QUANTIFYING UNCERTAINTY
3.1 Sources of Uncertainty 3-1
3.2 Types of Uncertainty 3-1
3.3 Quantitative Approaches to Characterizing Uncertainty in Radon Risks ...... 3-2
3.3.1 Variable Specification: PDFs 3-2
3.3.2 PDF Selection 3-3
3.3.3 Uncertainty Analysis 3-8
3.3.4 Sensitivity Analysis • 3-10
4.0 VARIABILITY AND UNCERTAINTY IN RISK FROM INHALATION OF RADON
PROGENY FORMED FROM RADON RELEASED FROM 4-1
4.1 One-Compartment Method 4-2
4.1.1 Basic Equations 4-2
4.1.2 Probability Density. Functions (PDFs) 4-3
4.1.3 Results 4-12
4.1.4 Sensitivity Analysis 4-14
4.2 Three-Compartment Model Method 4-14
4.2.1 Model Description 4-15
4.2.2 Monte Carlo Implementation of the Model 4-16
4.2.3 Results 4-16
4.3 Comparison of One- and Three-Compartment Models 4-18
5.0 VARIABILITY AND UNCERTAINTY IN EXPOSURE TO RADON GAS
RELEASED FROM HOUSEHOLD WATER 5-1
5.1 One-Compartment Method .• ' 5-1
"5.1.1 Basic Equation 5-1
5.1.2 Probability Density Functions (PDFs) 5-2
5.1.3 Results 5-2
5.1.4 Sensitivity Analysts 5-3
5.2 Three-Compartment Model Method 5-3
5.2.1 Results 5-4
5.2.2 Sensitivity Analysis 5-4
continued-
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Table of Contents - continued
page
5.3 Comparison of One- and Three-Compartment Models 5-5
5.4 Estimated Population Risk 5-5
6.0 VARIABILITY AND UNCERTAINTY IN RISK FROM INGESTION OF
RADON PRESENT IN WATER 6-1
6.1 Basic Equations 6-1
6.2 Probability Density Functions 6-2
6.2.1 Volume Ingested (V) 6-2
6.2.2 Fraction Not Volatilized (F) 6-3
6.2.3 Ingestion Risk Factor 6-4
6.2.4 Summary of PDFs 6-11
6.3 Results 6-11'
6.4 Sensitivity Analysis 6-13
6.4.1 Local Rate of Change 6-13
6.4.2 Partial Rank Order Correlation Coefficients 6-13
7.0 RELATIVE MAGNITUDE OF THE RISK FROM RADON IN WATER COMPARED
TO NON-WATER SOURCES OF RADON 7-1
7.1 Combined Risks from Radon in Water 7-1
7.2 Exposure and Risk from Radon in Outdoor Air 7-2
7.2.1 Average Outdoor Exposure 7-2
7.2.2 Unit Risk 7-6
7.2.3 Population Risk 7-6
7.3 Exposure and Risk from Radon in Indoor Air 7-7
7.4 Relative Magnitude of Risks from Radon in Water 7-7
7.5 Effect of Alternative MCL Values 7-7
8.0 REFERENCES 8-1
APPENDIX PAGE
1 Properties of Some Useful Distribution Functions A1-1
2 Statistical Properties of the Lognormal Distribution A2-1
3 Mathematical Details of the Three Compartment Model A3-1
4 Selection of PDFs for Three-Compartment Model Variables A4-L
5 Uncertainty in Organ-Specific Cancer Fatality Risk Per Unit Radiation Dose A5-1
V
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LIST OF FIGURES
figure
ES-1
ES-2
3-1
44
4-2
4-3
4-4
4-5
4-6
4-7
4-8
4-9
4-10
5-1
5-2
5-3
5-4
6-i
6-2
6-3
6-4
7-1
PAGE
Estimated Annual Cancer Deaths by Exposure Pathway Attributable to
Waterborne Radon Using the One-Compartment Model ES-
Annual Deaths Avoided as a Function of Maximum Contaminant Level ES-
20 Plausible Realizations of an Uncertain Cumulative Density Function 3-
Credible Interval for the Distribution of Radon Progeny Inhalation
Unit Dose Estimated from One-Compartment Model 4-
Credible Interval for the Distribution of Radon Progeny Inhalation
Unit Risk Estimated from One-Compartment Model 4-
Credible Interval for the Distribution of Radon Progeny Inhalation
Individual Risk Estimated from One-Compartment Model 4-
Example Concentration Profile for Radon Gas and Radon Progeny in the
Shower Estimated by 3-Cotnpartment Model 4-
Credible Interval for the Distribution of Radon Progeny Unit Dose
Estimated from 3-Compartment Model 4-
Credible Interval for the Distribution of Radon Progeny Unit Risk
Estimated from 3-Compaitment Model 4-
Credible Interval for the Distribution of Radon Progeny Individual Risk
Estimated from 3-Compartment Model 4-
Partial Rank-Order Correlation Coefficients for the Parameters in the
3-Compartment Model for Radon Progeny Individual Risk 4-
Comparison of One-Compartment and Three-Compartment Model Estimates for
Individual Inhalation Risk for Radon Progeny 4-
Credible Interval for the Distribution of Radon Gas Inhalation Unit
Dose Estimated from One-Compartment Model 5-
Credible Interval for the Distribution of Radon Gas Inhalation Unit
Dose Estimated from 3-Compartment Model 5-
Estimated Partial Rank-Order Correlation Coefficients for the Parameters
in the 3-Compartment Model for Radon Gas 5-
Comparison of Unit Dose Estimates from One-Compartment and
Three-Compartment Models for Inhalation Exposures to Radon Gas ' 5-
Credibie Interval for the Distribution of Radon Gas Ingestion Unit
Dose Estimated from One-Compartment Model 6-
Credible Interval for the Distribution of Radon Gas Ingestion Unit
Dose Estimated from One-Compartment Model 6-
Credible Interval for the Distribution of Radon Gas Ingestion Individual
Risk Estimated from One-Compartment Model 6-
Partial Rank-Order Correlation Coefficients for Ingestion Exposures
to Radon Gas Using 1-Compartment Model - 6-
Credible Interval for the Distribution of Combined Unit Risk (inhalation
and Ingestion) Estimated from One-Compartment Model 7-
continued-
jh
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List of Figures - continued
FIGURE PAGE
7-2 Credible Interval for the Distribution of Combined Individual Risk
(Inhalation and Ingestion) Estimated from One-Compartment Model 7-
7-3 Estimated Annual Cancer Deaths by Exposure Pathway Attributable to
Waterborne Radon Using the One-Compartment Model 7-
7-4 Annual Deaths Avoided as a Function of Maximum Contaminant Level 7-
\£ir
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LIST OF TABLES
TABLE PAGE
2-1 Summary of Proposed and Revised Calculations of Unit Risk from
Inhalation of Radon Progeny 2-
2-2 Ingested Radon Doses (rads/pCi) and Variation for Individual Organs 2-
2-3 Ingestion Doses and Risks by Cancer Site 2-
2-4 ' " Risk Per Unit Dose Estimates (Fatalities/Low-Let Rad) . . 2-
2-5 Summary of Proposed and Revised Calculations of Unit Risk from
Ingested Radon Gas 2-
2-6 Summary of Proposed and Revised Risk Estimates for Radon in Water 2-
4-1 Summary of the Distributions for Variables Used in Calculation of
Water to Air Transfer Factor 4-
4-2 Summary of Measured and Calculated Transfer Factors 4-
4-3 Summary of the Uncertainty in the Risk Factor for Radon Progeny 4-
4-4 Radon Occurrence Data for Non-Transient, Community Ground Water
Supply Systems 4-
4-5 Summary of Inhalation Unit Risk Input Distribution Functions 4-
4-6 Variability and Uncertainty in Inhalation Exposure and Risk to Radon
Progeny Estimated Using One-Compartment Model 4-
4-7 Variability and Uncertainty in Inhalation Exposure and Risk to Radon
Progeny Estimated Using Three-Compartment Model 4-
4-8 Rate of Change in Radon Progeny Individual Risk Estimate Calculated
Using the Three-Compartment Model 4-
5-1 Variability and Uncertainty in Unit Dose for Radon Gas 5-
5-2 Local Rate of Change in Radon Gas Unit Dose Estimated Using the
Three-Compartment Model 5-
6-1 Summary of Data on Water Ingestion Rates 6-
6-2 Reported Volatilization Fractions for Direct Tap Water 6-
6-3 Uncertainty Associated with Organ Doses 6-
6-4 Uncertainty Distributions for Factors Affecting the Estimates of Alpha
Particle Risk to the Stomach, Colon, and Lung , 6-
6-5 Uncertainties in Radon Ingestion Risk Factors 6-
6-6 Summary of Distribution Functions Used to Evaluate Exposure and Risk
from Ingestion of Radon 6-
6-7 Variability and Uncertainty in Ingestion Exposure and Risk to Radon Gas .... 6-
7-1 Variability and Uncertainty in Combined Exposure and Risk from
Radon in Water
7-2 Estimated Annual LCD from Radon in Indoor Air .
7-3 Detailed Summary of Uncertainty in Inhalation Risk Factor . . . .
7-4 Detailed Summary of Risk Estimates for Radon in Indoor Air . .
7-5 Relative Magnitude of Radon Risks .
viii
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EXECUTIVE SUMMARY
1.0 BACKGROUND
In accord with the authority and requirements of the Safe Drinking Water Act, the U.S.
Environmental Protection Agency (EPA) has published a Proposed Rule for radionuclides in drinking
water. Because radionuclides are classified as Group A carcinogens (known to cause cancer in
humans), the Rule proposed to establish a Maximum Contaminant Level Goal (MCL) of zero for each
radionuclide. However, because it is not feasible to attain a level of zero, the Rule proposed a non-
zero Maximum Contaminant Level for each radionuclide. The proposed value for radon is
300 pCi/L. This proposed MCL is based in part on calculations which indicate that there is
significant cancer risk to the U.S. population from current levels of radon in drinking water. The
purpose of this document is to summarize the calculations which have been performed to estimate the
cancer fatality risk from radon in water for exposed populations served by community ground water
supplies, and to provide a quantitative analysis of the uncertainty associated with the calculations.
2.0 ORIGINAL RISK CALCULATIONS AND RECENT CHANGES
Risk from radon in drinking water may arise from three distinct exposure pathways: (1) radon in
water may volatilize into indoor air and be inhaled as such; (2) radon in indoor air decays to
radioactive progeny, and these progeny may be inhaled; and (3) water containing radon may be
directly ingested before the radon volatilizes. Because exposure and dosimetry are different for each
of these pathways, the risks from radon are estimated by calculating die risk tor each pathway
separately, and then summing the risks.
ESri
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The risk estimates which were performed to support the Proposed Rule are summarized in Table ES-
1. Since the time the Proposed Rule was developed and published in the Federal Register, the EPA
has used new data on radiation dosimetry and risk to improve the accuracy of the calculations.
Specifically, an NAS reevaluaxion of the relative dosimetry of radon decay products in mines and
homes suggested that the dose per pCi/L of radon in air may be 20-30% lower in homes than mines.
(This finding was mentioned in the Proposed Rule.) Consequently, the estimated fatal lung cancer
risk via inhalation of radon progeny was changed from 360 lung cancer deaths (led) per 10^ person-
WLM to 224 led per 106 person-WLM. The risk factor for ingested radon has also been revised,
based on revised organ-specific risk coefficients and additional modifications of intestinal and lung
dosimetry treatment. The result was to increase the risk factor by a factor of 2.3, mostly because of
increased estimates of dose to stomach and colon. These new risk estimates are also shown in Table
ES-1. The uncertainty analysis describe! below is based on the revised risk estimates for inhalation
of radon progeny and ingestion of radon gas.
3.0 BASIC METHODS OF UNCERTAINTY ANALYSIS
The risk from exposure to radon by a pathway such as inhalation of radon progeny or ingestion of
radon in water is calculated by multiplying together a series of terms which describe radon
concentration levels, human exposure levels, radiological dose per unit exposure, and cancer risk per
unit radiological dose. Each of these terms is based on the best available data, but there is
uncertainty in each of the values. This uncertainty is of two basic types. The first type is due to
natural variability in a term. For example, there can be large differences between public water
systems in the concentration of radon present in water, differences between houses in the amount of
radon which builds up in indoor air, and differences between people in the amount of radon they
breathe in their home or ingest in the water they drink. The second type of uncertainty is due to lack
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of knowledge about the true value of some parameters. For example, there is uncertainty about the
true mean drinking water intake rate, the true average concentration of radon in water, the true mean
fraction of time spent in the house, etc. It is important to recognize the difference between variability
and uncertainty, because each may have different impacts on risk management decisions. In this
document, variability (differences between people, houses, water systems, etc.) is designated with the
subscript "v", while uncertainty due to lack of knowledge is designated by the subscript "u".
Both the variability and the uncertainty in a parameter can be described by probability density
functions (PDFs). A PDF is a mathematical expression which gives the probability that the variable
will have any specific value or range of values. There are many different types of PDF. including the
familiar normal and lognormal distributions, as well as other types such as triangular, uniform,
empirical, and beta. Each PDF is specified by one or more parameters. For example, each normal
PDF is specified by a mean and standard deviation. Choice of the best PDFs to characterize the
variability and uncertainty in a variables depends on what is known about the shape and location of
the distribution of the variable and about the possible values for the parameters of the PDF. In
general, both PDFys and PDFus are selected to incorporate as much information as is available, but
not to impose any assumptions or restrictions that are not supported by data or expert opinion.
Once each input variable has been characterized by an appropriate PDFy and/or PDFu, the variability
and uncertainty in output variables (in this case, exposure and risk from radon) can be calculated. In
this analysis, these calculations were performed using Monte Carlo simulation techniques. Monte
Carlo simulation is a computer-based method for repeated calculation of the output variable, based on
random sampling from the input variable PDFs. After a sufficient number of calculations (iterations),
the distribution of the calculated values can be used to estimate any statistic of interest (mean,
geometric mean. 95th percentile, etc.).
ES<3
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In order to help maintain a distinction between variability and uncertainty, the Monte Carlo
simulations were ran in a rwo-dimensionai (nested) manner. In the outer Monte Carlo loop, values
are selected ("realized") for each of the uncertain parameters. Then, holding these values constant,
the inner Monte Carlo loop perfoims a series of iterations to characterize the variability of the output
PDF. From the results of this inner loop, a series of statistics (e.g., the 5th, 25th, 50th, mean, 75th,
and 95th percentiles) of die PDFy are recorded. This process is then repeated for many realizations,
resulting in an uncertainty distribution for each of the PDFy percentiles selected.
4.0 UNCERTAINTY AND VARIABILITY IN THE RISK FROM INHALED RADON
PROGENY
Two separate approaches were used to investigate the exposure and risk from water-related radon
progeny in indoor air. The first approach (the one-compartment model) estimates daily average
human exposure to radon and its progeny by assuming that the rate of radon released from water into
indoor air is continuous, and that the concentration of radon progeny in air is uniform (i.e., in steady
state) throughout the entire house. The second approach (the three-compartment model) recognizes
that most household water uses are episodic rather than continuous, and room barriers (walls, doors)
may restrict the rapid mixing of radon released into air in one location with whole-house air, leading
to occasional high levels of radon and radon progeny in some rooms (especially those with high water
usage, such as the shower or laundry).
ES*T
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4.1 Onft-Cnmpartmenf Model
4.1.1 Equation and PPFs
The basic equation used by (he one-compartment model to calculate individual risk from inhalation
exposure to radon progeny derived from radon released from water is as follows:
IR - [C][TF]
0.01 WL
pCi/L
OF
EF
51.6 WLM
WL-yr
[RF]
(1)
where:
IR = Individual risk of lung cancer death (led) from inhalation exposure to radon progeny
derived from radon released from water (led/person-yr)
C = The concentration of radon in water (pCi/L)
TF = Transfer factor (the increase in radon concentration in indoor air per unit radon
concentration in water) (pCi/L air per pCi/L water).
EF = Equilibrium factor (the fraction of the potential energy of radon progeny that actually exists
in indoor air compared to the maximum possible energy under true equilibrium conditions).
OF = Occupancy factor (the fraction of full-time that a person spends indoors).
ES-5"
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RF = Risk factor (lung cancer deaths per person-WLM of exposure).
The PDFs chosen to model the variability and uncertainty in each of these terms are summarized
below.
Concqntnujpn of Radon in Watgy
There is a substantial data base on the level of radon in drinking water systems, especially those that
use groundwater as the source. These data reveal there is wide variability between different systems,
and that small systems tend to have higher levels than large systems. The distributions of radon in
water systems stratified according to system size are well described by lognormal PDFys. These
PDFs may be combined, weighting each according to the number of people served, to estimate the
population-weighted lognormal PDFy for radon in water. The estimated arithmetic mean is 246
pCi/L, with a geometric mean (gm) of 200 pCi/L and a geometric standard deviation (gsd) of 1.85.
Transfer Factor
The transfer factor (TF) describes the average increase in radon in indoor air due to 1 pCi/L of radon
in water. The value of TF has been measured in a number of homes, and it has also been calculated
from measurements of house size, water use rates, ventilation rates, and the rate of radon escape from
various in-house water uses. Most studies agree the mean value is about 1E-04, with an estimated
credibility interval of 0.7E-04 to 1.9E-04. Based on a study of a large number of houses, the
variability of TF is believed to be described by a lognormal PDFy with a gm of 6.57E-05 and a gsd
of 2.88.
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Equilibrium Factor
The equilibrium factor (EF) has been measured in a number of homes, and a value of about 0.5 is
believed to be typical in the United States. However, the true mean could lie between 0.35 to 0.55,
so a uniform PDF was selected to represent the uncertainty in the mean. The value of F has been
observed to vary from less than 0.1 to more than 0.85. This variability was modeled as a beta
distribution, with a minimum of 0.1 and a maximum of 0.9.
The occupancy factor (OF) varies widely from person to person, but a value of 0.75 is believed to be
representative for most residents in the United States. However, the true mean could lie between
0.65 and 0.80, and this uncertainty about the mean is represented by a uniform PDFu (min = 0.65,
max = 0.80). Variability in the occupancy factor was modeled as a beta distribution, with a
minimum value of 0.33 (this assumes an average of 8 hrs/day spent at home) and a maximum of 1.0
(full time spent at home).
Risk Factor for Radon progeny
The risk factor for inhaled radon progeny is based on a number of epidemiological studies of lung
cancer risk in miners, and there is inherent uncertainty in the estimated value. In addition, exposure
conditions in a mine are different in a number of aspects from the conditions in a typical home, so it
is necessary to make several adjustments in the risk factor in order to extrapolate the value to
residents. Based on the combination of the uncertainty from all these sources, the geometric mean of
the risk factor in homes is estimated to be 2.83E-04 lung cancer deaths (led) per year per
ES=>-
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person-WLM of exposure, with a GSDu of 1.53. Available data do not allow for an evaluation of the
inter-person variability of the risk factor.
Summary of PDFs
Table ES-2 summarizes the PDFs selected to describe the variability Mid uncertainty in each of the
input variables needed to calculate the cancer risk from inhalation of radon progeny using the one-
compartment model.
4.1.2 Results of One-Compartment Model Simulation
As discussed above, two-dimensional Monte Carlo simulation was used to estimate the variability and
the uncertainty in exposure and risk from radon progeny. The results are shown in Table ES-3. The
estimated mean unit dose is about 1.8E-05 WLM/yr per pCi/L, the mean unit risk is about 5.1E-09
led/person-yr per pCi/L, and the mean individual risk is about 1.3E-06 led/person-yr. The estimated
population risk is 110 led/yr, with a credible interval of 42 to 260 led/yr.
Variability in unit dose between different people in different houses (as indicated by the ratio of the
95th percentile to the 5th percentile) is about 50-fold. This index of variability does not increase for
unit risk, because the risk factor is modeled as an uncertain constant (i.e., it does not add to
variability). Variability in individual risk and population risk increases to nearly 100-fold, due to the
added variability in the radon concentration factor.
•
Uncertainty in any particular exposure statistic (characterized as the ratio of the upper bound divided
by the lower bound) is about 2-4 fold for unit dose, and this increases to about 6-7 fold when the
PS-K-
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uncertain risk factor Is incorporated to calculate unit risk. Uncertainty increases only to about 6-8
fold when the concentration term is included to yield individual risk and population risk. Thus,
uncertainty in the risk factor is the primary source of uncertainty in both individual and population
risk estimates.
4.2 Thrw-CQtnpapnwtH Model
4-2.i gqwatjpns and ppf$
The three-compartment model employed is basically that of McKone (1987). This model predicts the
concentration of a volatile chemical in water (in this case, radon) in each of three compartments of a
house: the shower, the bathroom, and the remainder of the house. Because concentrations are not
constant, results are calculated as a function of time throughout the day. Based on the time- and
compartment-specific concentration values, human exposure levels in each compartment can then be
calculated.
Because the exposure of chief concern is to radon progeny rather than radon gas itself, the McKone
model was modified somewhat to account for the formation and loss of radon progeny by radioactive
decay, and for loss of progeny due to plating out. Appendix 3 presents the mathematical details of
the modified model.
There are over twenty independent variables in the three.-compartment model for radon and radon
progeny. As detailed in Appendix 4. available information on each variable was collected and
reviewed, and PDFys and PDFus were derived to describe the variability and uncertainty in each.
The resulting PDFs are shown in Table ES-4.
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4.2.2 Results of Threfr-Comnartment Model Simulation
The variability and uncertainty in exposure and risk from inhalation of radon progeny estimated using
the three-compartment model are shown in Table 4. Comparison of the values in Table ES-4 with
those in Table ES-2 reveal that the rsHmatw of unit dose, unit risk, individual risk and population
risk derived from the three-compartment model are all quite similar to the estimates derived using the
one compartment model. The similarity of these two model predictions tends to support the concept
that dose estimates derived by either model are likely to be reasonable. However, it is also true that
both models rely upon some of the same studies for their input (e.g., the data on bouse size and
ventilation rate used in the three compartment model were also used to derive the distribution of the
transfer factor used in the one-compartment model). Thus, the apparent cross-validation of the
models is not as robust as might first be concluded. On the other hand, the similarity of the outcomes
does support the conclusion that the simple one-compartment (steady-state) model does not seriously
underestimate daily average exposures, even though the model does not explicitly evaluate peak
exposures due to events such as showering.
ES~H>
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5.0
UNCERTAINTY AND VARIABILITY IN THE RISK FROM INHALED RADON
GAS
5.1
Onc-Companmcnt Model
5.1.1 Equation and PDFs
The basic equation for calculating exposure to radon gas based on the one-compartment model is as
follows:
UD = Unit dose (pCi inhaled per year per pCi/L in water)
TF = Transfer Factor (the increase in radon concentration in indoor air per unit radon
concentration in water) (pCi/L air per pCi/L water).
BR = Breathing rate (L/day).
OF = Occupancy factor (the fraction of time that a person spends indoors).
The PDFs used to characterize variability and uncertainty in TF, OF and BR are the same as
discussed previously (see Table ES-2 and Table ES-4).
UD = TF-BR-OF-365^2
(2)
year
where:
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51.2 Results of One-Compartment Model
Table ES-6 (top half) shows the estimated variability and uncertainty in the unit dose for inhaled
radon gas derived using the one-compartment model. The average unit dose is estimated to be 380
pCi/yr per pCi/L (credible interval - 250 to 540 pCi/yr pet pCi/L), while the 95th percentile unit
dose is about 3,5 times higher (1,300 pCi/yr per pCi/L, credible interval » 800 to 2000 pCi/yr per
pCi/L). Overall variability in unit dose (as indicated by the ratio of the 95th percentile to the 5th
percentile) is about 40 to 50-fold, while uncertainty about any particular unit dose statistic is about 2-
4 fold.
5.2 Three-Compartment Model
Exposure to radon gas was evaluated with the three-compartment model as described above for radon
progeny. The PDFs are summarized in Table ES-4.
The results are shown in Table ES-6 (bottom half). As shown, the three-compartment model tends to
predict a higher unit dose than the one-compartment model, especially at the low end of the
distribution, although the values become more nearly similar for the mean and 95th percentile of the
distribution. This is because the one-compartment model does tend to under-predict the exposure to
radon gas associated with showering events (USEPA 1993), and the relative importance of the shower
(compared to the main house) is largest at the low end of the exposure distribution.
5.3 Population Risks
-------
Ho PDF (either for uncertainty or variability) has been developed for the risk factor for inhaled radon
gas, so it was not possible to use Monte Carlo simulation to estimate the distribution of either the unit
risk or the individual risk. However, population risk can be estimated from the mean unit dose, as
follows:
PR - UD RF • C,B • N
mean mean
where:
RF - Inhalation risk factor for radon gas (1.1E-12 per person per pCi inhaled)
C « Mom concentration of radon in water (246 pCi/L)
mean
N = Number of people exposed (8.11E+07)
Based on these values, the following estimate of population risk are derived:
Exposure
Model
Estimated Population Risk (cases/yr)
Lower Bound
Median
Upper Bound
One-compartment
5
8
12
Three-compartment
9
12
15
As shown, inhalation exposure to radon gas is likely to contribute only 8-12 additional cancer cases
per year, with a credible range of 5 to 15 cases/yr.
6,0 UNCERTAINTY AND VARIABILITY IN THE RISK FROM INGESTED RADON
GAS
6-1 Equation and PDFs
The basic equation for calculating cancer fatality risk/person/year from ingestion of radon gas in
drinking water is:
-------
R - (C) (F) (V-365 d/yr) (RF)
C3)
where:
R = -Risk of fatal cancer (per person, per year) from ingestion of radon in water
C = Concentration of radon in water (pCi/L)
F = Fraction of radon remaining in water at time of ingestion
V = Mean volume of water ingested that contains radon (L/day)
RF = Ingestion cancer risk factor fur radon gas (cancer fatality risk per pCi radon ingested)
The variability arid uncertainty in the concentration term have been described previously. The variability
and uncertainty in the other variables are briefly described below.
Because radon is a gas, it begins to escape from water as soon as the water is discharged from the tap. It
is believed that essentially all radon escapes from water used for cooking or in prepared beverages, so the
only important source of radon ingestion is water consumed shortly after being drawn. Based on a limited
number of studies, a value of 0.2 seems representative of the fraction lost, with an estimated credibility
interval from 0.1 to 0.3. Thus, the fraction which remains (F) has a typical value of 0.8, and ranges from
0.7 to 0.9, The ftill range (i.e., variability) of F is also difficult to estimate, but a range of 0%-50%
volatilized (50%-100% remaining) seems reasonable. Based on this information, a beta distribution was
used to model die variability in the F term.
ES>W
-------
Volume ingested
Reliable information on the amount of tap water ingested is available from a survey of a large number
of U.S. citizens. The distribution is lognormal in shape, with a gm of 0.526 L/day and a GSD of
1.92.
Risk Factor
The risk factor (risk/pCi) for ingested radon is calculated based on a toxicokinetic analysis of the dose
of radon (rad/pCi) to various tissues, coupled with the estimated organ-specific fatal cancer risk to
each tissue (risk/rad). The best estimates of the levels of radon which reach different tissues of the
body are derived by biokinetic modeling using data extrapolated from a study in humans using xenon
gas as a surrogate for radon. The tissues which receive the highest dose are the stomach and the
intestine, but estimating the dose to these tissue is complicated by i) uncertainty about the possible
concentration gradient in the epithelium of the gastrointestinal tract and 2) the possible sweeping
effect by the blood whereby radon and its short-lived progeny may be swept away from the tissue
prior to decay. In addition, there is uncertainty regarding how the dose to tissues depends on the age
of the person. Overall, the uncertainty in the dose to various tissues is estimated to have combined
GSDu values ranging from 1.56 to 1.94.
An independent source of uncertainty in the ingestion risk factor is uncertainty about the cancer risk
per unit dose for each of the exposed tissues. These estimates are based mainly on studies of cancer
risk in atomic bomb survivors, and there are a number of sources of uncertainty in these estimates.
Specifically, uncertainty is contributed by: 1) sampling variation; 2) age/time dependence of risk; 3)
extrapolation of the data from the Japanese population to the U.S. population; 4). errors in dosimetry,
and 5) uncertainty in the relative biological effectiveness of alpha panicles.
Monte Carlo modeling was employed to estimate the overall uncertainty in the risk factor (risk per
pCi ingested), taking into account each of the sources of uncertainty in dose (rad per pCi) and risk
(risk per rad) discussed above. The uncertainty distribution is well described by a lognormal PDF
with a GM of 1.24E-11. Because of the numerous sources of uncertainty, GSDu values are quite
large, ranging from 2.5 to 3.2 for different tissues, with an overall GSDU of 2.42.
5
-------
Table ES-7 summarizes the PDFs used to evaluated ingestion exposure and risk to radon gas.
6 2 Results: Variability and Uncertainty in Ingestion Risk
Table ES-8 summarizes the variability and uncertainty in exposure and risk from ingestion of radon
gas in water. The variability in unit dose between different people in different houses (as indicated by
the ratio of the 95th percentile to the 5th percentile) is about 10-fold. This range in variability is
significantly lower than for inhalation of radon progeny (about 50-fold; see Section 4) because there is
much less variability in the amount of water people drink than in the size and ventilation rates of their
houses. This variability index does not increase for unit risk.'because the risk factor is modeled as an
uncertain constant (i.e., it does not add to variability). Variability in individual risk and population
risk increase to about 20-fold, due to the added variability in the radon concentration factor.
Uncertainty in any particular exposure statistic (characterized as the ratio of the upper bound divided
by the lower bound) is about 1.5 fold for unit dose, and this increases to about 20-fold when the
uncertain risk factor is incorporated to calculate unit risk. Uncertainty increases only slightly when
the concentration term is included to yield individual risk and population risk. Thus, uncertainty in
the ingestion risk factor is clearly the primary source of uncertainty in both individual and population
risk estimates.
7.0 RELATIVE MAGNITUDE OF THE POPULATION RISKS FROM RADON IN
WATER COMPARED TO NON-WATER SOURCES OF RADON
71 Combined Population Risks from Radon in Water
Figure ES-1 summarizes the population risks attributable to inhalation of radon progeny and ingestion
of radon gas attributable to water, alone and in combination. As seen, the combined population risk
from radon in water is estimated to be about 170 cancer cases per year, with a credible range of 70 to
410 cases per year. Of these cases, about 2/3 are due to the inhalation of radon progeny, with about
1/3 due to ingestion of radon gas in water. As discussed above,.inclusion of the risk from inhalation
of radon gas would increase this value by about 8-12 cases/yr (credible range = 5 to 15 cases/yr).
ES"it>
-------
7.2 Population Risks from Radon in Outdoor Air
Risks from radon progeny in outdoor air may be estimated using the same basic equation and method
as described in Section 4.1. PDFs used to characterize the input parameters are summarized below.
Risk Factor
The risk factor (lcd/WLM) depends on the unattached fraction and the aerodynamic properties of
particles to which the attached fraction is bound. While conditions are not likely to be identical
indoors and out, it seems likely that the risk factor for outdoor air will be similar to that for indoor
air. For example, even if the unattached fraction in outdoor air were half that in indoor air, the risk
factor would only be 25% lower. Thus, the same PDFU has been used to describe the inhalation risk
factor in outdoor air as indoors (lognormal, GM = 2.8E-04, GSDu =¦ 1.53).
Average Outdoor Radon Level
Based on a set of outdoor radon measurements collected during the National Ambient Radon Study,
the best estimate of average outdoor radon concentration is 0.3 pCi/L. This is assumed to have a
lognormal uncertainty distribution, with GM = 0.3 pCi/L and a GSDU = 1.3.
Equilibrium Factor
Radon progeny are nearly in equilibrium with radon in outdoor air, with measured values of EF
ranging from 0.77-0.85. A value of 0.8 is taken as the best estimate. The uncertainty about this
value is assumed to be given by a lognormal distribution with a GSDu of 1.05.
Time Spent Outdoors
On average, adults spend only 2.3% of the day outdoors, with an additional 5.4% spent in transit.
Assuming this is spent in cars or other vehicles where the air is similar to outdoor air, then the total
fraction of the day spent breathing outdoor air is about 0.075. The uncertainty is assumed to be
lognormally distributed about this value with a GSDU of 1.10.
ES-ir
-------
Results- Risk from Ration Prngpny in Outdoor Air
Employing die nominal values described above, the number of lung cancer deaths in the entire U.S.
population (2.5E+08 people) is estimated to be 520 led/year. Employing the lognormal PDFu terms
assumed for each variable, die 90% credibility interval about this estimate is estimated to be
280-1,500 led/year.
7.3 Population Risks frnm Total Rarinn in Inrinnr Air
Estimates of lung cancer deaths attributed to total indoor air radon exposure (waterborne radon and radon
from infiltration from soil into house) with associated uncertainties have been quantified by the Office of
Radiation and Indoor Air (formerly Office of Radiation Programs) of the U.S. Environmental Protection
Agency. Hie detailed analysis was described in Chapter 2 of the EPA report entitled Technical Support
Dnrnmfnt for thy 1992 Citizen's fiiiirin in Barinn (USEPA, 1992a). Based on this analysis, the estimated
excess annual lung cancer deaths due to radon (all sources) in indoor air is 16,000 led/yr, with a credible
interval of 6,790 to 30,590 led/yr.
7.4 Relative- Population Risk From Radon in Water
Hie mean risk estimates for exposure to radon from different sources are summarized in Table ES-9. It is
apparent that the number of cancer deaths per year attributable to water is a relatively small fraction (about .
1 %) of the total cancer deaths attributable to radon.
i
7.5 P.ffent of Rstahlishing an Mfll
Even though risk from radon in water is a relatively small fraction of the total risk from radon, this does
not mean that establishment of an MCL for radon would not result in the saving of a significant number of
lives each year. Figure ES-2 shows the estimated number of lives which would be saved each year as a
function of what value is assumed for the MCL. If the MdL were set at 200 pCiIU it is expected that
about 129 lives would be saved, with a credible range of 47 to 350. If the MCL were set to 300 pCi/L, it
is expected about 81 lives/year would be saved (credible range = 26 to 255). At an MCL of 2000 pCi/L,
the estimated number of lives saved would be 15 livese/yr with a credible range of 10 to 60.
ESJ8
-------
Figure ES-1 Estimated Annual Cancer Deaths by Exposure Pathway
Attributable to Waterborne Radon Using the One-Compartment Model
450
400 --
350 --
£ 300 ----
- 250 --
D
Q.
a 200 --
Q 150 --
100 --
50 --
0 j i r-
Inhalation
Ingestion
Combined
-------
Figure ES-2
Annual Cancer Deaths Avoided for Different Maximum
Contaminant Levels of Radon-222 in Community Drinking Water
350
300 --
250 --
200 --
S
100 --
200
300 500 700 1000
Maximum Contaminant Level, pCi/L
2000
-------
TABLE ES-1 SUMMARY OF PROPOSED AND REVISED FATAL CANCER
RISK ESTIMATES FOR RADON IN WATER
Lifetime Cancer Risk per pCi/L in Water
Exposure Pathway
Proposed
Revised
Inhalation of radon progeny
due to radon released from water
4.9E-07 (74%)
3.0E-07 (43%)
Inhalation of radon gas released
from water to indoor air
0.2E-07 (3%)
0.5E-07 (7%)
Ingestion of radon gas in direct
tap water
1.5E-07 (23%)
3.5E-07 (50%)
Sum of all pathways
6.6E-07 (100%)
7.0E-07 (100%)
-------
TABLE ES-2 SUMMARY OF DISTRIBUTION FUNCTIONS USED IN THE
ONE COMPARTMENT MODEL TO EVALUATE RISK FROM RADON PROGENY
Variable
PDF
V
PDFU
Values
Transfer factor
TF - TLN(gm,gsd,min,max)
litom)*- TS(m,s,qf)
In^gsd) «- INVCH(s.qf)
m - ln(6.57E-05)
s « ln(2.88)
min * 6E-06
max = 8E-04
qf - 25
Equilibrium
factor
EF ~ U(min,max)
min « U(a,b)
max = U(c,d)
a = 0.35 b = 0.55
c = 0.1 d = 0.9
Occupancy
factor
OF ~ B(iriean.mode,min,max)
mean = U(a,b)
mode = U(mean,max) or
U(min.mean)
a - 0.65
b = 0.80
min = 0.17
max = 0.95
Risk factor
RF - Uncertain constant
RF - LN(gm,gsd)
gm » 2.83E-Q4
gsd = 1.53
Radon
concentration in
water
C - LN(gm,gsd)
Intern) *- TS(m,s,qf)
In (gsd) lNVCH(s.qf)
m « ln(200)
s - ln(l.B5)
qf *» 10
Definitions:
"TLN «
U =
& =
. LN =
TS =
INVCH =
truncated lognormal distribution
uniform distribution
beta distribution
lognormal distribution
function which selects a value from Student's t-distribution and returns the corresponding value for the mean, based on a sample
mean m, sample standard deviation s, and sample size qf
function which selects a value from the chi-squared distribution and returns the corresponding value for the standard deviation,
based on a sample standard deviation s and sample size qf
-------
TABLE ES-3 VARIABILITY AND UNCERTAINTY
IN INHALATION EXPOSURE AND RISK TO RADON PROGENY
ESTIMATED USING ONE-COMPARTMENT MODEL
Exposure or Risk
Parameter
Variability
Statistic
Uncertainty
Lower Bound
Median
Upper Bound
Unit Dose (WLM/yr
per pCi/L)
Sth Percentile
6.5E-07
1.2E-06
2. lE-06
Median
6.2E-06
9.4E-06
1.5E-05
Mean
1.2E-05
1.8E-05
2.7E-05
95th Percentile
3.9E-05
6.4E-05
1.0E-04
Unit Risk (Icd/person-yr per
pCi/L)
Sth Percentile
1.3E-10
3.4E-10
8.9E-10
Median
1.1E-09
2.6E-09
6.1E-09
Mean
2.1E-09
5.1E-09
1.2E-08
95th Percentile
7.2E-09
I.8E-08
4.2E-08
Individual Risk (Icd/person-
yr)
Sth Percentile
1.8E-08
5.4E-08
1.5E-07
Median
2.1E-07
5.4E-07
1.4E-06
Mean
5.2E-07
1.3E-06
3.2E-06
95th Percentile
1.9E-06
5.0E-06
1.3E-05
Population Risk (lcd/yr/a^
-
42
110
260
(a) Assumes a population of 8.11E+07 people are exposed. All values expressed to two significant figures.
-------
Table ES-4 - continued
TABLE ES-4 SUMMARY OF PDFs USED IN THREE-COMPARTMENT MODEL
OF EXPOSURE AND RISK FROM RADON PROGENY
Variable
PDF
PDF
Values
Number of people per
house
PNUM - cmpMcai
NA
1 - .192 4 - .164
2 m .328 J - .013
3 - .183 6 - .049
Volume of shower
Vs - U(mis.maji)
nun - U(t,b)
n>i - U(c,d)
a - 1000 b - 1500
c • 2300 d - 3000
Volume of bathroom
Vb - TLN(gm. gsd. rain, max)
Intgm) «- TS 30,000
max - 700.000
qf- 100
Vc3 - TLN(gm.gsd,imn.tiiax)
In£gm) — TS(ra.j.qf)
bi(gid)- INVCH(m.qO
m - lii(99.000)
i - lnU.68)
mis - 25.000
max - 450.000
qf - 100
Vt4 - TLN(gm.gsd,mui,max!
InUm) •- TSfm.j.qO
In (gjd) — INVCHCra.qf)
m - 1 *{89.000)
i - lnC1.67)
mill - 20.000
max - 400.000
qf - 100
Vt3 - TLN(gm.gsd.min.max)
ln£gm) •• TS(m.s.qO
In (gid) •- INVCH(m.qf)
m - InHS .000)
j -Ml.70)
min - 15.000
max - 350.000
qf - 100
Vt6 ~ TLN(gm.gsd.mui.max)
InLgm) - TSdn.s.qf)
In (gsd) - INVCHfm.qf)
m - ln(54,000)
i - Ml.71)
min ¦> 10.000
max - 300,009
qf - 100
Shower flow rate
SFR - TLN(gm.g*d.min.maJt)
Iniginl •-TSfm.s,qf) '
In (gsd)- INVCHfm.qf)
m - Inf7.1)
1 - ln(1.54)
mill * 3
max * 24
qf - 100
Per capita water use m
bathroom
WUb - U(mm,mu)
mia - (J(a.b)
max - U(c.d)
a - 15 b - 20
c - 75 d - 80
-------
Table ES-4 - continued
Vinable
PDF
PDF
Values .
Total per capita water
use
WUtl - TLN(gm,|sd,min,mai)
liUgm) — TS(m,s.qf)
In (gsd)-lNVCH(m.qf)
m - ln(304)
s - ln(1.32)
rain » 150
max m 360
qf - 25
WUt2 - TLNfgm.gsd.min.max)
Intgm) — TS(m,s.qf)
In (gsd) - INVCH(m.qf)
m - IIK256)
s - ln(1.32)
min - 130
max - 520
qf - 25
WUt3 - TLN(gm.gsd.min.max)
Irtfgm) — TS(in.s,qf)
In (gsd) - INVCH(m.qf)
m - IiK258)
s - ln(1.23)
min - 110
max — 480
qf - 25
WU|4 - TLN(gm.gsd.min.max)
ln^pn) — TS(m.s.qf)
In (gsd) - INVCHCm.qO
m - ln(232)
i - ln(l.26)
min ¦ 90
max — 440
qf - 25
WUiS - TLN(gm.gsd.min.majt)
Inlgm) •- TS(m.s.qf)
In (gsd) - INVCH(m.qO
m = ln(214)
i - In(l.l6)
min - 70
max ™ 400
qf - 10
WUt6 - TLN(gm.gsd.min.max)
Intgm) — TSfm.s.qO
In (gsd) - INVCH(m.qf)
m - ln(214)
s - ln< 1.16)
min - 70
max — 400
qf - 10
Shower air residence
lime
Ra - U(min.max)
nun - U(a.b)
max — U(c.d)
a - 2 b - 3
c — 4 d - 6
Bathroom air residence
time (door open)
Rbl - U(min.max)
nun — U(i.b)
max - U(c.d)
a - 20 b - 30
c >40 d « JO
Bathroom air residence
time (door closed)
Rb2 — U(min.max)
min — U(a.b)
max - U(c.d)
a - 20 b - 30
c - 150 d - 250
Bathroom fan exhaust
rate
EXFR - TRI(nun, max.model
mode - U(a.b)
min ¦" 1000 max - 5000
a - 2000 b • 2500
Main house ventilation
rate
VRa - TLN(gm,gjd.nun.m»x)
lnum) •- TSfm.s.qO
In (gsd) •- INVCH(m.qf)
m » ln(0.68)
s - ln(2.0l)
min - 0.1
max " 2
qf - 25
Radon transfer
efficiency in shower
Ps - U(min.max)
min - U(a.b)
max — U(c.d)
a -0.5 b-06
c - 0.7 d - 0.8
Radon transfer
efficiency in bathroom
Pb - U(min.max)
min - U(a.b)
max - L'(c.d)
a - 0.15 b - 0.25
c - 0.33 d - 0.45
Radon transfer
efficiency in main
house
Pa — Li'(min.max)
min - U(a.b)
max - Ufc.d)
, . 0.4 b - 0.5
c - 0.7 d >08
-------
Table ES-4 - continued
VariaMe
PDF
K>F
Vaisss
Unattached fraction
UFRACT - B(mean.iBode.miii.max)
mean - U(».b)
mode - TRKmin. mean,(mm+mean)/2)
a -0.05 b » 0.15
min - 0
max * i
Deposition velocity of
uaioscJsed fraction
DVu - U(oim,iaax)
nin - U(a,b)
max - U(c,d)
a ¦ I b - 4
c - 16 d - 22
Deposition velocity of
imfhirf ffSCt§Qfi
DVa - U(min,m«)
nin - U(a,b)
max - U(c.d)
a - 0.01 b - 0.0S
c - 0.1 d - 0.3
Time in shower
Ts - TLNfgjn.gKl.niiaBUU)
tattn) «- TSftn,i,qf)
la (gsd) *• INVCH(m.qf)
m - N6.8)
s - UKI.6)
tmn » |
max - 30
<|f — too
Time in bathroom
Tb - U(rain,max)
min - U(i.b)
mix - Ufc.d)
a - 1 b - 10
c - 20 d - 30
Breathing rate
BR - tX(ineao.ssl.i!iis.nax)
»
mean»-TS(ii,s,qf)
ltd ~INVCH(ni.i|0
m <¦ 9.1 s - 2.0
min • 2.6 max - 46.6
qf- 10
Occupancy factor
OF - B( mean, mode,tmn.mix)
mean - USi,b)
mods - U(meaa.max) or Wmia.mBan)
> - 0 65 b - 0.80
min - 0.33
max — 1.0
-------
TABLE ES-S VARIABILITY AND UNCERTAINTY
IN INHALATION EXPOSURE AND RISK TO RADON PROGENY
ESTIMATED USING THREE-COMPARTMENT MODEL
Exposure ik Risk
Parameter
Variability
Statistic
Uncertainly
Lower Bound
Median
Upper Bound
U«M Dose (WLM/yr
Slh Percentile
I.4E46
2.IE-06
2.IE-06
per pCi/L)
Median
7.5E-06
1.0E-05
, I.4E-05
Mean
I.2E-05
I.6E-0S
2.4E-05
95lh Percentile
3.9E-4W
5.2E-0S
7.9E-05
Unit Ride (led/person yi pel pCi/L)
3ih Percentile
2.7E-IO
5.8E-IO
I SE-09
Median
1.3E49
2.9E-09
6.9E-09
Mean
2 JE-09
4.8E-09
I.1E-08
95lh Percentile
7.JE-09
I.SE4B
3.JE-08
Indivqkul Risk (k:d/person-yr)
5th Percentile
3.1E-08
8.7E-08
2.3E-07
Median
2.SE-07
6.JE-07
I.6E-06
Mem
4.9E-07
ME 06
3 4E-06
9Sth Percentile
1.76-06
4.9E-06
I.2E-05
(»)
PopuUuon Risk (Icd/yri
40
110
280
U) A«um«* a piipulaium »l 8 IIE + 07 people ire exposed. AU values expressed lo iwo significant figures
-------
TABLE ES 6 VARIABILITY AND UNCERTAINTY IN UNIT DOSE FOR INHALED RADON OAS
Exposure
Model
Variabilis
Suuslic
Unit Doic (pCi/jrr per pCi/L)
Lower Bound
Median
Upper Bound
One-Compartment
5lh Percentile
1.7E+0I
3.2E+01
J.7E+0I
Median
ME+02
2.IE+02
J.IE+Q2
Mean
2.JE+02
3.8E+U2
5.4E+02
95th Percentile
8 0E+02
I.3E+03
2.0E+03
ThKc-Compsnmem
5ih Percentile
H6E+UI
I.2E+02
I.5E + 02
Median
3.2E+02
4.1E+02
S.lB+02
Mean
4.3E+02
5.5E+02
7 0E+02
OJih Pcrccmik
1.IE+03
I.4E+03
I.VE+03
-------
TABLE ES-7 SUMMARY OF DISTRIBUTION FUNCTIONS USED
TO EVALUATE EXPOSURE AND RISK FROM INGESTION OF RADON
Variable
PDF
V
PDF
u
Values
Volume
ingested
V - LN(gm.gsd)
InCgm) — TS(m,s,qf)
In tgsd) - INVCH(s.qf)
m = ln(0.526)
s = ln( 1.922)
qf = 100
Fraction
remaining
F - BETA(mean. mode, min. max)
mean =* U(a,b)
mode = U(mean,max) or
U(min,mean)
a = 0.7
b - 0.9
min = 0.5
max = 1.0
Risk factor
RF - Uncertain constant
RF - LN(gm.gsd)
gm = 1.24E-11
gsd « 2.42
Radon
concentration
in water
C - LN(gm,gsd)
InCgm) *- TS(m.s.qf)
In (gsd) - INVCH(s.qf)
m ¦ ln(200)
s » lzi(1.85)
qf = 10
-------
TABLE ES-8 VARIABILITY AND UNCERTAINTY
IN INGESTION EXPOSURE AND RISK FROM RADON GAS
Exposure or Risk
Parameter
Variability
Statistic
Uncertainty
Lower Bound
Median
Upper Bound
Unil Dose (pCi/yr
per pCi/L)
5th Percentile
3.8E+01
5.0E+0I
6.2E+01
Median
1.3E+02
I.5E+Q2
J.8E+02
Mean
1.6E+02
1.9E+02
2.3E+02
9Sih Percentile
3.8E+02
4.6E+Q2
5.6E+02
Unil Risk (lcd/person-yr per
pCi/L)
5ih Percentile
1.5E-I0
6.0E-10
2.9E-09
Median
4.6E-I0
1.8E-09
8.8E-09
Mean
5.9E-I0
2.3E-09
1.IE-08
95th Percentile
I.4E-09
5.6E-09
2.7E-Q8
Individual Risk (icd/person-yr)
5th Percentile
I.7E-08
8.3E-08 .
3.4E-07
Median
8.6E-08
3.9E-07
1.6E-06
Mean
1.3E-07
6.2E-07
2.6E-06
95th Percentile
4.0E-07
1.9E-06
7.9E-06
ia\
Population Risk (Icd/yr)
--
11
50
210
(a) Assumes a population of 8.11E+07 people ire exposed.
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TABLE ES-9
RELATIVE MAGNITUDE OF RADON RISKS
Radon
Source
Exposure
Route
Exposure
Location
Excess Fatal Cancer Risk
Deaths/yr
% Total
Water
Inhalation
Indoors
no
0.7
Water
Ingestion
Indoors
50
0.3
Soil
Inhalation
Outdoors
520
3.1
Soil
Inhalation
Indoors
15840(a)
95.9
(a) This value is equal to the total of 16,000 deatbs/yr estimated by EPA (1992a) minus the
contribution from water (160 deaths/yr).
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1.0 INTRODUCTION
1.1 Background
Section 1412 (b) (3) (A) of the Safe Drinking Water Act, as amended in 1986. requires the
Administrator of the U.S. Environmental Protection Agency (EPA) to publish a Maximum
Contaminant Level Goal (MCLG) and promulgate a National Primary Drinking Water Regulation at a
specified enforceable Maximum Contaminant Level (MCL) for each contaminant which, in the
judgment of the Administrator, may have adverse effects on public health and which is known or
anticipated to occur in public water systems. The MCLG is nonenforceable and is set at a level at
which no known or anticipated adverse health effects in humans occur and which allows for an
adequate margin of safety. Factors considered in setting the MCLG include health effects data and
sources of exposure other than drinking water. The MCL is set as close as feasible to the MCLG,
taking considerations such as economic impact, treatment technologies, and other factors into account.
lit Proposed Rule for Radionuclides in Drinking Water
Based on the requirements of the Safe Drinking Water Act, the EPA Office of Water (OW) published
a Proposed Rule for Radionuclides in Drinking Water on July 18, 1991. The radionuclides covered
by the rule include radon, uranium, radium, gross-adjusted alpha emitters, and beta and photon
eminers. The proposed MCLG for radon is set to be zero because radon is a group A human
carcinogen according to EPA's classification scheme. The proposed MCL for radon in public
drinking water supplies is 300 pCi/L (Federal Register 56:33051): This proposed regulation is based
in pan on calculations which indicate that there is significant cancer risk to the U.S. population from
current levels of radon in drinking water.
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In support of the Proposed Rule for regulating radon in drinking water, the EPA Office of Water prepared
a draft document entitled Hrinlring Water Criteria nnnimcnl fnr Rarinn (USEPA, 1991a). This document
describes the health effects from exposure to radon, and includes a detailed description of how individual
lifetime fatal cancer risk from exposure to waterborne radon was estimated. Briefly, the fatal cancer risk
from exposure from waterborne radon is derived by adding risks from three exposure pathways: 1) lung
cancer deaths (led) due to inhalation of radon progeny derived from radon gas volatilized from water; 2)
fatal cancer risk due to inhalation of radon gas volatilized from water; and 3) fatal cancer risk due
ingestion of radon in drinking water. The fatal cancer risk estimate from the first pathway is derived
primarily from epidemiological studies of radon-exposed miners, while the risk estimates from the two
other pathways are based on human radiocarcinogenic data, animal data on relative effectiveness on alpha
particle, and biokinetic modeling (USEPA, 1991a).
1.1.2
The Radiation Advisory Committee (RAC) of the Science Advisory Board (SAB) was briefed on the
Agency's risk assessment for radionuclides in drinking water. The Criteria Document for Radon in
Drinking Water was revised based on the Committee's recommendation prior to publication of the
Proposed Rule (RAC/SAB, 1991). The RAC subsequently commented on the Proposed Rule and the
revised Criteria Document with several SAB memoranda (RAC/SAB, 1992a, 1992b, 1992c). One major
remaining concern of the SAB regarding the Agency' risk assessment on waterborne radon was that
quantitative uncertainty analyses on the cancer risk estimates from both ingestion and inhalation pathways
had not been performed. The fact that radon volatilized from water used in the tame is a relatively small
contributor to total radon concentration in indoor air was also discussed in the SAB memoranda
(RAC/SAB, 1992b, 1992c).
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1.1.3 Chafee Amendment
The Proposed Rule for Radionuclides in Drinking Water was published in July 1991. The original
deadline for the final rule was April 15, 1993. However, this deadline has been postponed due to the
Chafee Amendment to the Safe Drinking Water Act. As described in the Congressional Record
dated September 25, 1992, die Chafee Amendment requires a regulatory moratorium and a report on
radon in drinking water. Specifically, it requires the Administrator of EPA to conduct a multimedia
risk assessment associated with various routes of exposure to radon in drinking water. The
amendment further states that the SAB shall review the Agency's study and submit a recommendation
to the Administrator, and then the Administrator shall report the SAB's recommendations and the
Agency's findings to the Senate Committee on Energy and Commerce no later than July 31, 1993.
The Administrator is directed, if additional time is required to establish the radon standard, to seek an
extension of the deadline contained in the judicially imposed consent decree for promulgation of the
radon standard.
12 Quantitative Uncertainty Analysis Report
In response to SAB's recommendations regarding the Proposed Rule and the Radon Criteria
Document, and in accord with the requirements of the Chafee Amendment, the Agency prepared a
draft quantitative uncertainty analysis of cancer fatality risk estimates for radon from multimedia
exposure. This document was completed in April, 1993. The exposure routes considered in the draft
document included inhalation of radon progeny stemming from radon gas released from water,
ingestion of radon in water, and inhalation of radon progeny in outdoor and indoor air. The draft
document reviewed the methods used to derive the estimated cancer risk levels from various exposure
routes, quantified the uncertainty around each variable used in the risk assessment, and provided the .
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overall quantitative uncertainty of the fatal cancer risk estimates resulting from various routes of radon
exposure.
This draft report was reviewed by the RAC and the Drinking Water Advisory Committee (DWAC) of
the SAB, These committees provided comments to EPA, which were evaluated and responded to as
detailed in a special report EPA prepared for Congress (USEPA 1994a). In addition, die draft report
was reviewed by the Department of Energy (DOE) and USEPA Office of Research and Development
(ORD). The current document is the final report on the uncertainty in risks from radon in water,
having been revised in response tu the comments received from SAB, DOE and ORD.
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2.0
ORIGINAL ESTIMATES AND RECENT CHANGES IN CANCER RISK FROM
WATERBORNE RADON
Humans may be exposed to radon in household water via three main pathways: 1) inhalation of
radon gas volatilized from water, 2) inhalation of radon progeny formed from volatilized radon, and
3) ingestion of radon in drinking water. This section summarizes the methods that were used by EPA
to derive the risk estimates for each of these exposure pathways as presented in the Proposed Rule
(USEPA 1991), along with a number of changes which have occurred since that time which influence
the current estimates of risk.
The EPA estimated the risk from inhalation exposure to radon gas released from water into indoor air
using the following basic equation:
2.1
Inhalation of Radon Gas
2.1.1 Estimate in the Proposed Rule
Rnn " c ' TF ' BR ' 0F • ED • iRFlta
(I)
where:
= Risk of fatal cancer from inhalation of radon gas
C = Concentration of radon in water (pCi/L)
TF = Transfer factor (pCi/L of air per pCi/L in water)
BR = Breathing rate (L/day)
OF = Occupancy factor (fraction of time spent at home)
-------
ED = Exposure duration (days)
iRFj^n =* Risk Factor for inhaled radon gas (cancer deaths/person per pCi)
The risk factor for fatal cancer per pCi of radon Waled (iRFp^) was estimated to be 4.7E-13
(USEPA, 1989b). This value was derived from the RADRISK model using organ-specific radiation
doses (rad/pCi) and cancer risk coefficients (risk/rad). Organ-specific doses were estimated by
quantitative evaluation of absorption rate, distribution, metabolism, and excretion of radon and its
progeny (Dunning et al., 1980; Sullivan et al., 1981). Organ-specific risk coefficients were derived
by quantitative evaluation of epidemiological data on human cancer risk following exposure to several
types of ionizing radiation (USEPA, 1989b).
The Agency used an average transfer factor of 1E-04 to evaluate inhalation exposure to radon released
- from household uses of water (USEPA, 1991b). With this transfer factor, 1 pCi/L of radon in water
gives rise to l.E-04 pCi/L of radon in air. Assuming ari occupancy factor of 0.75 and a breathing rate
of 22,000 L/day (USEPA, 1989b), an individual inhales a total of 4.2E+04 pCi of radon per pCi/L
in water over an exposure duration of 70 years (25550 days). Multiplying this by the risk factor of
4.7E-I3 fatal cancers per person per pCi of radon gas inhaled (USEPA, 1989b) yields a risk estimate
of 2.0E-O8 cancer deaths per person per pCi/L in water.
2.1.2 Revisions Since the Proposed Rule
Recently, the EPA has revised the estimated risk factor for inhaled radon from 4.7E-13 to 1. IE-12
per pCi inhaled. This is based on revised organ-specific risk-per-'unit-dose estimates and modification
of dosimitry treatment (USEPA 1994b). Incorporating this revised risk factor with the exposure
assumptions used earlier (transfer factor = 1E-04. breathing rate = 22,000 L/day, occupancy factor
-------
= 0.75), the total inhaled dose over 70 years is 4.2E+04 pCi per pCi/L, and the corresponding
lifetime excess individual risk is 5.0E-08 per pCi/L (USEPA 1994a, 1994b).
2.2 Inhalation of Radon Progeny
2.2.1 Estimate in the Proposed Rule
The EPA estimated the risk from inhalation of radon progeny derived from radon released from water
into indoor air using the following basic equation:
R = C • TF • 0 01 WL • EF • 51,6 WLM • OF • RF (2)
p • pCi/L WL-yr p
where:
Rp = Risk of lung cancer death (led) from inhalation exposure to radon progeny derived
from radon released from water
EF = Equilibrium factor (the fraction of the potential energy of radon progeny that
actually exists in indoor air compared to the maximum possible energy under true
equilibrium conditions).
RFp = Risk factor for radon progeny (led per person-WLM of exposure).
The values selected for each of the terms and the resulting risk estimates are presented below.
-------
Risk Factor for Radon Progeny
The risk factor for exposure to radon progeny in the air is derived from several epidemiological
studies of miners (NAS, 1988; ICRP. 1987). Epidemiologic studies provide strong evidence that
inhalation exposure to radon decay products causes lung cancer in miners. The dose to sensitive cells
of the lung from inhalation of radon decay products is not calculated directly. The concentration of
radon decay products in air has been designated with a special unit, the Working Level (WL), and the
unit for cumulative exposure to radon decay products is the Working Level Month (WLM). The
units for the risk factor are lung cancer deaths per WLM (Icd/WLM).
The estimated led risk via inhalation of radon progeny used in the proposed rule was 360E-06
Icd/WLM (NAS. 1988). Dose-response relationships are generally linear, with increased risk of lung
cancer often observed even in the lowest exposure groups (NAS, 1988).
In terms of toxicokinetics, it is important to compare the exposure conditions in mines and homes.
The BEIR IV committee of the National Academy of Sciences considered that the radiation dose to
the lung received in a mine and in a home would be nearly equal for a given measured radon decay
product concentration in WLM. This near-equality results from an approximate balancing of the
effects of the smaller panicles and greater unattached fraction in a home that would make the dose
higher and of the slower breathing rate that would make the dose lower (NAS, 1988).
Inhalation of radon progeny was quantified based on a transfer factor of 1E-04, an occupancy factor
of 0.75 and an equilibrium factor of 0.5. Based on these values, the lifetime (70-year) fatal risk
estimate calculated in the Proposed Rule was 4.9E-07 led per pCi/L water (USEPA, 1991a).
-------
2.2.2
Revisions Since the Proposed Rule
EPA has recently revised the led estimate of inhalation exposure to radon decay products based on a
1991 EPA survey of indoor radon level in U.S. residences and a 1991 NAS report on comparative
dosimetry between mines and homes. The details and rationale of the revision have been presented in
a report entitled. Technical Support Document for the 1992 Citizen's Guide to Radon (USEPA,
1992a). The NAS reevaluation of the relative dosimetry of radon decay products in mines and homes
suggested that the dose per pCi/L of radon in air may be 20-30% lower in homes than mines (NAS,
1991). This finding was mentioned in the Proposed Rule. The fatal lung cancer risk via inhalation
(risk factor) of radon progeny was changed from 360 lung cancer deaths (led) per 10^ person-WLM
to 224 led per 10^ person-WLM. Based on the same exposure assumptions used in the Proposed
Rule, and using the revised risk factor of 224E-06 lcd/WLM, the individual lifetime led risk is
3.0E-07 led per pCi/L in water, a 39% decrease from the estimate of 4.9E-07 led per pCi/L water in
the Proposed Rule. These calculations are summarized in Table 2-1.
2.3 Ingestion of Radon in Drinking Water
2.3.1 Risk Estimate in the Proposed Rule
The basic equation used by EPA for calculating cancer fatality risk/person/year from ingestion of
radon gas in drinking water is:
Rw = C • F • IR • ED • oRF^ (3)
-------
where:
Rw = Risk of cancer (per person, per year) from ingestion of radon in water
C = Concentration of radon in water (pCi/L)
F = Fraction of radon remaining in water at time of ingestion '
IR = Ingestion rate of water that contains radon (L/day)
ED = Total number of days that water is ingested (days/lifetime)
oRF^ = Oral cancer risk factor for radon gas (cancer fatality risk per pCi radon ingested)
The values selected for each of the terms and the resulting risk estimates are presented below.
Oral Risk Factor for Radon
Ingested radon passes from the gastrointestinal (GI) tract, principally from the small intestine, to the
blood. From the blood it is circulated to all organs of the body before eventually being exhaled from
che lungs (Suomela and Kahlos, 1972; Hess and Brown. 1991). The dose of radiation resulting from
exposure to radon gas by ingestion varies from organ to organ. While retained in the body, radon
and its decay products irradiate all soft tissues with alpha particles, especially the stomach, intestines,
liver, and lungs. Because the halftimes of radon and radon progeny in the body are short, "buildup"
of dose is negligible and the risk per pCi ingested (RF) can therefore be written as a sum over target
tissues:
RF = I dj r (4)
J
-------
where d. and r. represent the dose (rad) per pCi ingested and the risk (cancer fatality) per rad of
high-LET radiation for the target tissue site j, respectively.
The organ doses and risks associated with ingested radon have been discussed in the Draft Criteria
Document for Radon (USEPA. 1991a). The dosimetric model employed was adapted from that
proposed in a draft report to the EPA entitled A Calculation of Organ Burdens. Doses and Health
Risks from Rn-222 Ingested In Water (Crawford-Brown. 1990). Crawford-Brown's model uses
# *
measurements of the kinetics of xenon in humans (Correia et al., 1987) to calculate the radon
retention time in eight organ compartments. The absorbed radiation dose per pCi radon ingested
rad/pCi) in each particular organ was then calculated based on the retention time, decay rate, the
energy of each decay event, and the fraction of emitted energy that is absorbed in the particular organ
(USEPA, 1989b; Crawford-Brown 1990). The only departure in the Draft Criteria Document from
Crawford-Brown's recommendations on the calculation of organ doses was the assumption that all
218
radon decay products beyond Po produced in the stomach wall are swept away in the blood before
decaying. This assumption reduced the estimated doses to stomach by 40%. The individual organ
doses are listed on Table 2-2. The individual organ risks per unit radiation dose (r., risk/rad) were
calculated using current EPA methodology based on the BEIR in risk model described in the
NESHAPS background information document {USEPA, 1989b) and the Radon Criteria Document
(USEPA, 1991a), using an alpha particle relative biological effectiveness (RBE) of 8, Based on these
assumptions, the calculated risk factor, RF, for cancer fatality per pCi ingested radon is 7.4E-12.
The calculation of the ingestion risk factor is summarized in Table 2-3.
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Eipnsure Assumptions
Ingestion exposure was evaluated based on an intake rate of 1 L/person/day of direct tap water (water
consumed directly from the tap without heating or mixing), with a 20% 1ms (80% retention) of the initial
radon content during the processes of filling a glass awl drinking the water (USEPA, 1991a, 199 lb).
Individual [ ifr.timr. Cantor Fatality Riskinihf. Bropnsttri Rnlr
Using the risk factor of 7.4E-12 and the exposure assumptions described above, individual lifetime
(70-year) risks from radon ingestion per pCi/L of radon in water were estimated to be 1.5E-07 for fatal
cancers.
2.3.2 Revisions-SuicaJkoposetLRule
After publication of the Drinking Water Proposed Rule for Radionuclides, EPA proposed a revised
methodology for estimating the organ-specific risk coefficients from specified doses of ionizing radiation,
based on updated scientific data (USEPA, 1992h, 1992c, 1994b; Puskin & Nelson, 1995). Subsequently,
the ingestion risk factor was re-calculated with the revised organ-specific risk coefficients and additional
modifications of intestinal and lung dosimetry treatment. The derivation of the revised risk factor is
described below and is summarized in Table 2-3.
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Revision of Orgin-sreiffc Risfc Ctttffiaena
Revised estimates of organ specific risk per unit radiation dose (fetal cancer risk per rad) have been
developed by EPA (USEPA, 1994b; Puskin & Nelson, 1995). Preliminary estimates, shown in Table
2-4, are based on the geometric mean of risk coefficients in multiplicative and N1H project models
described by Land and Sinclair (1991). From this table it can be seen that the EPA estimates are in
general accord with the independent analysis by Gilbert (1991). The risk per rad values of Table 2-3
are derived from the GMC estimates of Table 2-4 by multiplying by a relative biological effectiveness
(RBE) of 10. The RfiE accounts for the higher biological effectiveness of alpha radiation in
comparison to the acute exposure to low-LET radiation.
Revision of Intestinal Dosimetry
In the calculating risk to the intestine, current methodology weights the doses as follows: small
intestine, 20%, ascending colon, 40%, descending colon, 40%. U.S. cancer statistics indicate,
however, that mortality from cancer of the small intestine is very low compared to colon cancer
(NCI, 1981). Moreover, no evidence has been found for radiogenic risk of small intestine cancer
(NAS, 1990). Therefore,-it appears more sensible to calculate the risk of cancer in the intestine based
simply on an average dose to the colon. Therefore, for the revised analysis, EPA has neglected the
dose to the small intestine and calculated the total risk to the intestine based on: 1) an average dose to
the ascending and descending colon, and 2) the revised estimate of risk per unit dose for the colon.
Virtually all the energy deposited by radon is due to the absorption of alpha particles having an
energy of 7 Mev or less. Because alpha particles of this energy have a 70 micron maximum range,
nearly all of the dose to tissue arises from the decay of radon and its progeny within the tissue. For
-------
example, radon decay in the digestive system contents plays virtually no role in tissue exposure. Only
radon migrating from the intestinal contents into the epithelial layer contributes dose, and therefore risk, to
the digestive system. Thus, the question of gastrointestinal radon dosimetry reduces to one of determining
the amount of energy deposited in the epithelium.
Estimates of gastrointestinal radiation dose are based on measurements of radon kinetics after ingestion,
and on several assumptions dealing with the level of radon within the stomach and intestinal epithelium.
• Critical assumptions relate to the concentration of radon as a function of epithelial depth, the location of
target cells within the epithelium, and decay product mobility within the epithelium.
Previous dosimetric estimates in other studies have generally been based on the assumption that the
concentration of radon in the epithelium of the G1 tract is equal to that in the adjacent lumen (Hursh et al.,
1965; Suomela and Kahlos, 1972). Noting that the concentration of radon in blood remains much lower
than that in the GI tract, a more realistic assumption would be a linearly decreasing gradient of radon
concentration from the lumen to the blood supply located on the other side of the epithelial layer
(Crawford-Brown, 1990; USEPA, 1991a). In the Draft Criteria Document, it was assumed that a
diffusion gradient of radon was established across the epithelial wall of the stomach (taken to be 40 >un
thick), and that the target nuclei were located 30 ftm from the lumen. The effect of this assumption was to
reduce the estimated stomach dose by a factor of 3 below that calculated on the assumption of a uniform
radon concentration through the epithelium.
In addition, it was assumed that all radon progeny produced in the stomach wall beyond 2,,Po are swept
away into the general circulation by the blood before decaying. This assumption further reduced the
estimated dose to the stomach by 40% (see Table 2-2).
-------
The Draft Criteria Document applied the diffusion gradient assumption to stomach and smalt intestine
dosimetry but not to colon. Similarly, the sweep assumption was only applied to the stomach but not
intestine. The main reason that gradient corrections were not applied to the colon was a judgment that the
radon concentration in the colon was similar to that in the general tissue. Upon re-examination, this
judgment may be inconsistent with Correia's xenon data and the equations used by Crawford-Brown to
model retention (Correia et a!., 19E7; Crawford-Brown, 1990). Therefore, in the revised methodology
presented here, both die gradient and sweep corrections that were applied in estimating stomach dose are
also applied in estimating colon dose. The combined effect is to reduce the colon dose estimate by a factor
of 5 from that in die Draft Criteria Document.
Dosimetry to the gastrointestinal tract is summarized in the following formula:
ose(rad) = fC(t)df3 7E*4 dps-( 19.2-SWP)-^- 1.6x10 -g-?^--GR (5)
J jiCi decay Mev
where:
C(t) — The luminal concentration of radon in /iCi/mL as a function of time. Tissue density is
taken to be 1.
SWP = The Sweep Factor, a measure of the immobility of radon decay products. For example,
an assumption that decay products after a,Po are swept away recces energy deposition
to 11.5 Mev per radon decay and the SWP = 11.5/19.2 = 0.6
2-M
-------
GRA
Gradient Factor, the ratio of dose at target cells to that in the GI lumen. For a
linear gradient through a 40 nm epithelium with target cells at 30 ^m the GRA =
1/3.
In the revised dose calculations, a SWP of 0.6 and a GRA of 0.33 were assumed for stomach as well
. as intestine (small intestine and colon) (see Table 2-2). The SWP estimate was based on the
assumption that energy from ^^Rn and 218Po decay is deposited at the site of radon decay. Decay
progeny after 2*®Po were assumed to have diffused from the epithelium into the bloodstream and
been swept away. The GRA estimate was based on the assumption of a linear radon gradient and of
target cells at a depth of 30 /xm in a 40 urn epithelial layer.
Direct numerical integration of the Correia et al. (1987) data produces doses similar to those
calculated by Crawford-Brown on the basis of a multicompartment kinetic model. From these data, a
direct estimate of the geometric standard error for the integral can be estimated. These values are
listed in Table 2-2 with entries indicating the effect of sweep and gradient assumptions. Doses based
on the Correia et ai. (1987), data are within 30% of those estimated by Hursh et al. (1965), and by
Suomela and Kahlos (1972) using greatly simplified assumptions.
Revision of Lung Dosimetry and Risk Calculation
Crawford-Brown developed a methodology for calculating dose to the alveoli and to the basal cells of
the bronchial epithelium (generations 5, 10, and 16). In-each case the dose consists of two
contributions: (1) from in-situ decays and (2) from decays of radon gas exhaled into the air spaces of
the lung. The dose from the in-situ decays was estimated in two ways: assuming that the radon
concentration was the same as in the liver or as in the general tissue, respectively. The former
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(higher) estimate would appear to be more appropriate for calculating the alveolar dose since the
a>
alveoli are supplied with blood from the liver (portal circulation). His was the assumption adopted
by Crawford-Brown in bis draft report and by EPA in die Draft Criteria Document. Presumably
because the risk estimate was entirely based on alveolar dose, no choice of assumptions regarding
radon concentration in the tracheo-broochial (T-B) tissue was specified in either document. It would
appear, however, that T-B tissue receives most of its blood supply directly from the aorta: hence, the
T-B radon concentration is assumed to be equal to that in the general tissue.
It has been the practice of EPA to calculate lung cancer risks from internally deposited radionuclides
{other than inhaled radon daughters) by applying the entire estimate of lung cancer risk per unit dose
to the calculated pulmonary (alveolar) dose. This practice was adopted in response to a
recommendation by the National Academy Report on "Hot Particles" and Is ordinarily conservative
because lung doses are generally maximal in the alveolar region (NAS, 1976). The relevance of the
alveolar dose is questionable, however, since few, if any, human hing cancers have been (bund to
originate in the alveoli.
In estimating the revised lung cancer risk here, a simple mean of alveolar and (generation S) basal
cell doses is used, calculated assuming that the radon concentration is die same as in the liver and in
the general tissue. Thus, the alveolar dose listed in Table 2-3, 1.8E-09 rad/pCi, is the sum of
alveolar tissue radon dose, 1.5E-09 rad/pCi (from measured liver concentration), and the dose from
radon decay .in exhaled air, 3.3E-10 rad/pCi (Crawford-Brown, 1990). The basal cell dose,
8.41-10 rad/pCi, is the sum of intracellular basal cell .radon, 6.7E-10 rad/pCi (from measured general
. - *
tissue concentration), and the dose from decays in exhaled air at fifth generation bronchioles,
1.7E-10 rad/pCi. Since the alveolar dose is only about twice the basal cell dose and since the lung is
2^3
-------
a relatively minor contributor to the total risk, the final risk estimate is insensitive to how doses from
the two parts of the lung are weighted.
Revised Risk Factor
It can be seen from Table 2-3 that the revised estimate of fatal cancer risk per pCi of radon ingested
(1.7E-11) is about 2.3 times higher than in the Draft Criteria Document (7.4E-12). Mostly, this
increase reflects higher estimates of the risk per unit dose for alpha irradiation of the stomach and
colon. Finally, if EPA were to employ the revised organ dose (nd/pCi) in Table 2-3 but
maintain the current risk/rad estimates cited in the Draft Criteria Document, the fetal cancer risk
estimate would be approximately 6.3E-12 per pCi of radon ingested. •
Revised Individual Lifetime Cancer Fatality Risk Estimate
The revised risk factor is 1.7E-11 cancer fatality per pCi ingested. Using the same exposure
assumptions (consumption 1 L/day, 20% radon volatilization prior to ingestion), the individual
lifetime (70-year) cancer fatality risk per pCi ingested is revised from 1.5E-07 to 3.5E-07. These
calculations are summarized in Table 2-5.
2»H
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Summary; Comparison of Fatal Cancer Risk Estimates in the Proposed Rule and
Estimatrs Derived with Revised Methodologies
2.4.1 Fata] Cancer Risk Estimates in the Proposed Rule
In the proposed rule, the estimated total lifetime fatal cancer risk from waterborne radon is 6.6E-07,
which includes the risks from inhalation of radon progeny (4.9E-07), inhalation of radon gas
(0.2E-07), and ingestion of radon gas (1.5E-07). The relative contributions of cancer risk from
inhalation of radon progeny, inhalation of radon gas, and ingestion of radon to total cancer risk from
water uses are 74%, 3%, and 23%, respectively. The total lifetime fatal cancer risk of from
waterborne radon at the proposed MCL level (300 pCi/L) is 2.0E-04.
2 4.2 Fatal Cancer Risk Estimation bv Revised Methodology
With the revised methodologies, the estimated total lifetime fatal cancer risk from waterborne radon is
6.8E-07, which includes the risks from inhalation of radon progeny (3.0E-07), inhalation of radon gas
(0.3E-07), and ingestion of radon gas (3.5E-07). The relative contributions of cancer risk from
inhalation of radon progeny, inhalation of radon gas, and ingestion of radon to total cancer risk from
water uses are 44%, 4%, and 52%, respectively.
Table 2-6 summarizes the risk estimates originally presented in the Proposed Rule and the revised risk
estimates based on more recent data and analyses.
-------
TABLE 2-1 SUMMARY OF PROPOSED AND REVISED CALCULATIONS OF
UNIT RISK FROM INHALATION OF RADON PROGENY
Term
Proposed Rule
Revised Value
Transfer factor
1E-04
IE-04
Equilibrium factor
0.5
0.5
Occupancy factor
0.75
0.75
Risk factor
3.60E-04
2.24E-04
Constant
0.516
0.516
Annual Unit Risk
7.0E-09
4.3E-09
Lifetime Unit Risk
4.9E-07
3.0E-07
-------
TABLE 2-2 INGESTED RADON DOSES (rads/pCi) AND VARIATION FOR INDIVIDUAL ORGANS
Assumes NO Gradient, NO Sweep
C-B/GSD
Criteria Doc/GSD
Direct | /GSD
Hursh
Suomella
Stomach
5.1x10 * ± 1.5
5.1x10"* ± 1.5
6.8x10 * ± 1.2
3.5x10"*
3.5x10"* (S)
Small Intestine
1.6x10"* ± 1.5
1.6x10"* ± 1.5
1.2x10 * ± 1.4
Ascending Colon
7.4xl0"y ±1.5 (S)
7.4x10 y ±1.5 (D)
Descending Colon
4.lxlG*y ± 1.5 (S)
u
4.1x10 ± 1.5 (D)
Liver
1.5xI0"y ± 1.5 (S)
I.5xl0"y ± 1.5 (D)(X)
Lung Alveoli
General Tissue
1.8x10^ 1.5 (S)
6.7x10
u
1.8x10 y A: 1.5 (X)
6.7x10
Assumes Gradient but NO Sweep
C-B/GSD
Criteria Doc/GSD
Direct I /GSD
Hursh
Suomella
Stomach
1.7x10 * ± 1.5 (S)
1.7x10 * ± 1.5
2.3x10 * ± 1.2
1.2x10*
1.2x10"*
Small Intestine
5.2xl0"y ± 1.5(S)
II
5.2x10 ± 1.5 (D)
u
4.1x10 ± 1.4
Ascending Colon
2.5xl0~y ± 1.5
2.5xl0"y ± 1.5
Descending Colon
1.4xl0"y ± 1.5
1.4xl0*y ± 1.5
Assumes Gradient AND Sweep
C-B/GSD
Criteria Doc/GSD
Direct I /GSD
Hursh
Suomella
Stomach
1.0x10 * ± 1.5
1.0x10 * ± 1.5 (D)(X)
1.4x10 * ± 12
1 {]
6 9x10 y
7,0xl0"y
Small Intestine
3. Ixl0"y ± 1.5
3.1x10 y ± 1.5 (X)
2.5x10 y ± 1.4
Ascending Colon
|l
1.5x10 ± 1.5
(i
1.5x10 ± 1.5 (X)
Descending Colon
8.2xlO"IU± 1.5
8.2xI0*IU ± 1.5 (X)
First Column Set: Using Values from Crawford-Brown, 1991. (S) indicates the values chosen by Crawford-Brown for his analysis.
Second Column Set: Using values from Criteria Document. (D) indicates the values chosen in the document and the Proposed Rule. (X)
indicates values used in this document as the revised dosimetry.
Third Column Set: Using calculated geometric median and GSD from integration of raw Correia data.
Fourth and Fifth columns taken from Hursh, I96S, and from Suomela and Kahlos, 1972, calculations. Source data indicated by (S).
Hursh's calculations assumed 11.5 Mev deposited per radon decay.
Gradient calculation divides dose from lumen by 3.
Sweep calculation multiples dose from lumen by 11.5/19.2 = 0.6.
-------
TABLE 2-3 INGESTION DOSES AND RISKS BY CANCER SITE
Cancer
Draft Criteria Document
Revised
Site
Rad/pCi
Risk/rad
Risk/pCi
Rad/pCi
Risk/rad
Risk/pCi
Stomach
l.OxlO"8
3.7XI0"4
3.7xl0"12
l.OxlO"8
8.9x10^
8.9xl0"12
Intestme(a)
SI
5.2xI0"9
3.7xl0"5
l.9xl0"13
ALI
7.4xl0"9
7.3xlQ"5
5.4xl0"13
DLI
4.1xl0"9
7.3xl0"5
3.0xi0*13
Colon
1.2xl0"9
2Jxl0"3
2.6xlO"U
Liver
l.SxlO'9
4.0X10"4
6.0xl0"13
1.5xlO"9
3.0X10"4
4.5xl0'13
Lung
Alveoli
1.8xl0"9
5.7xl0"5
l.OxlO"12
1.8xlO'9
Basal
8.4xl0"10
Average
1.3xl0"9
1.7xl0'3
-12
2.2x10 "
General
6.7X10*10
1.6xl0*5
l.lxlO"12
6.7x10"10
4.2X10"3
2.8X10"12
TOTAL
7.4xl0"12
1.7X10"11
(a) Abbreviations: SI: Small Intestine; ALI: Ascending Large Intestine; DLI; Descending Large Intestines.
-------
TABLE 2-4 RISK PER UNIT DOSE ESTIMATES (FATALITIES/LOW-LET RAD)W
Cancer
Land and Sinclair (1991)
. Site
GMC^
Multiplicative
Additive
Gilbert (1991)
Stomach
88.7x10"®
29.3x10"®
27,4x10"®
74.3x10"®
Colon
224.X10"6
381x10*®
155x10*®
149x10"®
Lung
165.X10"6
265x10"®
114x10"®
149x10"® .
Liver
30x10"®
30x10"®
30x10"®
(a)
lb)
Model risks have been calculated with 1980 US vital statistics assuming a Dose Reduction
Effectiveness Factor of 1.
GMC: Geometric Mean Coefficient based on the multiplicative and additive transport models.
-------
TABLE 2-5 SUMMARY OF PROPOSED AND REVISED CALCULATIONS
OF UNIT RISK FROM INGESTED RADON GAS
Term
Proposed Rule
Revised Rule
Fraction not volatilized
0.8
0.8
Volume ingested
1.0
1.0 '
Risk Factor
7.4E-12
1.7E-11
Constant
365
365
Annual Unit Risk
2.2E-09
5.0E-09
Lifetime Unit Risk
1.5E-07
3.5E-07
9
-------
TABLE 2-6 SUMMARY OF PROPOSED AND REVISED RISK
ESTIMATES FOR RADON IN WATER
Lifetime Cancer Risk per pCi/L in Water
Exposure Pathway
Proposed
Revised
Inhalation of radon progeny
due to radon released from water
4.9E-07 (74%)
3.0E-07 (43%)
Inhalation of radon gas released
from water to indoor air
0.2E-G7 (3%)
0.5E-07 (7%)
Ingestion of radon gas in direct
tap water
1.5E-07 (23%)
3.5E-07 (50%)
Sum of all pathways
. 6.6E-07 (100%)
7.0E-07 (100%)
-------
3.0 METHODS FOR CHARACTERIZING AND QUANTIFYING UNCERTAINTY
3.1 Sources of Uncertainly
In an environmental risk assessment, there are generally three broad sources of uncertainty: (I)
scenario uncertainty, (2) model uncertainty, and (3) variable uncertainty. Scenario uncertainty involves
the basic appropriateness of the facts, assumptions, and inferences used to select the exposure scenarios
of concern. Model uncertainty refers to the uncertainty and potential for error introduced by a
mathematical model's simplified representation of an exposure scenario or a dose-response relationship.
Variable uncertainty refers to the inability to determine accurate values for the variables in an exposure
or risk model, due to factors such as measurement error, systematic error, or random error. The focus
of this report is mainly on variable uncertainty within the radon exposure scenarios considered and risk
models employed.
3.2 Xypes-otLUncertainty
There are two fundamentally different types of uncertainty (IAEA, 1989; Finkel, 1990; Morgan and
Henrion, 1990; Frey, 1992; Helton, 1993). The first type of uncertainty (natural or stochastic
variability) is due to variation or heterogeneity among different members of a set or population. For
example, there are differences between peuple in the amount of water they drink and the amount of
time they spend indoors, differences between houses in room size and ventilation rate, and differences
between water systems in radon concentration. Because of this variability, then; is no unique answer to
a question such as "What is the risk from radon in water." Rather, the answer must take the form of a
range of possible values, most commonly described in terms of statistics such as the average, median,
geometric mean, 95th percentile, etc.
-------
The second type of uncertainty results from lack of knowledge about the parameters of the variables
of a model or system. Thai is, it .is only possible to provide a range of alternative estimates of the
true (but unknown) value of a parameter. This type of uncertainly can, in principle, be reduced by
gathering better data. Examples of knowledge uncertainties in this analysis include uncertainty around
the true mean and/or the standard deviation of variables such as radon concentration in water, water
intake rates, the water-to-air transfer factor, etc.
3.3 Quantitative Approaches to Characterizing Uncertainty in Radon Risks
3.3.1 Variable Specification: PDFs
Continuous stochastic variables are most conveniently and completely described in terms of
Probability Density Functions (PDFs), while discrete stochastic variables are described by Probability
Mass Functions (PMFs). For convenience, PDF is used generically in this document to refer to
either continuous or discrete variable distributions. A PDF is a mathematical formula which describes
how frequently the variable will have any specific value or range of values. There are many different
types of PDFs, including the familiar normal ami lognormal distributions, as well as others such as
uniform, triangular, and beta. Appendix 1 provides information on the PDFs that were found to be
useful in describing the distribution of stochastic variables in this evaluation.
Each PDF is completely specified by one or more parameters. For instance, normal and lognormal
PDFs are specified by the parameters n and a. For a normal distribution, m is estimated from the
mean of a sample drawn from the population, while a is estimated from the sample standard
deviation. For a lognormal distribution, ^ and a are estimated from the mean and standard deviation
of the log-transformed values of a sample.
3JT
-------
Because the parameters of a PDF characterizing an exposure or toxicity-related variable are typically
estimated from a limited set of observations, the data may not be representative of the entire
population, and sample statistics (mean, standard deviation, etc.) may not be accurate estimates of the
true values of the population parameters. To account for this, a PDF can be used to describe the
range of possible credible values for each parameter. In this report, PDFs which describe variability
among different members of a population are designated with the subscript v (PDF,), while PDFs
which describe uncertainty about a parameter are designated with the subscript u (PDFJ.
3.3.2 PDF Selection
In choosing what type of PDF to use to describe variability or uncertainty, it is important to take
advantage of all the information that is available, but not to make any assumptions or to impose any
restrictions that are not supported by data or by expert opinion. In this analysis, it was found that
most variables could be classified into one of three categories, as follows.
Loenormal Distributions
Many of the variables employed in these calculations are observed to have a distribution that is
skewed to the right, and have values that span several order of magnitude. This type of data set can
often be modeled by a lognormal (LN) distribution. As noted above, this type of PDF is specified by
a location parameter n and a shape parameter a:
PDFy(X): X - LNOi.ff)
[Note: the symbol " - " should be read "is distributed as".]
3*
-------
As noted above, die values of n and a can be estimated from the geometric mean (gm) and geometric
standard deviation (gsd) of a sample drawn at random tan the distribution, but there is uncertainty
associated with this approximation. This uncertainty about n and o were modeled as follows:
24# - T.„ («)
«/^T
- cmsa . a)
tr
where:
m - ln(gm) of a sample drawn from the population
s = ln(gsd) of a sample drawn from the population
n « number of measurements in the sample used to calculate gm and gsd
T^| = Student's t-distribution with n-1 degrees of freedom
CHISQ^j =» Chi-squared distribution with n-1 degrees of freedom
For convenience, the process of choosing a random deviate from the Student t-distribution and
calculating the corresponding value of n is designated in this report as a function called TS(m,s,n),
and the process of choosing a random deviate from the chi-squared distribution and calculating the
corresponding value of a is designated by a function called INVCH(s.n).
When considering the uncertainty in the parameters of a distribution, it is important to remember that
uncertainty depends not only on sample size (n), but also on the
representativeness of the sample. For example, if a study of ventilation rates in 1000 new homes
located in Maine in January identified a mean and standard deviation of 0.35 ± 0.03 air changes per
hour , it would not be prudent to assume that this relatively precise estimate was representative for
homes of all ages in all states in all seasons. Therefore, in modeling the uncertainty about ji and a.
-------
the value of n in the PDFy equations above was replaced by a subjective "quality factor" (qf) that
reflects not only the number of samples in the study, but also how well the sample was judged to
represent the population of interest (the entire population of the US). In order to simplify the process
and avoid creating a false sense of precision, only three different values of qf were employed. A
value of 10 was assigned to studies that had only a small number of observations or were judged to be
based on a subpopulation not likely to be characteristic of the entire population. A qf value of 100
was assigned to studies that were based on a large number of observations drawn from a population
that was judged to be reasonably characteristic of the entire population. Other studies (intermediate in
sample size and/or representativeness) were assigned a qf of 25.
An important characteristic of the lognormal distribution is that the range of the variable is
O^X < oo. in order to exclude selection of random deviates that are outside the range of plausible
values for the variable, the distribution was truncated by replacing any values selected during the
simulation that were below a specified minimum or above a specified maximum with a new selection.
The minimum and maximum values were chosen, often in a subjective fashion, to represent values
judged to be the lowest and highest credible values the variable might assume. Typically these
truncation limits had only a small effect on the mean of the distribution (well within the range of
uncertainty about the mean).
In summary, variables that can be approximated as truncated lognormal distributions were modeled as
follows:
PDFy(X): X - TLNOx.o.min.max)
PDFu(m): ii - TS(m.s.qf)
PDFu(a): a - INVCH(s.qf)
3-5
-------
where:
m
s
qf
ln(gm)
ln(gsd)
10, 25, or 100 (selected based on extern and representativeness of data)
Beta Distributions
Several of the model terms may only assume values over a narrow range (e.g., between zero and
one). Included in this category are the occupancy factor, equilibrium factor, and unattached fraction
(used to model inhalation exposure), and the fraction not volatilized (used to model ingestion
exposure). Although data are limited for most of these variables, it i$ considered likely that the shap<
of the distributions of these variables is unimodal, with a mode intermediate between the minimum
and maximum values. However, information was generally not available about the mode, but rather
about the mean. The PDF that most conveniently incorporates this type of information on shape and
location is the beta distribution.
The beta PDF is specified by four parameters, as- follows:
PDF„(X) - B(a,,a1.min.max) ' (8;
The values of a, and a, are related to the mean, mode, minimum, and maximum by the following
equations:
3W
-------
a , (mean-min)(2 • mode-min-max) ^ > ^ ^
1 (mode-mean)(max-min) 1
a.(max-mean)
aj - -f (a, > 1) (10)
(mean-mxn)
Uncertainty about the mean was usually modeled as uniform (U). If the mean selected was left of the
0>
mid-point of the range (mean < (min+max)/2), the mode must lie between the mean and the
*
minimum, but there is no information on where in this interval is most likely. Thus, a uniform (U)
distribution was assumed, ranging from the minimum to the mean. If the mean selected was located
to the right of the mid-point of the range (mean > (max+min)/2), the mode was modeled as
uniform, ranging from the mean to the maximum.
In summary, variables which were found to be well represented by beta distributions were modeled as
follows:
~
PDFv(X): X - BETA(mean.mode.min.max)
PDFu(mean): mean - U(a,b) (a = low end of plausible range of mean)
(b =high end of plausible range of mean)
PDFu(mode): mode - U(min, mean) (mean < (max+min)/2)
mode - U(mean.max) (mean > (max+min)/2)
Uniform Distributions
For some variables, very little information was available on either the shape of the PDF or on the
best estimate of central tendency or range of plausible values. In these cases, the variable was
modeled as uniform, with uncertain minimum and maximum values, as follows:
-------
PDFy(X): X ~ U(min.max)
PDFu(min): oiin - U(a,b)
PDFu(max): max - U(c,d)
where:
a = low end of plausible range for minimum
b = high end of plausible range for minimum *
c = low end of plausible range for maximum
d = high end of plausible range for maximum
3-3.3 vn
-------
Carlo modeling (Law and Kelton, 1991; Morgan and Henrion, 1990). Monte Carlo modeling is a
computer-based methodology for repeated calculation of an output variable based on multiple random
sampling from specified input variable distributions. The distribution of the results (i.e., the
distribution of the multiple estimates of the output variable) can then be used to estimate any statistic of
interest (mean, geometric mean, 95th percentile, etc.).
It is important that quantitative uncertainty analyses be performed in a way that allows a separate
characterization of stochastic variability and knowledge uncertainty, since this provides the most
complete and representative information to the risk manager. To this end, the calculations performed
in this effort employed a two-dimensional (nested) Monte Carlo approach. This approach was
patterned after the methods described by Hammond, Hoffman and Helton et al. (1993a, 1993b, 1993c).
References to "two-dimensions" or "nesting" are intended to emphasize differentiation between
sampling in "variability space" and sampling in "uncertainty space". In the outer Monte Carlo loop, a
value is selected ("realized") for each of the uncertain parameters. Then, holding these values
constant, the inner Monte Carlo loop performs a series of iterations to characterize the variability of the
output PDF. From the results of this inner loop, a series of statistics (e.g., the 5th, 25th, 50th, mean,
75th, and 95th percentiles) of the PDFV are recorded. This process is then repeated for many
realizations, resulting in an uncertainty distribution for each of the PDFy percentiles selected.
Figure 3-1 provides an illustration of this process. Each line in the figure represents the distribution
derived from an inner loop simulation based on one particular set of PDF parameters chosen in the
outer loop. Since the shape and location of the distribution depends on the parameter values selected in
the outer loop, a new distribution is generated for each outer loop. The steepness of the individual
distributions is an indication of how much variability there is in the output (a steep curve indicates
-------
less variability than a shallow curve), and the "spread" between different distributions reflects how
much uncertainty there is in the outcome.
3.3.4 Sensitivity Analysis
The output of the nested Monte Carlo analysis above does not provide any information on the relative
importance of each variable in the calculations, and which variables are the primary contributors to
the variability and uncertainty in the output parameters. In order to investigate these issues, the
following types of sensitivity analysis were performed.
Local Rate of Change
One convenient way to investigate the sensitivity of the model is to calculate how much the output
variable changes per small unit increase (e.g., 1 %) in an input variable. This rate of change depends
on the values selected for each of the model inputs, so the median values of the mean of each variable
(derived from the Monte Carlo simulation) were used. Variables which are important determinants of
dose will cause changes on the scale of +1 % (the dose increases when the variable increases) or -1 %
(the dose decreases when the variable increases). Variables which have little impact on the outcome
are identified by a rate of change that is close to zero.
Partial Rank Order Coefficient (PRCC)
A second method for investigating model sensitivity is to calculate the partial rank order correlation
coefficient (PRCC) between the output variable and each of the input variables (Iman and Helton
1991). The PRCC is a measure of the strength of the monotonic relation between the input and the
-------
output variable after a correction has been made for the monotonic effects of other input variables.
The PRCC for the model
Y a ffXpXj, • • • Xn)
(11)
is given by
(12)
where C is the symmetric (n+1) by (n+1) rank correlation matrix for the n input variables, C is
the inverse of C. and C
is the element of C-l corresponding to the rank correlation between X.
and Y.
Because of the uncertainty in input parameters, the PRCC values will vary between each outer loop of
the simulation, so each PRCC is. best expressed as a distribution. For convenience, these distributions
are shown in the results sections as box-and whisker graphs where the box shows the 25th, 50th, and
75th percentile values, and the whiskers show the 3th and 95th percentile values. Model inputs which
are both 1) important determinants of outcome (as evaluated above), and 2) a significant contributor
to the variability in the output parameter will have box-and-whiskers that are close to plus one (the
dose increases when the variable increases) or to minus one (the dose decreases when the variable
increases). Inputs which are either 1) not an important determinant of outcome (as evaluated above)
or 2) have low variability (at least compared to other model terms) will have box-and-whisker plots
that are close to zero. The width of the distribution (the difference between the ends of the whiskers)
provides some sense of the relative contribution each variable makes to the uncertainty in the output,
but the width also depends in a complex way on the relative variability and uncertainty in other
variables, so the width should not be over-interpreted.
-------
Figure 3-1 20 Plausible Realizations of an Uncertain Cumulative Density Function
LOO
0.90
0.80
0.70
g 0.50
£ 0.40
0.30
0.20
0.10
0.00
Random Variable X
77
-------
4.0
VARIABILITY AND UNCERTAINTY IN RISK FROM INHALATION OF RADON
PROGENY FORMED FROM RADON RELEASED FROM WATER
This chapter presents a quantitative analysis of the variability and uncertainty in estimated levels of
risk associated with exposure to radon progeny attributable to radon released from household uses of
water. Descriptors of exposure and risk which were evaluated included the following:
• Unit Dose (UD): This is the exposure to radon progeny per pCi/L in water
• Unit Risk (UR): This is the risk of death from lung cancer (led) per person per pCi/L
of radon in water
• Individual Risk (IR): This is the risk of lung cancer death in an individual exposed to a
specific radon concentration in water
• Population Risk (PR): This is the expected number of lung cancer fatalities per year
occurring in the population of U.S. residents exposed to radon in water
The basic approach followed for quantifying variability and uncertainty in these parameters is the two-
dimensional Monte Carlo method described in Section 3.3.3.
Section 4.1 describes an analysis of the variability and uncertainty in exposure and risk from radon
progeny calculated using the one-compartment (transfer factor) method approach previously employed
by EPA. In order to investigate whether the one-compartment method adequately accounts for peak
-------
exposures that occur during events such as showering, estimates of exposure and risk were also
calculated using a three-compartment model. These calculations are presented in Section 4.2.
4.1 One-Compartment Method
4.1.1 Basic Equations
As discussed in Section 2.2, the basic equations for calculating exposure and risk based on the one-
compartment model are as follows:
UD - [TF] [0.01 WL/(pCi/L) • EFJ [OF -51.6 WLM/WL-yr] <13>
UR = UD-RF <14>
1R =• UR-C <15>
PR = IR__ • N (16)
meiB
where:
UD = Unit dose (WLM/yr per pCi/L)
TF = Transfer Factor (the increase in radon concentration in indoor air per unit radon
concentration in water) (pCi/L air per pCi/L water).
-------
EF = Equilibrium factor (the fraction of the potential alpha energy of radon progeny that
actually exists in indoor air compared to the maximum possible alpha energy
under true equilibrium conditions).
OF * Occupancy factor (the fraction of time that a person spends indoors).
UR = Unit risk" (led per person-yr per pCi/L)
RF = Risk factor (led per person-WLM of exposure).
IR = Individual risk (led/yr per person)
C ¦ Concentration of radon in water (pCi/L)
PR = Population risk (led/yr)
IRmean ~ Mean individuai risk (led/yr per person)
N = Number of people exposed to radon from household water
The variability and uncertainty in each of these terms are discussed below, along with the PDFs
selected to model these variables.
4,1.2 Probability Density Functions (PDFs)
Transfer Factor (TF>
The concentration of radon in indoor air that results from release from water is highly variable.
Levels vary from room to room and as a function of time, depending on water use patterns, room
4^
-------
-------
1. Based on the results of Nazaroff et al. (1987), the value of TF was modeled in this evaluation as a
truncated lognonnal distribution with uncertain gm and gsd:
PDFy(TF) - TLN(gm,gsd,min,max)
where:
PDFu(ln(gm))
PDFu(ln2(gsd»
m
s
*- TS(m,s,qf)
- INVCH(s.qf)
- ln(6.57E-05)
= ln(2.88)
No information was located to estimate the credible lower and upper truncation limits of TF, so the
1st and 99th percentile values calculated from the lognonnal distribution were selected:
min = 6E-06
max = 8E-04
Because this distribution is calculated rather than measured, and because the number of observations
in the component studies ranges from 21 to 6000, an intermediate qf of 25 is judged to be appropriate
for estimating uncertainty about the gm and gsd. This value of qf yields a credibility interval around
the mean of about 0.8E-04 to 2E-04, which is consistent with most of the mean values for TF located
in the literature (see Table 4.2). The value reported by Hess et al. (1990) is outside this interval, but
this is probably because the subset of houses studied by Hess were significantly larger than average.
>5
-------
Equilibrium Factor (EF)
At radiologic^^Juijibrium< 1 pCi/L of radon in air corresponds to a concentration of 0.010 WL of
radon progeny. Undei household conditions, processes such as ventilation and plating out of
progeny prevent achievement 01 «ouilibrium, and the level of radon progeny present is normally less
than 0.010 WL. The equilibrium factor c=P) is the ratio of the alpha energy actually present in
respirable air compared to the theoretical maximum equilibrium. Thus, the value of EF may be
empirically estimated as:
EF - (19)
0.010-Rn
where:
P = concentration of radon progeny in air (WL)
Rn = concentration of radon gas in air (pCi/L)
The value of EF has been measured in a number of homes in a number of studies. These studies
have been previously reviewed by ORIA (USEPA, 1992a), which found that a value of 0.5 is the
most appropriate estimate of the mean for U.S. homes, with a credibility interval around the mean of
0.3S to 0.SS. Within each study, individual values may range rather widely, from less than 0.1 to
more than 0.85. Based on these data, the value of EF was modeled as an uncertain beta distribution,
as follows:
PDFv(EF) - BETA(mean.mode.min.max)
-------
PDFu(m«u») - 11(0.35,0.55)
PDFu(mode) - U(min,mean) (mean < (max+min)/2)
- U(jueaa,max) (mean > (max+min)/2)
nun » 0.1
max » 0.9
Occupancy Factor fOFi
The occupancy factor (the of tune thai a person spends at home) varies with age and
occupational status- f or example, a study sponsored by EPR1 (GEOMET, 1981) found values of
0.62, 0 92, and 0.86 for people employed outside the home, homemakers, and the elderly,
respectively. This and other studies on the occupancy factor have been reviewed by OR1A (USE!
1992a), who found that a value of 0.75 is the most appropriate point estimate of the mean, with a
credibility interval around the mean of 0.65-0.80. The minimum plausible value is estimated ~« 1
0.33, based on the expectation that nearly ail people will spend an average of about 8 hours/day a
home. The maximum plausible value was set at i.0. Based on these values; occupancy factor wi
modeled as a beta distribution, as follows:
PDFv(OF) - BETA(mean,mode,min,max)
PDFu(mean) - U(0.65,0.8)
PDFu(mode) - U(min,mean) (mean < (max+min)/2)
~ U(mean.max) (mean > (max+min)/2)
min = 0.33
max = 1.0
-------
Risk Factor (RF)
ORIA (USEPA, 1992a; Puskin 1992) has previously performed an analysis of the uncertainty in the
risk factor for inhaled radon progeny. This analysis is based on the adjusted BEIRIV model used in
%
conjunction with lifetabie calculations employing 1980 U.S. vital statistics.. The analysis considered
uncertainty due to statistical variability in epidemiological data from studies of miners, projection of
risk over time, age dependence of risk, and differences between mines and homes that may influence
dosimetry. Each of these sources of uncertainty were modeled as lognormal, and it was assumed the
uncertainties were multiplicative. The calculations performed by ORIA are summarized in Table 4-3.
The best estimate of central tendency is 224E-06 led per person-WLM, with a credibility interval
from 140E-06 to 57GE-06 led per person-WLM (USEPA, 1992a). Assuming a lognormal
distribution, this corresponds to a GSDU of 1.S3, with a geometric mean of the credibility interval of
283E-06 led per person-WLM.
It is important to recognize that the uncertainty evaluation for the risk factor does not include all
sources of uncertainty. Important sources of uncertainty which have not been quantified include the
following.
Smoking. The risk model assumes that the risk from radon exposure is proportional to the baseline
lung cancer rate in a population. Effectively, this means that a multiplicative interaction between
radon and all other causes of lung cancer, including smoking, is assumed (Puskin and Yang, 1988).
If, as suggested by some of the epidemiological data, the interaction is submultiplicative. then the
model will overpredict radon risk for smokers but underpredict the risk for people who never smoked
(NAS, 1988). Since the prevalence of smoking among the miner cohorts was generally higher than in
the U.S. adult population, this would probably mean an increase in the radon risk estimate for
-------
residential exposures. The problem of projecting the effect of smoking on radon risk is further
complicated by questions of risk to former smokers and shifting patterns of smoking among birth
cohorts (Puskin, 1992).
Extrapolation to low doses ami dose rates. Many of the radon exposed underground miners upon
which risk estimates are based received much higher exposures than wouid ordinarily be received in
residences. Nevertheless, statistically significant numbers of excess lung cancers have been observed
in miners who received about SO WLM, only about 3 times the average lifetime residential exposure.
The exposure rate among the miners was generally much higher than in homes, however. Laboratory
studies on alpha panicle irradiated animals and cells (ICRP, 1991), as well as epidemiological data on
radon exposed miners (Lubin et ai., 1994), wouid indicate that the risk per WLM is maximal at low
doses and low dose rates (i.e., under residential exposure conditions), with no expectation of a
threshold. The BEIRIV Committee's analysis of 4 miner cohorts found no evidence of non-linearity
in the dose response, except for U.S. miners receiving more than 2,000 WLM, and these miners were
excluded from the analysis (NAS, 1988). Likewise the Committee found no consistent indication of
an exposure rate effect. A more recent analysis of 11 miner cohorts (Lubin et al., 1994) did show an
increased risk at low exposure rates, but the extrapolated risk of the U.S. population was comparable
to that projected by BEIR IV.
Effect of other mine exposures. Underground miner cohorts, upon which radon risk estimates are
based, were exposed to other potentially toxic substances such as silica, uranium dust, blasting fumes,
and engine exhaust. Animal studies, however, have shown no effect of such agents of lunch cancer
risk from radon (NAS, 1988). There is also epidemiological evidence that silica exposure is not a
strong corifounder in the epidemiological studies on miners (Radford and Renard, 1984; Samet et al.,
1994).
-4-9"'
-------
Because of these uncertainties riot quantified, the PDF^ selected to model uncertainty about the risk
factor is likely to be somewhat too narrow. Available data are not considered adequate to derive a
quantitative estimate of inter-person variability in the risk factor.
CQBCgrowfrB 9f Rafon in
The most complete data set on the occurrence of radon in public water systems is provided in the
National Inorganics and Radionuclides Survey (NIRS) (Longtin, 1990). NIRS was a random sample
of 982 of the nation's community groundwater supply systems, stratified according to the size of the
system. The radon concentration in each system was measured by a liquid scintillation method with a
minimum repotting level (MRL) of about 100 pCi/L (Glaser et al., 1981). Table 4-4 summarizes the
NIKS community groundwater supply data.
Approximately 28% of the NIRS sites (275 out of 982) had radon-222 concentrations below the MRL.
Radon concentrations were assumed to be represented by a type I censored distribution; chat is, the
distribution was assumed to continue below the censoring point (see Kendall and Steward, 1979;
Johnson and Kotz, 1970: Aitchison and Brown, 1966; Gilbert. 1987; Schneider, 1986). Maximum
likelihood and least squares methods for type I censored samples were employed to investigate the fit
of the radon concentration data to various skewed distributions. The downhill simplex method
developed by Nelder and Mead (1965) as implemented by Press et al. (1989, 1991) was used for
parameter estimation.
Five distributions were fitted to the occurrence data: lognormal, 2-parameter Weibull, 2-parameter
gamma. Pearson Type V and Pearson Type VI. These distributions were selected because they
exhibit varying degrees of skewness and tail flatness. Critical values for the Kolmogorov-Smimov
4-JflT
-------
and Anderson-Darling tests were available for the lognormal. Weibull and gamma distributions (Law
and Kelton, 1991; D'Agostino and Stephens, 1986). Critical values were not available for the
Pearson V and VI distributions. Generally, the NIRS occurrence data were best fit by a 2-parameter
gamma distributions. However, the data were also well-fit by lognormal distributions, even though
there were systematic deviations from lognormality at the high end (upper tail) of the distributions.
Overall, the marginal gains in fit provided by the gamma distribution over the more familiar and
more easily manipulated lognormal distribution were judged not to be worth the added complexity and
loss in simulation speed. Based on this, lognormal distributions were chosen to represent all five
groundwater system strata. The best fit statistics (gm, gsd) for each strata are shown in Table 4-4.
Deviations from lognormality at the higher radon concentrations may be expected to affect estimates
of high-end risks by systematically biasing the estimation of high-end risks towards underestimation.
In order to simplify the Monte Carlo analysis of exposure, the five separate PDFs by strata were
combined into a single population-weighted PDF. That is:
PDF,(C)=EVPDFv(Ck) (2°)
where:
\k = the ratio of people served by the kth strata to the total of all people served by all 5
strata
PDFv(Cj{) = the lognormal PDF for radon concentration in the kth strata
Information on the number of people served by water systems in each strata (X^) were obtained from
the Federal Reporting Data System (FRDS) database. These data are also shown in Table 4-4. The
-------
resulting population-weighted combined PDF was well fit by a lognormal distribution with an
arithmetic mean of 246 pCi/L, a geometric mean of 200 pCi/L, and a GSD of 1.8S. In keeping with
the general approach described above for estimating uncertainty about these parameters, the value of
C was then modeled as follows:
PDFy - LN(gm,gsd)
PDFu(ln(gm)) - TS(m,s,qf)
PDFu(ln2(gsd)) - INVCH(s.qf)
m =* ln(200)
s = ln(1.85)
A quality factor of 10 was selected for modeling the uncertainty around the parameters of this
distribution, even though the data set is derived from nearly 1000 different water systems. This is
because the population-weighted PDFy for C is dominated (weighting-factor = 0.6) by the large/very
large size stratum, for which there are only 28 data points, 11 of which are censored.
Summary of PDF s and PDF s
Table 4-5 summarizes the PDFys and PDFus selected to model exposure and risk using the one-
compartment model.
4.1.3 Results
As discussed in Section 3.3.3, two-dimensional Monte Carlo modeling was used to propagate the
PDFvs and PDFus which characterize the variability and uncertainty in the parameters of the one-
-------
compartment model. The simulation for the one-compartment model involved 1,000 outer loop
realizations of uncertain parameters and 2,500 inner loop iterations per realization. The results are
shown in Figure 4-1 (unit dose), Figure 4-2 (unit risk), and Figure 4-3 (individual risk). The lower-
bound, median, and upper-bound cumulative density functions (CDFs) for unit dose, unit risk, and
individual risk are all well-fit (R^ > 0.99) by lognormal curves, as shown in the graph inserts.
Selected numerical values from these graphs are summarized in Table 4-6, along with population risk
estimates.
As seen in these figures and table, the variability in unit dose between different people in different
houses (as indicated by the ratio of the 95th percentile to the 5th percentile) is about 50-fold. This
index of variability does not increase for unit risk, because the risk factor is modeled as an uncertain
constant (i.e., it does not add to variability). Variability in individual risk and population risk
increases to nearly 100-fold, due to the added variability in the radon concentration factor.
Uncertainty in any particular exposure statistic (characterized as the ratio of the upper bound divided
by the lower bound) is about 2-4 fold for unit dose, and this increases to about 6-7 fold when the
uncertain risk factor is incorporated to calculate unit risk. Uncertainty increases only to about 6-8
fold when the concentration term is included to yield individual risk and population risk. Thus,
uncertainty in the risk factor is the primary source of uncertainty in both individual and population
risk estimates.
-------
4.1.4
Sensitivity Analysis
Local Rate of Change
Because the one-compartment model is strictly linear in all of the model input terms, the rate of
change in any output parameter is 1 % per 1 % change in input variable.
Partial Rank Order Correlation Coefficients
Figure 4-4 shows the PRCCs for each of the independent variables used in the one-compartment
model for radon progeny. As discussed in Section 3.3.4, the "height" of the box (the distance from
the zero axis) is an indication of the relative importance of each term to the variability of the output,
and the "width" of the box (the distance between the ends of the "whiskers") is a complex function of
both uncertainty and variability in the parameter. As shown, all of the one-compartment input
variables have high correlation coefficients, although the value for the occupancy factor is somewhat
lower than for the others. This is because the occupancy factor varies over a somewhat smaller range
than the other variables.
4 .2 Three-Compartment Model Method
The one-compartment model employed above estimates daily average human exposure to radon and
its progeny by assuming that the rate of radon released from water into indoor air is continuous, and
that the concentration of radon progeny in air is uniform (i.e., in steady state) throughout the entire
house. However, most household water uses are episodic rather than continuous, and room barriers
(walls, doors) may restrict the rapid mixing of radon released into air in one location with whole-
-------
house air. This can lead to high levels of radon and radon progeny in some rooms (especially those
with high water usage, such as the shower or Jaundry) and this in turn can lead to episodic peak
exposures of people who are in those rooms when water use is occurring. These high peaks of
exposure raise the issue of whether the use of a simple one-compartment (steady-state) model might
lead to an underestimate of the true exposure level. In order to investigate this issue, the levels of
radon exposure and risk predicted by the one-compartment model were compared with exposure
estimates calculated using a three-compartment house model.
4.2.1 Model Description
The three-compartment model employed is basically that of McKone (1987). This model predicts the
concentration of a volatile chemical in water (in this case, radon) in each of three compartments of a
house: the shower, the bathroom, and the remainder of the house. Because concentrations are not
constant, results are calculated as a function of time throughout the day. Based on the time- and
compartment-specific concentration values, human exposure levels in each compartment can then be
calculated.
Because the exposure of chief concern is to radon progeny rather than radon gas itself, the McKone
model was modified somewhat to account for the formation and loss of radon progeny by radioactive
decay, and for loss of progeny due to plating out. Appendix 3 presents the mathematical details of
the modified model. Figure 4-5 presents an example output of the model, showing the concentration
of radon (pCi/L) and radon progeny (WL) in each room throughout the day. In this example, there
were two people assumed to live in the house, and the two peaks due to the two showering events are
clearly visible. Levels of radon and radon progeny are relatively steady during the remainder of the
day, falling to lower levels overnight when water uses in the house are assumed to cease.
-------
4.2.2 Monte Carlo Implementation of the Model
A similar approach was used to evaluate the variability and the uncertainty in exposure and risk
estimates calculated using the three-compartment model as was used to evaluate the otie-compartment
model predictions. That is, each of the inputs to the three-compartment model were specified in
terms of a PDFy with associated PDFus to describe uncertainty in the parameters of those
distributions. Appendix 4 details the selection of these PDFs. A two-dimensional simulation was
then performed, with 250 realizations of uncertain parameters and 2000 iterations of variable terms
per realization.
4.2.3 Results
The results of the three-compartment modeling are shown in Figure 4-6 (unit dose). Figure 4-7 (unit
risk), and Figure 4-8 (individual risk). Selected numerical values from these graphs are summarized
in Table 4-7, along with population risk estimates.
As seen in these Figures and table, the variability in unit dose between different people in different
houses (as indicated by the ratio of the 95th percentile to the 5th percentile) estimated by this model is
about 25- to 30-fold. This index of variability does not increase for unit risk, because the risk factor
is modeled as an uncertain constant (i.e., it does not add to variability). Variability in individual risk
and population risk increases to about 50-fold due to the added variability in the radon concentration
factor.
^-4"+6~
-------
Uncertainty in any particular exposure statistic (characterized as the ratio of the upper bound divided
by the lower bound) is about 2-fold for unit dose, and this increases to about S-fold when the
uncertain risk factor is incorporated to calculate unit risk. Uncertainty increases only to about 6-7
fold when the concentration term is included to yield individual risk and population risk. Thus,
uncertainty in the risk factor is the primary source of uncertainty in both individual and population
risk estimates.
Ureal Rare
-------
with the properties of the main house (residence time, volume, transfer efficiency, water use) and
radon progeny level (unattached fraction, deposition velocity of unattached fraction) are the most
important. Parameters related to shower and bathroom size and ventilation are relatively less
important, since the majority of radon progeny exposure occurs in the main house (USEPA 1993a).
Partial Rank OrrW Pnra»latinn rre»ffit»i*nK:
Figure 4-9 shows the PRCCs for each of the independent variables used in the three-compartment
model for radon progeny. As seen, variables related to the main house compartment (volume of the
main house, residence time in the main house, and water use in the main house) are all important
sources of variability in the output, as are the main determinants of equilibrium fraction (unattached
fraction, deposition velocity of unattached fraction). Naturally, occupancy factor and radon
concentration in water are also important sources of variability.
4.3 Camparison-otjDne--aniLThreezCompacimenLModtils
Figure 4-10 compares the cumulative distribution functions for individual risks from radon progeny
estimated using the one-compartment and three-compartment models. As is readily apparent, the two
models yield results that are not significantly different from each other. The similarity of these two
model predictions tends to support the concept that dose estimates derived by either model are likely to
be reasonable. However, it is also true that both models rely upon some of the same studies for their
input (e.g., the data on house size and ventilation rate used in the three compartment model were also
used to derive the distribution of the transfer factor used in the one-compartment model). Thus, the
apparent cross-validation of the models is not as robust as might first be concluded.
4AS
-------
On the other hand, the similarity of the outcomes does support die conclusion that the simple one-
compsrtment (steady-state) model does not seriously underestimate daily average exposures, even
(hough the model does not explicitly evaluate peak exposures due to events such as showering. As
discussed in USEPA 1993a), this Is because the large majority of the daily dose occurs while ia the
main house, where the assumptions of the one-compartment model ate approximately correct.
4-19—
-------
Figure 4-1 Credible Interval for the Distribution of Radon Progeny
Inhalation Unit Dose Estimated from One-Compartment Model
100
90
80
70
.5* 60
CB
JD
©
UD05 ~ LN(-
UD50 ~ LN(-
UD95 - LN(-4J
50
40
30
20
10
0
1.0E-07 1.0E-06 1.0E-05 1.0E-04 1.0E-03
Radon Progeny Inhalation Unit Dose, WLM/year per pCi/L
-------
Figure 4-2 Credible Interval for the Distribution of Radon Progeny
Inhalation Unit Risk Estimated from One-Compartment Model
100
UR05-LN(-8.98,0.528)
UR50-LN(-8.59,0.524)
UR93 ~ LN(-8.22,0.507)
80
.o
CQ
X5
2
20 --
1.0E-07
1.0E-08
1.0E-G9
1.0E-10
1.0E-11
Radon Progeny Inhalation Unit Risk, led/person-year per pCi/L
-------
Figure 4-3 Credible Interval for the Distribution of Radon Progeny
Inhalation Individual Risk Estimated from One-Compartment Model
-08 1.0E-07 1.0E-06 1.0E-G5 1.0E-04
Radon Progeny Inhalation Individual Risk, led/person-year
-------
Figure 4-4 Partial Rank-Order Correlation Coefficients for Inhalation
Exposures to Radon Progeny Using 1-Compartment Model
1.00
0.90
s 0.80
0
| 0.70
fa
6 0.60
10,0
If °-40
.2 0.30
1
^ 0.20
0.10
0.00
±
i i 1 1 r
IF EF OF CW
Individual Risk
TF EF OF
Unit Dose
TF EF OF
Unit Risk
-------
Figure 4-5 Example Concaatratiaa Profile far Radon Gas and Radon
Progeny in the Shower Estimated by 3-CompKtment Model
St IE-03 -•
0 100 70S m 400 JOO 400 NO MS MO 1000 1100 1100 1100 1400
Time, «¦»««***•
Bathroom
IE-02
t
I
|tM3
IE-OS I.
1E-04
lE-oa
0 100 200 SOO 400 300 <00 *00 100 900 1000 1100 1300 1)00 1400
Time, minutes
Main House
IE-02
IE-04
IE-OS 1.
[£-03
IE-OS
1E-OI
0 100 WO JOO 400 500 600 TO «00 WO lOOO 1100 I JOO 1JOO 1400
Time, minutes
-------
Figure 4-6 Credible Interval for the Distribution of Radon Progeny
Unit Dose Estimated from 3-Compartment Model
100
UD05 - LN(-5.I3,0.436)
UD50 ~ LN(-5.00,0.427)
UD95 - LN(-4.84,0.449)
90 .....
80 —
cu
20 --
10 -
1.0E-04
1.0E-05
1.0E-06
Radon Progeny Inhalation Unit Dose, WLM/year per pCi/L
-------
Figure 4-7 Credible Interval for the Distribution of Radon Progeny
Unit Risk Estimated from 3-Compartment Model
100
UR.05 ~ LN(-8.
UR50 ~ LN(-
UR95 - LN(-
o3 50
¦10 1.0E-09 1.0E-08 1.0E-07
Radon Progeny Inhalation Unit Risk, led/person-yr per pCi/L
-------
Figure 4-8 Credible Interval for the Distribution of Radon Progeny
Individual Risk Estimated from 3-Compartment Model
1.0E-08
IR05 - LN(-6.61,0.532)
IR50~LN(-6.19,0.536)
IR95 - LN(-5.80,0.526)
g 60 --
3 50
1.0E-07 1.0E-06 1.0E-05
Radon Progeny Individual Risk, led/person-year
1.0E-04
-------
Figure 4-9 Partial Rank-Order Correlation Coefficients for the Parameters in the
3-Compartment Model for Radon Progeny Individual Risk
0.8 -
J 0.6
«
1 0.4
o
U 0.2
-------
Figure 4-10 Comparison of One-Compartment and Three-Compartment Model
Estimates for Individual Inhalation Risk for Radon Progeny
1E-04 1 ;
1 ¦ II ^ ^
¦ ¦ ooe-corapastment j-L, r-J-i '
§E06 rt i TJ
2
g three-compartment
¦§E-07 ; 4l (_} :
"3 rj LJ
¦2
" : T '
1E-08 -I
0.05 median mean 0.95
Individual Inhalation Risk Statistic
one-compartment
ri
T
T
three-compartment
-------
TABLE 4-1 SUMMARY OF THE DISTRIBUTIONS FOR VARIABLES .USED
IN CALCULATION OF WATER TO AIR TRANSFER FACTOR00
Variable
Units
Sample Size
Geometric
Mean
(GM)
Geometric
Standard
Deviation
(GSD)
W
Water-use Rate
3
m per person
per hour
90
7.9E-03
1.57
V
Residential
Volume
3
m per person
6051
98.7
1.90
\
Air-Exchange Rate
hour"1
578
0.68
2.01
e
Transfer
Coefficient
unitless
21
0.55
1.12
TF
Water to Air
Transfer Factor
unitless
(derived)
6.5E-05
2.88
(a) Data from Nazaroff et al. (1987)
-------
TABLE 4-2 SUMMARY OF MEASURED AND CALCULATED TRANSFER FACTORS
Study
Average Transfer
Factor
Notes
AWWARF (1990)
1.3E-04 (7,700:1)
Measured value based on a
regression analysis of the reduction
of radon in indoor air due to
reduction of radon in water in 199
homes in three communities.
Becker and Lachajczyk (1984)
0.7E-O4 (14,000:1)
Calculated from "typical" values of
household parameters (selected after
review of literature).
Gessel and Prichard (1980)
1E-04 (10,000:1)
Based on a study of three homes
served with water containing 700-
2,000 pCi/L in water. Individual
values ranged from 5E-05 to 2E-04.
Hess ec al. (1982)
1.07E-04 (9,300:1)
Measured value, based on the slope
of the line relating radon levels in
bathroom air with radon levels in
water (n = 85). Similar
correlations with water were found'
in other rooms.
Hess et al. (1990)
0.24E-04 (42,000:1)
Based on 24-hour average
measurements in 40 homes in
Maine. The average size of the
homes was larger than the average,
perhaps accounting for why this
transfer factor is lower than others.
McKone (1987)
1.2E-04 (8,300:1)
This value not calculated by author,
but derived from typical house and
water use parameters reported by
author.
Nazaroff et al. (1987)
1.1E-04 (9,100:1)
Calculated based on mean data from
a large number of houses.
Small et al. (1990)
1.9E-04 (5,300:1)
This value not calculated by author,
but derived from typical house and
water use parameters reported by
author.
-------
TABLE 4-3 SUMMARY OF THE UNCERTAINTY IN THE RISK FACTOR FOR RADON PROGENY
Nature of the
Uncertainty
Study % Increase, mean
sqr error
0(a)
Composite:
Geometric
Mean, gsd
Adjusted BIER IV Model
+ U.S. 1980 Vital
Statistics
Results
Statistical Variability in
Miner Data
Eldorado 2.6(1.5)
1.3rfa)
d.27)^
224 per 10^ person-WLM
with GSD - 1.27
GM: 224 * 1.27 - 283
r i
Ontario 1.4(1.6)
Malmberget 1.4(2.6)
Colorado Plateau 0.6(1.5)
Projection of risk over
time
Geometric Mean, GSD
Composite
GSD = exp|^lnJ(1.27) + ln2(1.42) J
* 1.53
1.5 1.5
1.00 (1.28)
1.27(1.42)
Age dependence of risk
1.6 1.0
1.27 (1.15)
Extrapolation from
mines to homes.
1.4 1.4
1.00 (1.23)
i
(a) Calculated via
tn£k
InB
k In'a.
in 2 6 + In 1,4 +
£
k
In21.5 In31.6
1 1
In'c*
In11.5 In21.6
= 0.26 -• B « e
026
1.30
(b> Calculated via
GSD = cxp
= 1.27
-------
TABLE 4-5 SUMMARY OF INHALATION UNIT RISK INPUT
DISTRIBUTION FUNCTIONS
Variable
PDF
V
PDFu
Values
Transfer
factor
TF - TLN(gm,gsd,min,max)
ln(gm) *- TS(m,s,qO
ln2(gsd) - INVCH(s.qf)
1
m = In(6.57E-05)
s - In(2.88)
min = 6E-06
max = 8E-04
qf = 25
Equilibrium
factor
EF - U(min.max)
min = U(a,b)
max = U(c,d)
a = 0.35 b =
0.55
c = 0.1 d = 0.9
Occupancy
factor
OF ~
DETA(mcan.mode,miu,max)
mean = U(a,b)
mode = U(mean,max) or
U(min,mean)
a = 0.65
b = 0.80
min = 0.17
max = 0 95
Risk factor
RF - Uncertain constant
RF - LN(gm.gsd)
gm = 2.83E-04
gsd = 1.53
Radon conc.
in water
->
C ~ LN(gm.gsd)
ln(gm) «- TS(m,s,qf)
ln2(gsd) - INVCH(s,qO
m = ln(200)
s = ln(I.6S)
qf = 10
-------
TABLE 4 6 VARIABILITY AND UNCERTAINTY
IN INHALATION EXPOSURE AND RISK TO RADON PROGENY
ESTIMATED USING ONE-COMPARTMENT MODEL
Exposure or Risk
Parameter
Variability
Statistic
Uncertainty
Lower Bound
Median
Upper Bound
Unit Dose (WLM/yr
per pCi/L)
5th Percentile
6.5E-07
1.2E-06
2.IE-06
Median
6.2E06
9.4E-06
1.5E-05
Mean
1.2E-05
1.8E-05
2.7E-05
95th Percentile
3.9E-05
6.4E-05
1.0E-04
Unit Risk (led/person-yr
per pCi/L)
5th Percentile
1.3E-10
3.4E-10
8 9E-10
Median
1.IE-09
2.6E-09
6.1E-09
Mean
2.1E-09
5.1E-09
I.2E-08
95th Percentile
7.2E-09
1.8E-08
4.2E-08
Individual Risk
(led/person-yr)
5th Percentile
1.8E-08
5.4E-08
1.5E-07
Median
2.1E-07
5.4E-07
1.4E-06
Mean
5.2E-07
1.3E-06
3.2E-06
95th Percentile
1.9E-06
5.0E-06
1.3E-05
Population Risk (lcd/yr)^
..
42
110
260
(a) Assumes a population of 8.11E+07 people are exposed. All values expressed to two significant figures.
-------
TABLE 4-7 VARIABILITY AND UNCERTAINTY
IN INHALATION EXPOSURE AND RISK TO RADON PROGENY
ESTIMATED USING THREE-COMPARTMENT MODEL
Exposure or Risk
Parameter
Variability
Statistic
Uncertainty
Lower Bound
Median
Upper Bound
Unit Dose (WLM/yr
per pCi/L)
5th Percentile
1.4E-06
2.1E-06
2.8E-06
Median
7.5E-06
1.0E-05
1.4E-05
Mean
I.2E-05
1.6E-05
2.4E-05
95th Percentile
3.9E-05
5.2E-05
7.9E-05
Unit Risk (led/person-yr
per pCi/L)
5th Percentile
2.7E-10
5.8E-10
1.5E-09
Median
1.3E-09
2.9E-09
6.9E-09
Mean
2.3E-09
4.8E-09
I.IE-08
95th Percentile
7.3E-09
1.5E-08
3.5E-08
Individual Risk
(Icd/person-yr)
5th Percentile
3.1E-08
8.7E-08
2.3E-07
Median
2.5E-07
6.5E-07
1.6E-06
Mean
4.9E-07
I.4E-06
3.4E-06
95th Percentile
I.7E-06
4.9E-06
1.2E-05
Population Risk (lcd/yr)^
--
40
110
280
(a) Assumes a population of 8.11E+07 people are exposed. All values expressed to two significant figures.
-------
TABLE 4-8 RATE OF CHANGE IN RADON PROGENY INDIVIDUAL RISK
ESTIMATE CALCULATED USING THE THREE-COMPARTMENT MODEL
Variable
Percent Change in Individual Risk
per 1% Increase in Variable Value
Fan On
Fan Off
Average
Occupancy factor
1.39
0.86
1.12
Risk factor
LOO
1.00
LOO
Concentration in water
1.00
1.00
LOO
Residence time in main house
0.94
0.63
0.79
Volume of main house
-0.72
-0.56
-0.64
Transfer efficiency in main house
0.65 ,
0.37
0.51
Total water use in main house
0.65
0.37
0.51
Deposition velocity (unattached fraction)
-0.40
-0.42
-0.41
Unattached fraction
-0.40
-0.41
-0.40
Time in shower
0.16
0.57
0.37
Shower flow rate
0.11
0.47
0.29
Transfer efficiency in shower
0.11
0.47
0.29
Time in bathroom
-0.02
0.23
0.11
Transfer efficiency in bathroom
0.12
0.08
0.10
Total water use in bathroom
0.12
0.08
0.10
Volume of bathroom
0.04
-0.21
-0.09
Volume of shower
-0.04
-0.05
-0.04
Bathroom exhaust fan rate
-0.09
0.00
-0.04
Deposition velocity (attached fraction)
-0.04
-0.05
-0.04
Residence time in shower
0.06
0.00
0.03
Residence time in bath (door open)
0.00
-0.02
-0.01
Residence time in bath (door closed)
0.00
0.02
0.01
-------
5.0 VARIABILITY AND UNCERTAINTY IN EXPOSURE TO RADON GAS RELEASED
FROM HOUSEHOLD WATER
This chapter presents a quantitative analysis of the variability and uncertainty in estimated levels of
exposure from radon gas (as opposed to radon progeny) released from household uses of water. The
basic method followed is analogous to that in Section 4, above.
5.1 One-Compartment Method
5.1.1 Basic Equation
The basic equation for calculating exposure to radon gas based on the one-compartment model is as
follows:
UD * TF • BR • OF • 365^22 (21)
year
where:
UD = Unit dose (pCi inhaled per year per pCi/L in water)
TF = Transfer Factor (the increase in radon concentration in indoor air per unit radon
concentration in water) (pCi/L air per pCi/L water).
9
BR = Breathing rate (L/day). ?
OF = Occupancy factor (the fraction of time that a person spends indoors).
-------
5-1.2 ProtafrilttY Prosit fiwaipig (PPFs)
PDFs used to characterize variability and uncertainty in TF and OF have been presented in Section
4.1,2, and the PDF used for breathing rate has been presented in Appendix 4. No PDF (either for
uncertainty or variability) has been developed for the risk factor for inhaled radon gas, so it was not
possible to use Monte Carlo simulation to estimate the distribution of either the unit risk or the
individual risk. The mean unit risk can be estimated by multiplying the mean unit dose by the
estimated mean risk factor for radon gas (I.IE-12 per pCi),.and the mean individual risk can be
estimated by multiplying the mean unit risk by the population-weighted mean concentration of radon
in water (246 pCi/L). However, other portions of the variability and uncertainty distributions for unit
risk and individual risk cannot be estimated without information on the variability and uncertainty in
the radon risk factor.
5.1.3 Results
Figure 5-1 shows the credible interval for the distribution of radon gas unit dose estimated using the
one-compartment model. Selected numerical values are presented in the top half of Table 5-1. As
shown, the average unit dose is estimated to be 380 pCi/yr per pCi/L (credible interval =* 250 to 540
pCi/yr per pCi/L), while the 95th percentile unit dose is about 3.5 times higher (1,300 pCi/yr per
pCi/L, credible interval = 800 to 2000 pCi/yr per pCi/L). Overall variability in unit dose (as
indicated by the ratio of the 95th percentile to the 5th percentile) is about 40 to 50-fold, while
uncertainty about any particular unit dose statistic is about 2-4 fold.
-------
5.1.4 Sensitivity Analysis
T nml RatP nf
Because the one-compartment model is strictly linear in all of the model input terms, the rate of
change in unit dose is 1 % per 1 % change in input variable.
Partial Rank Order Correlation Coefficients
The PRCCs for each of the independent variables used in the one-compartment model are summarized
below:
Model
Variable
PRCC
Lower Bound
Median
Upper Bound
Transfer factor
0.98
0.99
0.99
Occupancy factor
0.69
0.84
0.90
Breathing rate
0.76 '
0.83
0.89
As seen, all three input variables have high PRCCs. indicating that all three are important
determinants of the variability in unit dose for radon gas.
5.2 Three-Compartment Model Method
The basic approach for using the three-compartment n\odel to estimate exposure to radon gas released
from water to indoor air is detailed in Appendix 3. The PDFs used to model the variable terms in the
model are presented in Appendix 4. As noted above, only unit dose was estimated by this model,
since no PDFu or PDFy has been developed for the radon gas inhalation risk factor.
•*rr
-------
5.2.1 Results
Figure 5-2 shows the credible interval for the distribution of radon gas unit dose estimated using the
three-compartment model. Selected numerical values are presented in the lower half of Table 5-1.
As shown, the average unit dose is estimated to be 550 pCi/yr per pCi/L (credible interval « 430 to
700 pCi/yr per pCi/L), while the 95th percentile unit dose is about 2.5 times higher (1,400 pCi/yr per
pCi/L, credible interval = 1,100 to 1,900 pCi/yr per pCi/L). Overall variability in unit dose (as
indicated by the ratio of the 95th percentile to the 5th percentile) is about 25- to 30-fold, while
uncertainty about any particular unit dose statistic is about 2-fold.
5.2.2 Sensitivity Analysis
Local Rate of Change
The percent change in radon gas unit dose per 1 % increase in each model variable is shown in Table
5-3. Results are calculated separately for the condition when the bathroom tin is used when the
bathroom is occupied ("Fan On") and for the condition when the fan is not used ("Fan OfF). The
mean of the two values is also shown, and the results are arranged in the table in decreasing order of
the absolute value of the mean. Thus, variables located at the top of the table have the largest effect
on the output (either positive or negative) per unit increase in the variable, while those at the bottom
of the table have the least effect.
As shown, there is a direct correlation between unit dose and the value selected for breathing rate.
This is because breathing rate is assumed to be independent of both time and compartment. There is
also a strong dependence of dose on occupancy factor. This value is less than 1.0 because the rate of
exposure is not uniform throughout the day, so absence from the house after the period spent
showering and in the bathroom (when exposure rates to radon gas are highest) leads to a less than
proportional decrease in total dose.
With respect to the variables which influence radon gas concentration, the most important include
shower duration, transfer efficiency in the shower, shower flow rate, volume of the main house, and
air residence time in the main house. Model inputs which have relatively little effect on the output
-------
include transfer efficiency in the bathroom, total water use in the bathroom, and residence time in the
bathroom (door open or closed). Other model inputs have an intermediate effect on output.
Partial Rank Order Correlation Coefficients
Figure 5-3 shows the PRCCs for each of the independent variables used in the three-compartment
model. As shown, the largest PRCCs are associated with main house volume (2), residence time in
the main house (6), and water use in the main house (13), along with occupancy factor (22) and
breathing rate (23). These findings are consistent with the concept that most exposure to radon gas
occurs in the main house, and that variability in the housing parameters are the dominant source of
variability in exposure.
5 3 Comparison of One- and Three-Compartment Model Results
Figure 5-4 compares the credible intervals for the unit dose distributions for radon gas estimated
using the one-compartment and three-compartment models. As shown, the three-compartment model
tends to predict a higher unit dose than the one-compartment model, especially at the low end of the
distribution, although the values become more nearly similar for the mean and 95th percentile of the
distribution. This is because the one-compartment model does tend to under-predict the exposure to
radon gas associated with showering events (USEPA 1993), and the relative importance of the shower
(compared to the main house) is largest at the low end of the exposure distribution.
5 4 Estimated Population Risk
As discussed above, because of the lack of information on the uncertainty and variability in the
inhalation risk factor for radon gas, Monte Carlo simulation cannot be used to derive quantitative
estimates of the variability and uncertainty in unit risk or individual risk. However, population risk
can be estimated from the mean unit dose, as follows:
where:
RF
^mean
PR » UD RF • C n • N
mean mean
Inhalation risk factor for radon gas (1. IE-12 per person per pCi inhaled)
Mean concentration of radon in water (246 pCi/L)
-------
N - Number of people exposed (8.11E+07)
Based on these values, and the range of plausible values for the mean unit dose shown in Table 5-1,
the following estimates of population risk are derived:
Exposure
Model
Estimated Population Risk (cases/yr)
Lower Bound
Median
Upper Bound
One-compartment
5
8
12
Three-compartment
9
12
15
As shown, inhalation exposure to radon gas is likely to contribute only 8 to 12 additional cancer cases
per year, with a credible range of 5 to 15 cases/yr. Thus, even though there the one-coropaitmem
model and three-compartment model differ somewhat in their estimates, the absolute magnitude of the
discrepancy is minor.
s-
-------
TABLE 5-1 VARIABILITY AND UNCERTAINTY IN UNIT DOSE FOR RADON GAS
Exposure
Model
Variability
Statistic
Unit Dose (pCi/yr per pCi/L)
Lower Bound
Median
Upper Bound
One- .
Compartment
5th Percentile
1.7E+01
3.2E+01
5.7E+01
Median '
1.4E+02
2.1E+02
3.1E+02
Mean
2.5E+02
3.8E+02
5.4E+02
95th Percentile
8.0E+02
1.3E+03
2.0E+03
Three-
Compartment
5th Percentile
8.6E+01 '
1.2E+02
1.5E+02
Median
3.2E+02
4.1E+02
5.1E+Q2
Mean
4.3E+02
5.5E+02
7.0E+02
95th Percentile
1.1E+03
1.4E+03
1.9E+03
-------
TABLE 5-2 LOCAL RATE OF CHANGE IN RADON GAS UNIT DOSE
ESTIMATED USING THE THREE-COMPARTMENT MODEL
Variable
Percent Change in Unit Dose per
1% Increase in Variable Value
Fan On
Fan Off
Average
Breathing rate
LOO
1.00
1.00
Time in shower
0.67
0.88
0.77
Occupancy factor
0.87
0.54
0.71
Transfer efficiency in shower
0.44
0.66
0.55
Shower flow rate
0.44
0.66
0.55
Volume of main house
-0.49
-0.38
-0.44
Residence time of main house
0.50
0.35
0.42
Transfer efficiency in main house
0.42
0.24
0.33
Water use in main house
0.42
0.24
0.33
Volume of shower
-0.32
-0.23
-0.27
Volume of bathroom
0.01
-0.34
-0.17
Residence time in shower
0.17
0.06
0.12
Time in bathroom after shower
-0.03
0.24
0.11
Transfer efficiency in bathroom
0.07
0.06
0.07
Total water use in bathroom
-0.13
0.06
0.07
Bathroom fan exhaust rate
0.00
0.00
-0.06
Residence time in bathroom (door open)
-0.01
0.04
0.02
Residence time in bathroom (door closed)
-0.01
-0.01
-0.01
-------
Figure 5-1 Credible Interval for the Distribution of Radon Gas
Inhalation Unit Dose Estimated from One-Compartment Model
100
UD05-LN(2.10,0.513)
UD50 ~ LN(2.32,0.488)
UD95 - LN(2.31,0.469)
cu
I
I
i
1.0E+04
1.0E+03
1.0E+01
1.0E+02
Radon Gas Unit Dose, pCi/year per pCi/L
-------
Figure 5-2 Credible Interval for the Distribution of Radon Gas
Inhalation Unit Dose Estimated from 3-Compartment Model
100
UD05 - LN(2.50,0.337)
UD50 - LN(2.61,0.329)
UD95 - LN(2.72,0.332)
a
a,
1.0E+04
1.0E+02
1.0E+01
Radon Gas Unit Dose, pCi/year per pCi/L
-------
Figure 5-3 Estimated Partial Rank-Order Correlation Coefficients for the
Parameters in the 3-Compartment Model for Radon Gas
u 0.2
¦a -0.2
1 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23
Three-Compartment Model
-------
Figure 5-4 Comparison of Unit Dose Estimates from One-Compartment
and Three-Compartment Models for Inhalation Exposures to Radon Gas
1E4
Q
Q.
L.
u
o.
1E3
U
Q-
O
V}
q 1E2
*5
1E1
JL
T
5th
median mean 95th
Radon Gas Inhalation Unit Dose Statistic
-------
6.0
VARIABILITY AND UNCERTAINTY IN RISK FROM INGESTION OF RADON
PRESENT IN WATER
As discussed in Section 2.2, the basic equations for calculating exposure and risk from ingestion of
radon gas in drinking water are:
yr
UR - UD-RF
IR « UR-C
PR - • N
where:
UD = Unit dose (pCi/yr per pCi/L)
V = Mean volume of water ingested (L/day)
F = Fraction of radon originally present that remains in water at time of ingestion
UR = Unit risk of cancer (per person per year per pCi/L,) from ingestion of radon in
drinking water
RF = Cancer risk factor (cases per person per pCi radon ingested)
IR = Individual risk (cases/yr per person)
Cw = Concentration of radon in water (pCi/L)
PR = Population risk (cases/yr)
N = Number of people exposed to radon from household water
-6=1—
-------
The PDFs selected to quantify the variability and uncertainty in each of these terms arc presented
below. .
62 Probability Density Functions
6.2.1 Volume Ingested m
The most complete survey of water intake patterns by people in the United States was performed by
the U.S. Department of Agriculture in 1977-1978. The study was a stratified random sample of more
than 30,000 individuals living in the continental United States, representing the noninstimtional U.S.
population living in households. The survey included a questionnaire covering weekly food purchases
and consumption for each participating household. Individuals were interviewed (24-hour dietary
recall) and completed a dietary diary for the following two days. Separate questions addressed the
t
number of 8-ounce cups of water consumed each day. The survey took place throughout the year and
data were collected for all days of the week, although weekends were under represented. The EPA
analyzed these data and found that water intake is.lognormally distributed, with a mean tap water
intake (all age groups) of 0.66 L/day and a standard error of the mean of 0.01 L/day (USEPA, 1984).
More recently, Ershow and Cantor (1989) reanalyzed data from the Department of Agriculture study.
As shown in Table 6-1, the average direct tap water intake by all ages was 0.65 L/day. Given the
size and quality of the Ershow and Cantor drinking water data, it would have been preferable to
model their data directly in the Monte Carlo simulation as an empirical PMF. However, the large
gaps between percentiles presented a complication, since there is no obvious means for how to fill in
the gaps. It was therefore decided to use an analytical density function to represent the data. A
linear regression was performed on natural logarithm of the drinking water rate versus the standard
normal deviate. The regression equation was forced to go through the mean and 99th percentile
^6=2
-------
direct tapwater ingestion rates to ensure that upper percentiles would not be underestimated in
subsequent analyses. Based on this regression, the estimated parameters of the lognormal density
were as follows: GSD — 1.92 and geometric mean = 526 grams of water ingested per day (r^ =
0.95). Because of the large number of people in this study, the quality factor was taken to be 100.
In summary, direct tap water' intake was modeled as follows:
PDFy(V)
- LN(gm,gsd)
PDFu(ln(gm))
— TS(m,s,qf)
PDFu(ln2(gsd))
- INVCH(s.qf)
m
= ln(0.526)
s
= ln(1.92)
qf
= 100
6.2.2 Fraction Not Volatilized (F)
Because radon is a gas, it tends to begin escaping from water as soon as the water is discharged from
the plumbing system into any open container or utensil. As would be expected, the fraction of radon
volatilized before consumption depends on time, temperature, surface area-to-volume ratio, and
degree of mixing or aeration. Essentially all radon is released from water that is boiled (Gesell and
Prichard, 1980), so it seems likely that nearly all radon is released from water used for cooking or for
preparing hot beverages (coffee, tea. soup, etc.). Water used to prepare cold beverages from
concentrates or mixes (e.g., lemonade, iced tea) could retain radon if the beverage were prepared
without extensive agitation. However, levels would decrease over time if the beverage were stored in
the refrigerator before consumption, and the volume of water consumed as cold beverages of this type
is only about 10% of total water intake (Pennington. 1983). Therefore, the amount of radon
-------
consumed in cold fluids (other than direct tap water) is likely to be small enough to be ignored. On
this basis, it seems likely that the only type of water which contributes significantly to radon ingestion
is water that is consumed shortly after being drawn from the tap. This will be referred to as "direct
tap water."
There is only limited information on the amount of radon volatilized from direct tap water. Table 6-2
summarizes data that are pertinent. As seen, estimated volatilized fractions vary widely depending on
test conditions. Although the data are too sparse to permit any rigorous statistical analysis of the
mean value, a value of 0.2 seems representative of the fraction lost, with an estimated credibility
interval from 0.1 to 0.3. Thus, the fraction not volatilized (F) has a typical value of 0.8, and ranges
from 0.7 to 0.9. The full range (i.e., variability) of F is also difficult to estimate, but a range of
0%-50% volatilized (50%-100% remaining) seems reasonable. Based on these data, F was modeled
as follows:
PDFV(F) - BETA(mean.mode.min.max)
PDFu(mean) - U(0.7.0.9)
PDFu(mode) - U(min,mean) (mean < (max+min)/2)
- U(mean.max) (mean > (max+min)/2)
min = 0.5
max = 1.0
6.2.3 Ingestion Risk Factor
Quantitative analysis of the uncertainty in the ingestion risk factor for radon gas can be divided into
two parts: a) evaluation of the uncertainty in the radiation dose delivered to different (issues of the
6>l
-------
body per unit dose ingested, and b) evaluation of the uncertainty in the cancer risk to each tissue per
unit radiation dose delivered. These two companents of uncertainty are considered in separately
below, and the combined uncertainty in the ingestion risk factor is evaluated.
6-2.3.1 Uncertainty in Tissue Dose Estimates
Measured Organ Concentrations
Crawford-Brown (1990) calculated dose estimates using data collected on human subjects ingesting
radioactive xenon (Correia et al., 1987). From his examination of the data, Crawford-Brown has
assigned a GSD of 1.5 to the doses due to the uncertainty in organ concentrations. To be consistent
with his recommendation, we assumed a lognormal uncertainty distribution for liver and general tissue
dose, centered about the nominal estimate, with a GSD =1.5. Dose estimate uncertainty, as
determined by direct numerical integration of the Correia et al. (1987) data, was slightly smaller than
the Crawford-Brown estimate for stomach, small intestine, and liver (see Table 2-2). From this table
it can be seen that other measured stomach doses vary by no more than 40% from the Crawford-
Brown (1990) values. Because of the similarity of estimates from several sources, a GM shift = 1
and a GSD = 1.5 for uncertainty in measurements will be assumed here.
With respect to the lung, there is, as discussed above, some additional uncertainty relating to the
respective weights that should be attached to alveolar and basal cell doses. The approach taken in
deriving the nominal lung dose estimates in Table 2-2 may be conservative: tha» lower basal cell dose
estimate should possibly be used as an approximate measure of dose to the lung, with little or no
weight being given to the alveolar dose. Lung dose and cancer risk due to radon ingestion is less
than 15% of the total. In view of the relatively minor change the assumption of assigning all risk to
6*3
-------
the basal cells would make in the overall risk estimate, we have, for simplicity, treated the uncertainty in
lung dose in the same way as the liver and general tissue dose uncertainties.
Epithelial BaHnn Hrarlipnt and 1 jyaHnn nf Targp.t Ollc in the fit Tract
Aside from the limitations in Correia's xenon measurements, the uncertainty in the estimated GI doses
stems from uncertainties in: (1) the thickness of the GI epithelium and the location of target cells relative to
the lumen; (2) the concentration profile of radon across the epithelium of the stomach and intestinal wall;
and (3) the contribution of radon progeny decays within the epithelium of these organs.
The doses in the GI tract were calculated under the assumption that the target cell nuclei are located at a
depth of 30 pm into a 40 ftm thick epithelium of the small intestine tunica mucosa. Assumption was also
made that there is a linearly decreasing gradient of radon concentration from the lumen to the blood supply
located on the other side of the epitheliuml of the whole GI tract. For this same thickness and an assumed
linear concentration gradient across the epithelium, the gradient factor (GRA) used in Equation 2-5 for
estimating doses at 0, 10, 20, 30 and 40 microns are 0.8, 0.65, 0.5, 0.33, and 0.2, respectively. In other
words, doses at 0, 10, 20, 30, and 40 microns into the epithelium are, respectively, 0.8, 0.65, 0.5, 0.33,
and 0.2 times the dose (at a depth of 30 /im) calculated assuming a uniform concentration throughout the
epithelium. On the same relative scale, the calculated dose to cells located at a depth of 50 pm into a 100
fim epithelium is 0.5.
As indicated in Section 2.3.2, the net effect of assuming target cell nuclei located a depth of 30 /im into
a 40 nm thick wall, and a linear radon gradient is to decrease the estimated dose to target cells in GI tract
by a factor of 3 (GRA = 0.33). To account for the uncertainty in gradient shape and in target
-------
cell depth, a range of GRAs from 0.2 lo 0.8 is assumed with a GM of 0.4 and a GSD of 1.5. Because
uncertainty limits (0.2 to 0.8) tend to be above the estimate of choice (0.33), a GM shift of 1.2
(=0.4/0.33) was applied.
Mobility of ttarirm Progeny
Another uncertainty relates to the decay of radon progeny produces in the thin epitheliuml of the GI tract.
At one extreme, one might assume that all short-lived progeny decay in the epithelium at the other
extreme, all the progeny may be swept away by the blood before decaying. The calculated dose under the
former assumption (SWP = 1) is 3 times that for the latter (SWP = 0.33) (Crawford-Brown, 1991). In
its assessment for the Proposed Rule, EPA assumed that the first decay product, (polonium-218 with a
3-minute half life), decays in the stomach epithelium where it is produced but that lead-214 (27-min half
life) and subsequent decay products are removed before decaying and do not, therefore, contribute to die
stomach dose (SWP = 0.6). The effect of this sweeping assumption was to reduce the dose estimate by
40% compared to what would be calculated assuming all progeny decay is the wall where they are
produced (USEPA, 1991a). In the revised risk factor calculation, the same sweeping assumption (SWP - '
0.6) was applied to the whole GI tract (stomach, small intestine, and colon).
*714 *51 *51
The assumption that Pb and 4Bi leave the epithelium before 4Bi can decay is based on speculation.
2|4
The possibility of Bi decay in the epithelium cannot be dismissed. Doses based on an assumption of
214
decay product migration (SWP = 0.6) must, therefore, be considered to be a lower limit. If Po decay
takes place in the epithelium, doses will be increased by a factor of 1.67 (SWP « 2). To encompass this
range, a GM shift = 1.2 and a GSD = 1.2 are proposed.
6^
-------
Age dependence of the Dose
An additional source of uncertainty in dose pertains to the effect of age. Crawford-Brown (1991,
Table 1 i) estimates significantly higher doses to children under the age of 10 than to adults, although
the empirical data on ingested Rn and Xe have all been obtained on adult subjects. The effect of
higher doses to young children on population risk (the end-point of ultimate interest for this analysis)
would be reduced by the fraction of such children in the population and their lower intake of tap
water (Ershow and Cantor,. 1989).
According to Table 11 of Crawford-Brown's 1990 report, the dose to the stomach (per pCi ingested)
does not vary much by age, but the dose to a 5 year old child for other target organs may be 2 or 3
times that to an adult. By age 10, however, the estimated dose is no more than about 50% higher
than for an adult. Even taking into account the higher estimated risk per unit dose for children - for
many organs, more than half the estimated risk from a given dose to a population is assigned to those
under age 20 - it would appear that incorporation of age dependent dosimetry would increase
population risk by less than a factor of 2.
Using the projections from Crawford-Brown (1991) Table VI, a rough estimate of the effect of
increased infant dose on mean population dose can be calculated. The increase is by a factor of 1.2
for the small intestines, 1.2 for ascending colon. 1.6 for descending colon, 1.5 for liver, 1.6 for lung
and 1.6 for general tissues. According to Crawford-Brown there is no age effect on stomach dose.
Appropriate geometric mean and GSD values for relevant target organs are list-d in Table 6-3.
-------
Summary nf Ti
It can be seen from Table 6-2 that about 80% of the estimated risk from radon ingestion comes from the
risk to the stomach, colon, and lung. The dose from radon and its progeny is from high-LET
-------
alpha particles. Consequently, in estimating the uncertainty, we can focus on items (1), (2), (3), (4) and
(6), above, for these three organs. EPA's preliminary estimates of the uncertainty distributions for these
factors (USEPA, 1993a) are summarized in Table 6-4. The factors in the table are normalized to unity for
the nominal risk per unit dose estimate. Thus, for example, if we consider only uncertainty in the
transport of risk from the Japanese atomic bomb survivors to the U.S. population, the nominal stomach
cancer risk estimate maybe high or low by about a factor of 3.
A less detailed assessment of the uncertainty in risk per unit dose was made for the organs other than
stomach, colon, and lung. With respect to items (1) through (3) above, the combined uncertainty was
assumed to have a log normal distribution with a GM shift = 0.8 and a GSD = l.S (about the same as the
corresponding uncertainty distribution calculated for the lung). The uncertainties associated with items (4)
and (6) were treated in the same way as for stomach, colon, and lung (see below).
The overall uncertainty in the risk per pCi of radon ingested was calculated by Monte Carlo methods,
using the distributions in Tables 6-3 and 6-4. In sampling for the Monte Carlo calculations, uncertainties
associated with each organ were assumed to be independent, with two exceptions from Table 6-4: the
uncertainty in risk per unit dose due to errors in (atomic bomb) dosimetry and the uncertainty in alpha
particle RBE. For these two sources of uncertainty, it was assumed that the multiplicative error is the
same for each organ.
Treating the former source of uncertainty in this way seems reasonable since, for any individual exposed at
Hiroshima or Nagasaki, the relative errors in the dose estimates should be roughly ".he same for all organs.
Treating the latter in this way is essentially equivalent to assuming that the same (but uncertain) value of
RBE applies to ail organs. Since variations in RBE between organs would tend to cancel, this approach
has the effect of maximizing the estimate of uncertainty.
6^
-------
6.2.3.3 Owrall ITnrwtalnty in Tngpctinn Riclr Farfnr
Using the results in Tables 2-3, 6-3, and 6-4, the uncertainties in the risks per rad and the risks per pCi
ingested were estimated with Monte Carlo methods. The results of the calculations are shown in Table 6-
5. The geometric mean estimate of the total fatal cancer risk from the ingestion of 1 pCi of radon is
1.24E-11 (GSD» = 2.42). The geometric mean is very close to the nominal estimates of risk presented
above: 7.4E-12, as given in the Draft Radon Criteria Document; 6.3E-12, based on EPA's current risk
estimates but with dosimetry modified from the Criteria Document; or 1.7E-11, based on modified
dosimetry and proposed risk estimates recently reviewed by the Science Advisory Board. The derived
uncertainty distribution is found to be approximately lognormal. The calculated 90% credibility interval,
3. IE-12 to 6.3E-11, easily encompasses all three of the alternative nominal estimates.
6.2.4 Summary nf PDFq
Table 6-6 lists the PDFs employed to represent the variability and uncertainty in the each input variable
used to estimated exposure and risk from ingestion of radon gas.
6.3 RrsiiIk
As discussed previously, two-dimensional Monte Carlo simulation was used to propogate the variability
and uncertainty in the exposure and risk estimates for ingestion of radon gas in direct tap water. The
simulation involved 1,000 outer loop realizations and 2,500 inner loop iterations p.:* realization. The
results are shown graphically in Figure 6-1 (unit dose), 6-2 (unit risk), and 6-3 (individual risk). Selected
values from these graphs are presented in Table 6-7, along with the population risk estimates.
6^1—
-------
As seen in these figures and table, the variability in unit dose between different people in different houses
(as indicated by the ratio of the 95th percentile to the 5th percentile) is about 10-fold. This range in
variability is significantly lower than for inhalation of radon progeny (about 50-fold; see Section 4) because
there is much less variability in the amount of water people drink than in the size and ventilation rates of
their houses. This variability index does not increase for unit risk, because the risk factor is modeled as an
uncertain constant (i.e., it does not add to variability). Variability in individual risk and population risk
increase to about 20-fold, due to the added variability in the radon concentration factor.
Uncertainty in any particular exposure statistic (characterized as the ratio of the upper bound divided by
the lower bound) is about 1.5 fold for unit dose, and this increases to about 20-fold when the uncertain risk
factor is incorporated to calculate unit risk. Uncertainty increases only slightly when the concentration
term is included to yield individual risk and population risk. Thus, uncertainty in the ingestion risk factor
is clearly the primary source of uncertainty in both individual and population risk estimates.
6.4 Sensitivity Analysis
6.4.1 I.nra! Ratp. nf Change
Because exposure and risk from ingestion of water is evaluated using a strictly linear model, the rate of
change in any output parameter is always 1 % per 1 % change in input variable.
6.4.2 Partial Ranlr Order f!nm»latir>n f-.ne.ffiriftnts ••
Figure 6-4 shows the PRCCs for each of the model inputs used to evaluate exposure and risk from radon
ingestion. As seen, both volume ingested and fraction not volatilized have high PRCCs for both unit dose
-------
and unit risk, indicating that both are important determinants of variability. For individual risk, the
relative importance of die fraction not volatilized decreases relative to the concentration in water and the
volume ingested, indicating that this variable is less significant in determining individual risk than the other
variables. This is consistent with the relatively narrow range over which fraction not volatilized is
assumed to range (0.5 to 1.0).
-------
Figure 6-1 Credible Interval for the Distribution of Radon Gas
Ingestion Unit Dose Estimated from One-Compartment Model
UD05~LN(2.09,0.301)
UD50~LN(2.18,0.292)
UD95 ~ LN(2.26,0.292)
ea 50
1.0E-KM
1.0E+02
Ingestion Unit Dose, pCi/yr per pCi/L
1.0E+03
-------
Figure 6-2 Credible Interval for the Distribution of Radon Gas
Ingestion Unit Risk Estimated from One-Compartment Model
l.OE-ll
UR05 - LN(-9.34,0.298)
UR50 - LN(-8.74,0.295)
UR95 ~ LN(-8.06,0.295)
1.0E-10 1.0E-09 1.0E-08
Ingestion Unit Risk, risk/person-year per pCi/L
1.0E-07
-------
Figure 6-3 Credible Interval for the Distribution of Radon Gas
Ingestion Individual Risk Estimated from One-Compartment Model
100
90
so
£}
CQ
X>
O
IR05 - LN(-7.07,0.412)
IR50 - LN(-6.41,0.411)
IR95 - LN(-5.79,0.416)
0
1.0E-08
1.0E-07 1.0E-06 1.0E-05
Ingestion Unit Risk, risk/person-year
1.0E-04
-------
Figure 6-4 Partial Rank-Order Correlation Coefficients for Ingestion Exposures
to Radon Gas Using 1-Compartment Model
1,00
0.90
c 0.80
,o
| 0.70
b
8 0.60
is
g 0.50
I
J 0.40
.2 0.30
I
^ 0.20
0.10
0.00
V FnV
Unit Dose
V FnV
Unit Risk
V FnV CW
Individual Risk
-------
7.2 Exposure and Risk from Radon in Outdoor Air
The basic equation for estimating the annual number of radon-induced led in the U.S. population of
2S0 million people due to exposure to radon in outdoor air is given by;
led » Ea
-------
Each of these terms is discussed below.
Average Outdoor Radon Level
No systematic study has been carried out to determine the distribution of outdoor radon levels in the
United States. However, the National Ambient Radon (NAR) Study measured the time-averaged
concentration of radon at 50 "ERAMS" stations, one in each state (Hopper et al.. 1991). The yearly
L
averages measured in air in the NAR Study ranged from 0.16 to 0.S7 pCi/L; the median and mean
levels were 0.39 pCi/L and 0.41 pCi/L, respectively. The 1988 UNSCEAR report reviewed data
from around the world and concluded that, for continental areas in temperate latitudes. Gesell's
estimate of 9 Bq/m3 (0.24 pCi/L) is probably representative (UNSCEAR, 1988; Gesell, 1983).
Noting that much lower values are generally observed on islands and coastal sites, UNSCEAR
3
estimated that the population-weighted average concentration in air is about 5 Bq/m (0.14 pCi/L).
Based on these observations, we have adopted a central estimate of 0.3 pCi/L for the average outdoor
radon concentration in the United States. The uncertainty is assumed to be distributed lognormally
with a GM of 0.3 pCi/L and a GSD of 1.3, corresponding to a 90% credibility interval of 0.19 to
0.46 pCi/L.
Equilibrium Factor
In outdoor air, radon decay products are nearly in equilibrium with radon gas. Measured values of
EF fall in the range 0.77-0.85 (UNSCEAR. 1988). Following the UNSCEAR (1988)
recommendation. 0.8 was adopted as a nominal best estimate. The uncertainty is assumed to be
distributed lognormally about this value with a GSD of 1.05.
-------
Time Scent Outdoors
On average, adults are estimated to spend only 2.3% of their time outdoors; in addition, they spend
an average of 5.4% of their time in transit (USEPA, 1989a). Most of this transit time is presumably
spent in cars and buses, which would be expected to reflect outdoor radon concentrations (although
9
the equilibrium factor may be somewhat lower). No ascertainment has been made of the time spent
outdoors by children; however, an examination of activity patterns published in USEPA (1989a)
suggests that it is roughly comparable to that for adults. For the purpose of this analysis, the nominal
estimate of "outdoor occupancy factor" is taken to be 7.5% (0.075). The uncertainty is assumed to
be distributed lognormally around this value with a GSD of 1.10.
Annual Exposure Estimate
From Equation (26), the average outdoor exposure is estimated to be:
E - (0.3) (0.516) (0.8) (0.075) WLM/y
/ /
= 9.3E-03 WLM/y
This is about 4% of the estimated average residential exposure. Because E^Vg is equal to a product
of factprs. each of which has a lognormal uncertainty distribution centered about the nominal
estimate, its uncertainty is also distributed lognormally about the nominal estimate above. The
resultant GSD, S^, is given by:
-------
log^ ¦* log2(1.3) + log*(1.05) + log^l.l)
SB = 1.33
(28)
Based on this, the 90% credibility interval for the outdoor exposure is 5.8E-03 WLM/year to
1.5E-02 WLM/year.
7.2.2 Unit Risk
The lung dose from inhaled radon progeny varies with the exposure conditions. In particular,
differences in aerosol characteristics (including the ultra-fine fraction) and in human activity patterns
(breathing rates) may give rise to a difference in the average dose per WLM outdoors compared to
indoors. Presumably, this difference would be reflected in the risk per WLM. In view of the sketchy
data on outdoor exposure conditions and the relatively minor contribution of outdoor exposure to total
exposure, we have not reviewed this question in depth, but the difference in average dose is unlikely
to be very large. The most sensitive variable would appear to be the unattached fraction. The NAS
"Comparative Dosimetry" report (NAS, 1991) estimated that about half the dose from indoor
exposures is contributed by the unattached fraction, taken to be 8%. Thus, if the outdoor unattached
fraction were only half the indoor value, the dose would be decreased by about 25%.
To estimate the effect of outdoor radon exposures, we have employed the same aominal central
estimate of risk as for indoor exposures: 2.24E-04 Icd/WLM. Also as for indoor exposures, the
uncertainty distribution is taken to be a lognormal centered about 2.83E-04 lcd/WLM with a GSD of
1.53.
-------
7.2.3 Population Risk
Substituting the nominal estimates for UR and EAyg into Equation (25), the mortality due to outdoor
radon is estimated as follows:
PR = (250E+06)(2.24E-04)(9.3E-03) led/yr ^
- 520 lcd/yr
The uncertainty distribution is assumed to be lognonnal, centered about a geometric mean of:
GM = (520X283/224) - 657 lcd/yr
The GSD is given by:
log2 GSD - log:(1.53) ~ log2( 1.33)
GSD -1.67
The resultant 90% credibility interval is then 280 led/year to 1,500 led/year.
-------
7.3
Exposure and Risk from Radon in Indoor Air
Estimates of lung cancer deaths attributed to total indoor air radon exposure (waterborne radon and
radon from infiltration from soil into house) with associated uncertainties have been quantified by the
Office of Radiation and Indoor Air (formerly Office of Radiation Program)-of the U.S. Environmental
Protection Agency. The detailed analysis was described in Chapter 2 of the EPA report entitled
Technical Support Document for the 1992 Citizen's Guide to Radon (USEPA, 1992a). The results '
are summarized in Tables 7-2 to 7-4. As shown, the extimated excess annual lung cancer deaths due
to radon (all sources) in indoor air is 16,000 lcd/yr, with a credibility interval of 6,790 to 30,590
lcd/yr.
7.4 Relative Magnitude of Risks from Radon in Water
The mean risk estimates for exposure to radon from different sources are summarized in Table 7-5.
It is apparent that the number of cancer deaths per year attributable to water is a relatively small
fraction (about I %) of the total cancer deaths attributable to radon.
7.5 Effect of Alternative MCL Values
Even though risk from radon in water is a relatively small fraction of the tdtal risk from radon, this
does not mean that establishment of an MCL for radon would not result in the saving of a significant
number of lives each year. Figure 7-4 shows the estimated number of lives which would be saved
each year as a function of what value is assumed for the MCL. These calculations were performed
by Monte Carlo simulation as described earlier, except that when a concentration value was selected
-------
that was above the MCL being evaluated, that value was divided by an assumed treatment efficacy factor,
as shown below:
Radon Concentration (pCi/L)
Assumed Treatment
Efficacy Factor
C < = MCL
1
MCL < C < 2-MCL
2
2-MCL < C < 5-MCL
5
C > 5-MCL
100
As shown, if the MCL were set at 200 pCi/L, it is expected that about 129 lives would be saved, with a
credible range of 47 to 350. If the MCL were set to 300 pCi/L, it is expected about 81 lives/year would
be saved (credible range = 26 to 255). At higher values, the estimated number of lives saved decreases,
reaching nearly no significant effect (15 lives/yr, credible range = 10 to 60) at an MCL of 2000 pCi/L.
f /
-------
Figure 7-1 Credible Interval for the Distribution of Combined Unit Risk
(Inhalation and Ingestion) Estimated from One-Compartment Model
100
UR05 -LN(-8.60,0.352)
UR50-LN(-8.22,0.344)
UR95 - LN(-7.82,0.306)
x:
20 -
10 --
1.0E-O7
1.0E-08
1.0E-10
Combined Unit Risk, cases/person-yr per pCi/L
-------
Figure 7-2 Credible Interval for the Distribution of Combined Individual
Risk (Inhalation and Ingestion) Estimated from One-Compartment Model
100
_o
CO
-O
o
IR05 - LN(-6.32,i
IR50 ~ LN(-5.91,
IR95 - LN(-5.51,
i i i 11
i i i i i i i
1.0E-07 1.0E-06 1.0E-05
Combined Individual Risk, cases/person-yr
1.0E-04
-------
Figure 7-3 Estimated Annual Cancer Deaths by Exposure Pathway
Attributable to Waterborne Radon Using the One-Compartment Model
450 ¦
400 - - J--
350 4-
s 300 -
u
Q.
Jc 200 --
cd
o
Q 150 --
J
100 --
U
50 --
M
Inhalation
Ingestion
Combined
-------
Figure 7-4 Annual Deaths Avoided as a Function of
Maximum Contaminant Level
350
- - ••"•••
A *
«
•
• * •- r
1
• 9
•• —
tr*:
—1 1 1
1 H
—-1—-1 1 f 1—
1 1
300 --
T3
u
"O
p 250
<
%
3
Q
200
g 150
(J
c;
<
100 -
50 --
200
300 500 700 1000
Maximum Contaminant Level, pCi/L
2000
-------
TABLE 7-1 VARIABILITY AND UNCERTAINTY IN COMBINED EXPOSURE
AND RISK FROM RADON IN WATER
Exposure or Risk
Parameter
Variability
Statistic
Uncertainty
Lower Bound
Median
Upper Bound
Unit Risk (cases/person-yr per
pCi/L)
5th Percentile
6.9E-I0
1.7E-09
5.0E-09
Median
2.5E-09
5.7E-09
I.4E-08
Mean
3.6E-09
8.4E-09
1.9E-08
95th Percentile
1 OE-08
2.4E-08
5.1E-08
Individual Risk (cases/person-yr)
5th Percentile
8.1E-08
2.3E-07
6.6E-07
Median
4.8E-07
1.2E-06
3.0E-06
Mean
8.6E-07
2.1E-06
5.0E-O6
95th Percentile
2.8E-06
6.9E-06
1.6E-05
(ay
Population Risk (cases/yr)v
-
70
170
410
(a) Assumes a population of 8.1 IE+07 people are exposed.
All values expressed to two significant figures.
-------
TABLE 7-2 ESTIMATED ANNUAL LCD FROM RADON IN INDOOR AIR(a)
Parameter/Statistic
Mean Unit Risk Factor
(annual lethal lung
cancers per 10 people
per WLM)
Mean Exposure
(WLM/year)
Average Annual
Lethal Lung
Cancers
Geometric Mean
GM
284
0.203
14,410
Geometric Standard
Deviation
GSD
i .53
1.18
1.58
Arithmetic Mean
311
0.206
16.000
Lower Bound
141
0.155
6,790
Upper Bound
572
0.267
30,600
(a) Summary of calculations described in USEPA (1992a)
-------
TABLE 7-3 DETAILED SUMMARY OF UNCERTAINTY IN INHALATION RISK FACTOR
Nature of the
Uncertainty
Study % Increase, mean
sqr error
P (a)
Composite:
Geometric
Mean, gsd
Adjusted BIER IV
Model + U.S. 1980
Vital Statistics
Results
Statistical Variability
in Miner Data
Eldorado 2.6( I.S)
l3°{m
(1.27)' '
224 per 10*® person-
WLM
with GSD = 1.27
GM: 224 x 1.27 « 284
r |
Ontario 1.4(1.6)
Malmberget 1.4 (2.6)
Colorado Plateau 0.6 (1.5)
Projection of risk over
time
Uj, a/1
Geometric Mean, GSD
Composite
GSD = exp[/lnJ(1.27) + InJ(1.42) ]
« 1-53
1.5 1.5
1 00 (1.28)
1.27(1.42)
Age dependence of
risk
1.6 1.0
1.27 (1.15)
Extrapolation from
mines to homes''
1.4 1.4
1.00 (1.23)
(a) Calculated via
inft
.... ' ln,g-
In 2.6 + In 1.4 +
lnJl.5 In11.6
I 1
V In1^ In11.5 In11.6
0.26 - B « e0-* = 1.30
(b) Calculated via
GSD = exp
1.27
-------
TABLE 7 4 DETAILED SUMMARY OF RISK ESTIMATES FOR RADON IN INDOOR A!R(a)
EXPOSURE
Average
Range, (L,U)
Geometric
Mean, (UxL)
GSD
Average
Concentration, C
1.25 pCi/L
<1.1;1.4)
1.24
1.076
Average Equilibrium
Factor, F
0.5
(0.35:0.55)
0.44
1.147
Average Occupancy
Factor, 0
0.75
(0.65;0.80)
0.72
1 065
Exposure Composite
0 206(b)
(0.154,0.268)
0.203(c)
1.183
ANNUAL RADON-INDUCED LUNG CANCER DEATHS
Radon-induced Lung
Cancer Deaths
BEIR IV
(224 per 10 ;l.27)x(0.203,l.l8)x250 million
people -(11,370:1.34)
BEIR IV as modified by EPA
(283 per 10 ;1.53)x(0,203,1.18)x250 million people
-(14,410:1.58)
Arithmetic Mean
11,860
16,000
Lower, Upper Bounds
7,020 - 18,400
6,790 - 30,590
(a) Summary of calculations described in USEPA (1992a).
(b) Estimating the mean exposure,
mean = 0.203 x exp
InJ( 1.183) I =0.206
(c) Converting from the average concentration to the geometric mean concentration.
GM, = E x J|
mean.
0.242 x | 1 x
1.25
0.439 | x [ (J.721
0.5
0.75
- 0 203
-------
TABLE 7-5 RELATIVE MAGNITUDE OF RADON RISKS
Radon
Source
Exposure
Route
Exposure
Location
Excess Fatal Cancer Risk
Deaths/yr
% Total
Water
Inhalation
Indoors
110
0.7
Water
Ingestion
Indoors
50
0.3 .
Soil
Inhalation
Outdoors
520
3.1
SoU
Inhalation
Indoors
I5,840(a)
95.9
(a)
This value is equal to the total of 16,000 deaths/yr estimated by USEPA (1992a) minus the
contribution from water (160 deaths/yr).
-------
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-8^t0—
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APPENDIX 1
PROPERTIES OF SOME USEFUL DISTRIBUTION FUNCTIONS
-------
Useful Uncertainty Distributions
Normal Distribution N(u,ct)
probability density function
/(,) - ——zex?
parameters
location parameter -¦» < p < '«•
shape parameter 0 * o «¦ -
mean
*
variance
1
a*
mode
U
median
U
maximum likelihood estimates
* *•! * 1 4-1 I
upper 95% confidence bound
X„ * p *1.645 « 1
AW'
-------
Lognormal Distribution
Ln(n»o)
probability density function
m
xoJSn
¥ I 2I « J;
0 < * < m
parameters
location parameter — < ii <
shape parameter 0 < a < -
mean
E(X) - «f>|u ~ |oJJ -
vanance
Var(X) » «zp|2(p * | c1) x (expfo2) - l)
median (geometric mean)
*»-*«- «*
mode
mode ¦ exp{(t - o3) « xme"{>
maximum likelihood estimates
"»¦ 1 * ¦ * *.j
upper 95% confidence bound
^ ¦ exp(|i * 1.645o) -
l.«4S«
ordering
mode < median « X*«>JJ1W, « mean <
geometric standard deviation
<£2)
gsd - exp(o)
-------
Triangular Distribution T(a,b,c) I
probability density function
M - 2(*Jfl) a s. x s. c I
(b - a) (c - a) J
/W » v2(;"*} . e < x & b
(b - a) (6 - c)
parameters
(aJfX) real numbers
location parameter a
scale parameter b-a
shape parameter e
mean
,—(a * b *c)
3
variance
Var(X) « -^~(a2 * b* *c* -ab-ac-be)
lo
mode
e
median
xx*b-s
(b - a) (c - a)
— is—— a i x i c
2
(b-a)(b -c) c
-------
| Uniform Distribution
U(a,b)
probability density function
m . atxtb
KB-a)
parameters
(aM red numbers
location parameter a
scale parameter b-a
mean
a*b
2
variance
Var(lf) - -£<*-«)*
mode
does not uniquely exist
median
a * b
2
parameter estimation
d « mm Xk i ¦ max Xk
Upper 95% confidence bound
• a * 0.95 (b - a)
-------
Log-uniform Distribution Lu(a*b)
probability density function
/to * * r «P(a) < * s «p (by
x(b~a)
parameters
«q>(a),exp(fc) real numbers
location parameter exp(<3)
scale parameter acp(b) -exp(a)
mean
e*p(a) * «xp(l»)
b-a
variance
2(b -«) i 6-a J
. mode
axp(a)
median
parameter estimation
d - mix ap(Xk) 6 - max exp(Xt)
i«*«• i«*«»
Upper 95% confidence bound
v -tu { ek
2 (A - a) U-aj
-------
APPENDIX 2
STATISTICAL PROPERTIES OF THE LOGNORMAL DISTRIBUTION
The lognormal distribution is the distribution of a van ate whose logarithm obeys the normal law of
probability. The lognormal distribution is a skewed, positive distribution often used to describe
biological and environmental variables. The probability distribution function (PDF) of a lognormal
random variable X is denoted as A (n.o2) and defined as
xm
0)
(2-1)
while the cumulative distribution function (CDF) for X is
Fx(X:£x * ) = | ft(x;ji,o)dx
The PDF and CDF of a lognormal distribution are illustrated in Figure 2-1.
(2-2)
Define Y==ln(X). The random variable Y is distributed normally, N(fi.ir), with mean n and variance
a1. Given a random sample of size n from A (#t,<^). denoted
X,,X: X„, the unbiased, minimum variance estimates of n and a1 given by:
-------
" Y JL InTX,)
i *Y 1l * Y H
tf n n
(2-3)
and
¦a . A (Y -Y)' _ ^ (2-4)
* tf (b-1) " £f (n-I)
Formulas relating these estimates to descriptive statistics for the lognormal distribution are presented
on the following pages.
The MEAN of a lognormal random variable X is termed the expected value of X and is denoted
E(X). The MEAN may be estimated as
E(X) - exptA-ia2). (2-5)
At
The MODE, or most frequently occurring observation in a lognormal distribution, is given by:
MODEx = exp^V) (2-6)
while the MEDIAN or 50* percentile point of the cumulative distribution is
MEDIANX = expOi). (2"7>
The MEDIAN may be estimated as
A2-£-~
-------
expm . exp . (X,X5tXj...X(1)'®.
i-i n
(2-8)
The right-most term in the expression for the estimated MEDIAN is also the expression for the
GEOMETRIC MEAN (GM) of the sample X„X2 X*
In addition to the mean, mode, and median, which are all measures of central tendency for a
distribution, estimates of percentile points are also of interest. The p* percentile of a distribution is
the smallest value of the random variable X such that the cumulative distribution function is greater
than or equal to p. That is:
Therefore, 100*p percent of the values of X in a distribution would be expected to fall below the
value Xr
For the lognormal distribution, the p* percentile is estimated as
where Zp is the largest standard normal deviate from the standard normal distribution such that
F(Zp) ss p. Estimates of the 5* and 95* percentile points from a lognormal distribution are
p "percentile = F(Xp)=p ie., F'^pJ-X,,.
(2-9)
Xp - exp(£ +Zpff)
(2-10)
5* % = expOx-1.645a) 95* % = exp(A* 1.645c).
(2-11)
-------
The following ordering exists for the lognormal distribution:
mode < geometric mean < mean <
The lognormal distribution depicted in Figure 2-1 is presented on a logarithmic scale in Figure 2-2.
Descriptive statistics for this distribution are also indicated on the graphic.
Lognormal Uncertainty Distributions
When a variable is assumed to follow a lognormal distribution, the properties of the lognormal
distribution can be used to approximately describe individual uncertainty factor distributions. The
uncertainty in the transfer factor of radon from water to air, discussed in more detail in Chapter 4, is
used in this section to illustrate the use of lognormal distributional properties to approximate the
distribution of an uncertainty factor.
A review of nine studies of the transfer factor of radon from water to air indicated that the mean
transfer factors from these studies ranged from 7.0E-Q5 to 1.9E-04. If the lower estimate is assumed
to approximate the 5th percentile of a lognormal distribution and the higher estimate is assumed to
approximate the 95* percentile of the distribution, then using the properties of the lognormal
distribution, the GEOMETRIC MEAN for a lognormal mean transfer factor distribution can be
estimated as follows:
GM = (5* % . 95* %)* (2"I2>
This is because
A2-4
-------
(5* % * 95* %)2 - [exp(p-1.645**0*~!.645*))]' =¦ expOO. (2'13)
For the transfer uncertainty factor, the geometric mean is estimated to be
(7.0E-05 • 1.9E-04)* = 1.15E-04.
Define GEOMETRIC STANDARD DEVIATION (GSD) as exp(ff). Then, using the properties of a
lognormal distribution, the GSD for an uncertainty factor can be approximated as
GSD - (9*5* %/$*%)™ (2"14)
because
(95* %/5"> %)TS = [exp<>+1.645
-------
E(X) - I.15E-04•exp(ipn(1.35)]2) - 1.15E-04-1,046 - 1.2E-04
•*>
(2-18)
Anaivji? gf NMriplicativ? Models
If two or more lognormal random variables are independently distributed; then the product of these
random variables also follows a lognormal distribution. This property of lognormal distributions leads
to the multiplicative model, which is the basis for EPA's uncertainty analysis for risk to human health
from radon in drinking water.
Define the random variable U to be the product of m independent, lognormal random variables. If the
m independent, lognormal random variables represent m uncertainty factors, then U defines the
multiplicative model, such that
U ¦ X,XjX3...Xm * nXj (2-19)
1*1
The variable U is distributed lognormally with ^ + - and
-------
The MEDIAN or GEOMETRIC MEAN of U is expC/iJ and is estimated as follows:
exp(Au)-exp(53 Aj)=nexp(Ap=nGMj
,.i j-i j-i
(2-20)
Likewise, under the condition of independence, the GEOMETRIC STANDARD DEVIATION of U,
exp{cru) can be estimated as
m
re
exp(au)"exp
E*j
j-'
-exp
*
^[IrKGSDj)]1
j-i
(2-21)
and the mean or expected value of U can be estimated as
E(U) - exp(Au-Io2u) - GMU . exp(i[ln(GSDu)]2)
(2-22)
Similarly, the upper 100*p^ percentile for U is estimated as
Up » exp(Au*Zpau) » GMjj * exp(Zpln(GSDu)) = GM0 • GSDj/'
(2-23)
while the lower 100*(l-p)th percentile for U is estimated as
-z.
= exp(Au-Zpau) - GMu-exp(ZpIn(GSDu)) = GM0 • GSDu '
(2-24)
The upper lOO^p0 and lower lOO^l-p)1" percentile estimates, for 0.5
-------
Under the assumption of Iognormality, the geometric mean and geometric standard deviation of each
uncertainty factor is estimated. Under the assumption that each of the uncertainty factors is
independently distributed, descriptive statistics for the overall uncertainty distribution are then
determined using the multiplicative model.
A2-6
-------
APPENDIX 3
MATHEMATICAL DETAILS OF THE
THREE COMPARTMENT MODEL
INTRODUCTION
The three-compartment model employed in this effort is basically that of McKone (1987), with a few
modifications. Conceptually, a home is envisioned as consisting of three compartments: shower,
bathroom, and main house. Within each compartment, radon gas is released from water into air as a
function of water use patterns, and the air is then redistributed throughout the house and to the outdoors
by bulk flow (ventilation). If water use were continuous in each compartment, a steady-state level of
radon and radon progeny would be established in the air of each compartment. However, water use is
episodic or intermittent, especially in the shower, so air concentration values in each room fluctuate as
a function of when water flow occurs. The following text presents the mathematical approach used to
calculate the concentration values of radon and radon daughters in air as a function of time in each cf the
three house compartments, and to estimate the level of human exposure to those chemicals.
CONCENTRATION MODEL
The fundamental equation for calculating the concentration of radon or any radon daughter in air as a
function of time (t) is as follows:
a2-r
-------
where:
C,+| = Concentration in air at time t+.l (pCi/L)
C, = Concentration in air at time t (pCi/L)
dC/dt = Rate of change in concentration (pCi/L per min)
At = Time increment (min) between time t and time t+1
Thus, if the concentration at time zero is known, then the concentration over time can be calculated in
an iterative series of steps (each result depending on the value before). That is:
C, =
- Co
+ dC/dt*At
c2
= C,
+ dC/dt*At
C3 =
¦ Q
+ dC/dt*At
etc.
A discussion of how each of the parameters in this basic equation are selected or calculated is presented
below.
-------
Selection of G,
Selection of Q, is essentially arbitrary. If zero is chosen, then the results of the calculations will show
how the concentration of the chemical in air rises in the compartment as a Auction of time due to release
from the source (water) and/or to transport in from adjacent rooms. If the value of Q is set to some high
value, then the calculations will show how the value falls due to removal by ventilation. In either case,
the concentration will reach a steady state value that depends only on the release rate and the ventilation
rate, and is not a function of C0.
While such accumulation or dissipation curves may be of interest, the concentration at time zero
(arbitrarily chosen to be 12:00 midnight) at the start of any given day will be equal to the concentration
at time - 12:00 midnight at the end of the preceding day. Thus, the value of Q can be calculated by
choosing any reasonable value as an initial guess, then running the model for one day. The value of C
at time = 12:00 midnight at the end of this run is then equal to the value of Q on the day of interest.
In practice, the initial guesses for the concentration of radon and its progeny are made using a simple
transfer factor approach, as follows:
Co(Rn) - Cw-lE-04
C0(Po) - Cw*lE-04
C0(Pb) - Cw*5E-05
Co(Bi) - CW2E-05
CafcMiaHQp pf dC/dt
The basic equation which gives the value of dC/dt in compartment i is:
A3r3"
-------
dC. t
± •
-------
3. loss by plating out to walls, etc. (Ouy (radon progeny-only)
The values of each of these influx and efflux rate terms for compartment i are calculated as follows.
Betof fr
-------
Ventilation
The basic equations describing influx and efflux due to ventilation are:
InVJ = EC,*?,,
and
OtaVJ - Ct*25?,, •
where:
Iiiy; = Influx into compartment i by air flow from other rooms (pCi/min)
Cj = Concentration of radionuclide in the air of compartment j (pCi/L)
qj,( = Air flow from compartment j into compartment i (L/min)
Out, , = Efflux out of compartment i due to ventilation to other rooms or to outdoors
(pCi/min)
C, = Concentration of radionuclide in the air of compartment i (pCi/L)
qUj = Flow rate of air from compartment i to compartment j (L/min)
The inter-compartment air flux rates (qy, L/min) are derived from data on compartment residence times
(R, min) and volumes (V, L) using the following fundamental relationships:
Air flow in = Air flow out = V/R
Figure 1 showes the intercompartment air flux terms needed to evaluate ventilation in this model.
—
-------
In McKone's model, all of die air flux terms were considered to be constant over the course of the day.
For this evaluation, a modification similar to that employed by Wilkes et al (1992) was employed.
Specifically, ventilation of the bathroom was evaluated under three different conditions. For most of the
day, it is assumed the bathroom is unoccupied and the door is open and the bathroom exhaust fan is off
(case 1). When the bathroom or shower is occupied, it is assumed that the bathroom door is closed,
resulting in a change in the air residence time in die bathroom from Rbl (door open) to Rb2 (door
closed). Further, it is assumed that the occupant may either leave the bathroom exhaust fan off (case 2),
or may turn the fan on (case 3). In case 3, it is assumed that the exhaust fan rate (EXFR) generates a
negative pressure in the bathroom relative to the rest of the house, and that air flux from the bathroom
to the house (qba) is zero. Air flux rates can then be calculated from the equation above with the results
shown below:
Flux
Case 1
(Bathroom door open,
fan off)
Case 2
(Bathroom door closed,
fan off)
Case 3 •
(Bathroom door closed,
fan on)
qsb
Vs/Rs
Vs/Rs
Vs/Rs
qbs
Vs/Rs
Vs/Rs
Vs/Rs
qbo
0
0
EXFR
qab
Vb/Rbl
Vb/Rb2
EXFR
qba
Vb/Rbl
Vb/Rb2
0
qao
Va/Ra
Va/Ra
Va/Ra - EXFR
qoa
Va/Ra
Va/Ra
Va/Ra
-------
jvf Fnrmatjon and Dccav
The rate of loss of each radioactive species due to decay is given by:
where:
o«fr, - -c,*v*kp
Out, p = Loss of parent due to radioactive decay (pCi/min)
Cp = Concentration of parent in air (pCi/L)
V » Volume of compartment (L)
kp = Radioactive decay constant of parent (1/min)
The rate of formation of daughter species due to decay of parent is:
lnr4 ' cP*V'kd
where:
In, d = Formation of daughter due to radioactive decay of parent (pCi/min)
Cp = Concentration of parent in air (pCi/L)
V = Volume of compartment (L)
= Radioactive decay constant of daughter (1/min)
A3-*~
-------
The values of In, and Out, for each member of the decay chain are as shown is Table 1.
Loss Due to Plating Out
The rate of radon progeny loss due to plating out is highly variable, depending on the rate of air mixing
within a room, the surface area of walls and furniture, ami the concentration of dust and other aerosol
particles in air (Vanmarke et al 198S, Reineking et al 1985, Knutson 1988, Hopke et al 1990). For a
well-mixed room, a rough estimate of plating out is given by the following equation:
Outp - * {l-fJ*DVa]*A
*
where:
C - Concentration of a radon daughter in air (pCi/m3)
fu = Fraction of progeny unattached to dust or aerosol
DV„ = Deposition velocity of unattached fraction (ra/min)
DV, = Deposition velocity of attached fraction (m/min)
A * Surface area of room (m1)
The value of A (surface area, including four walls plus ceiling and floor) can be estimated from the
volume of the room by assuming the room is square in shape and has a height of 2.4 m (8 ft), as follows:
£3*9
-------
Edge * JVflA
Area - 2*Edge1 * 4*(2.4*Edge)
Sdwtipn
-------
Time in bathroom after shower (TB)
Time leave bathroom after shower (LB =» ES + TB)
Time leave house after leaving bathroom (LH)
Time return home (RH)
Based on these parameters, it is possible to specify a series of "occupancy factors" for each room for each
minute of the day. If the person is in a room, the occupancy factor for that room for that time interval
is I. If a person is absent from a room, the value is zero. The incremental dose (ID) over the time
interval from time t to time t +1 is then:
ID, ¦ [ - C^OF,, • C^OF„ ] 41
where:
C = Average concentration between time t and time t+1
* 0.5-(C, + C,.,)
The dose over the entire day is simply the sum of the incremental doses over each of the 1440 minutes
of the day.
Dose Units for Radon Progeny Exposure
Exposure to radon progeny is generally expressed in terms of Working Level Months (WLM). One
WLM is equal to exposure to one WL for a period of one working month (172 hours). The concentration
-------
of radon progeny (expressed in units of WL) is calculated from the concentration of each radon Haughtw
(expressed in pCi/L) as follows:
WL - 0.0010'C(JI,Po) + O.Otm-CC'Pb) + O.OOSS'C^Bi)
The sum of the incremental doses (WL'min per day) calculated as above is converted to WLM per year
as follows:
WLM/yr = WL*min/day • 1/60 hr/min * 1/172 working month/hr • 365 days/yr
Dose Units for Radon Gas Exposure
The inhalation risk factor for radon gas is expressed in terms of risk per pCi radon inhaled. Therefore,
exposure is expressed as pCi inhaled per year. This is calculated from the average daily exposure
(calculated as (pCi/L)*min per day) as follows:
pCi/yr = (pCi/L)*min/day • Breathing Rate (L/min) • 365 days/yr
SUMMARY OF MODEL INPUT REQUIREMENTS
Table 2 summarizes the input parameters which are required to evaluate exposure using the three
compartment model.
A3=T2
-------
TABLE A3-1
RATE EQUATIONS FOR FORMATION AND DECAY
OF RADON AND RADON PROGENY
In,, -
Out,,
Radionuclide
pCi/rain
pCi/rain
Riv-222
-
C^-V-k^
Po-2i8
Wk*
Pb-214
B*
-------
TABLE A3-2
LIST OF REQUIRED INPUT PARAMETERS
Input Parameter
Symbol
Units
Concentration of radon in water
Cw
pCi/L
Volume of shower stall
Vs
L
Volume of bathroom
Vb
L
Volume of main house
Va
L
Air residence time in shower
Rs
min
Air residence time in bath (door open)
Rbl
min
Air residence time in bath (door closed)
Rb2
min
Air residence time in house
Ra
min
Bathroom exhaust fan rate
EXFR
L/min
Shower flow rate
SFR
L/min
Shower time
Ts
min
Number of showers taken per day
N
—
Time in bathroom after shower
Tb
min
Time start first shower
SSI
Total water used in bathroom
lb
L/day
Total water used in main house
la
L/day
Radon transfer efficiency in shower
Ps
—
Radon transfer efficiency in bath
Pb
—
Radon transfer efficiency in house
Pa
-
Unattached fraction
UFRAC
—
Deposition velocity of unattached fraction
DVu
m/min
Deposition velocity of attached fraction
DVa
m/min
Time exposed person leaves home
LH
-
- Time exposed person returns home
RH
-
Breathinhg rate
BR
L/min
—X3^14
-------
APPEND DC 4
SELECTION OF PDFS FOR THREE-COMPARTMENT MODEL VARIABLES
This Appendix presents the derivation of Probability Distribution Functions (PDFs) to describe both
the variability (PDFV) and uncertainty (PDFJ in each of the three-compartment model parameters.
The general approach employed is described in Section 3.3.1 of the main report.
1.0 NUMBER OF PEOPLE PER HOUSE (PNUM)
The U.S. DOE (1982) conducted a survey of 6051 randomly selected homes in the US. The relative
frequency of homes as a function of number of residents (PNUM) is shown below:
Number of People in
Relative
Home (PNUM)
Frequency
1
.192
2
.328
3
.183
4
.164
5
.083
6
.049
Since only integral values of PNUM are possible, this variable was modeled as an empirical PDF.,
choosing values from 1 to 6 in proportion to the frequency given above. Because this distribution is
based on over 6000 observations. PNUM was not treated as an uncertain variable.
A4J-
-------
2.0 COMPARTMENT VOLUMES
2.1 Volume of Shower fVs\
Only limited information was located oil shower volume. The available data are summarized below.
t
Reference
Vs (L)
Comments
Foster and Chrostowski
1986
1270 - low end
No discussion ot reference
McKone 1987
Typical ™ 2000
Range » 1300-3000
Values attributed to Foster and
Chrostowski, but data were not
located in that paper
McKone and Knezovich
1991
2300
Size of a single experimental system
used by authors
Trancrede et al. 1992
1500
Value is for a single "full size" test
shower
Wilkes et al. 1992
2000
Based on Axley 1988. Not stated if
value is measured or assumed.
Because these data are so limited, the value of Vs was modeled as uniform with uncertain minimum
and maximum values, as follows:
Vs - .U(min,max)
min - U(1000,1500)
max - U(250G.3Q0G)
£4-2""
-------
2.2 Volume of Bathroom (Vb>
Information located on bathroom volume is summarized below.
Reference
Vb (L)
Comments
Foster and
Chrostowski 1986
6000 » low end
No discussion or reference
McKone and
Knezovich 1991
9600
Size of a single experimental model
used by authors
McKone 1987
Typical = 10,000
Range « 6,000-50,000
No discussion or reference to source
of these values
Wilkes et al. 1992
13,000
Based on Axley 1988. Not stated if
value is measured or assumed.
The National Kitchen and Bath Association (NKBA) performs yearly surveys of its member
contractors regarding the size of bathrooms which have undergone repair or remodeling. The data for
1993 and 1994 are shown below.
Bathroom Area
(Square feet)
Bathroom
Volume (mV
Percent in Size Range
1993
1994
< 35
<7.8
15
14
35-75
7.8-16.7
44
41
75-100
16.7-22.3
27
30
100-200
22.3-44.6
11
13
>200
>44.6
3
5
(a) Assumes a ceiling height of 8 feet
A
-------
These data are well-fit by a lognormaj distribution with gra « 14 m3 (14,000 L) and gsd = 1 66.
Therefore, Vb was modeled as a truncated lognorraal with uncertain gm and gsd and fixed lower and
upper plausible bounds. It is suspected that the data set used to derive this PDF, is large and
reasonably representative, but since the number of bins was small and since no details were provided
on the sample set, an intermediate qf (25) was assigned. In summary:
PDFy(Vb) - TLN(gm,gsd,min,max)
PDF„(ln(gm))*- TS(m,s,qf)
PDF„(ln:(gsd)) - INVCH(s.qf)
m » ln( 14,000)
s - ln(1.66)
qf * 25
min ¦ 4,000
max a 60,000
2-3 VqItos 9f Main Hwt (Va)
The U.S. DOE (1982) conducted a survey of 6051 randomly selected homes in 14 different cities
across the United States. Each house was assigned to one of seven different size categories, based on
the total heated floor space, and the number of people residing in each home was noted. Nazaroff et
al. (1987) estimated the house volume from the floor area by assuming a wall height of 2.4 m (8
feet), and divided the volume by the number of people. The resulting per capita volume distributions
were well-fit by lognortnai PDFs, with the parameters shown below.
A4-r
-------
PNUM
gm (m3/person)
gsd
min
max
1
205
1.78
35
1100
2
144
1.74
30
700
3
99
1.68
25
450
4
89
1.67
20
400
5
75
1.70
15
350
6
54
1.78
10
300
Based on these data, the value of Vt was modeled as a set of truncated tognormal discributuions, as
described in Section 3.3.1. The maximum and minimum values shown in the table are approximately
equal to the 99th and 1st percentile values, estimated visually from graphs of the data presented by
the authors. Because this study involved a large number of homes from 14 different cities across the
US, a qf of 100 was assigned.
The value of Va (volume of the main house) is calculated first by selecting a value for the number of
people in the house (PNUM, see 1.0 above), and then choosing a value from the corresponding total
volume per capita (Vt) PDF above. Then:
x Va =¦ PNUM'Vt - Vb - Vs
In practice, this method for calculating Va allows for choosing large values for the volume of the
shower and/or the bathroom while choosing a small volume for total house volume, and occasionally
this approach leads to unrealistic values for Va (including values that are negative). Ideally, the
solution to this problem would be to specify a correlation coefficient that describes the degree of
correlation between the size of each of the three house compartments. However, since no information
was located on the nature or magnitude of this correlation, the problem of unrealistic combinations of
-------
selected compartment volumes was addressed simply by imposing a "reality check" on the calculated
value of Va. If the value of Va was smaller than 50% of the value of total house volume
(PNUM'Vi), then new values were selected for each of Vs. Vb, and Vt, and the reality check was
applied again.
3.0 WATER USAGE
31 5h
-------
to a gm and gsd of 7.1 and 1.54, respectively. Because the study by.James and Kruiiman involved a
large number of people, the qf assigned for this study was 100. In summary, SFR was modeled as
follows:
PDF.(SFR) • TLN(gm,gsd,minjnax)
PDFu(ln(gm)) *- TS(ra,s,qf)
PDFu(lnJ(gsd)) - INVCH(s.qf)
m - In(7.1)
s - ln(i.54)
qf ¦ 100
min * 3
max « 24
3 2 Time in Shower .(TS)
Brown and Caldwell (1984) reported data on the showering habits of 345 people in 162 houses.
These people took an average of 5.2 showers/week, with an average shower duration of 10.4 minutes.
James and Knuiman (1987) surveyed the showering habits of people in 2,500 households. The
probability distribution frequency for shower duration was well-fit by a lognomial in shape, with a
geometric mean of 6.8 minutes and a geometric standard deviation of 1.60. Because this study
involved a large number of people, the qf assigned for this study was 100. In summary, Ts was
modeled as follows:
bA*T~
-------
PDFy(Ts) - TLN(gm,gsdfmin,max)
PDFu(ln(gxn)) *- TS(m,s,qf)
PDF^lntgsd)2) - INVCH(s.qf)
m ¦ lri(6.8)
s = ln(1.6)
qf - 100
min =1.0
max =¦ 30
3.3 Total Per Capita Water Use in Shower
There are numerous reports on per capita water use during showering, as shown below. These
distributions are not used in the model per se. but can be used to determine whether the PDFs chosen
for SFR and TS are reasonable.
Reference
Shower Flow (L/person/day)
EPA 1978
36±11 (range = 21 tp 51)
Laak 1974
32.1
Cohen and Wallman (1974)
23.8 ± 10.4 (STD)
Ligman et al. 1974
47.2
Kreissl 1978
18-20
Bennett and Linsted 1975
33
Witt et al. 1974
38
Brown and Caldwell 1984
34-62
hfrtT
-------
Reference
Shower Flow (Uperson/day)
Partridge et al. 1979
76-114
Bond et al. 1973
75
Siegrist et al. 1976
38
As shown, nearly all values fall between 30 and 60 L/person/shower. The 50th percentile of the
distribution generated by multiplying the PDF tor SFR by the PDF for TS is 50 L/person/day,
suggesting that the PDFs selected for these variables are reasonable.
3.4 Water Use in Bathroom (lb)
A number of studies provide data on the amount of water used for toilets. These data are
summarized below.
Reference
Per Capita Toilet
Water Use (WUb)
(L/person/day)
EPA 1978
35 (21-52)
Laak 1974
74.8
Ligman et al. 1974
75.6
Kreissl 1978
20
Cohen and Wailman 1974
65 ±30 (STD)
Bennet and Linsted 1975
56
Witt et al. 1974
34
Brown and Caldwell 1984
53-83
Partridge et al. 1979
15-23
Siegrist et al. 1976
35
-------
Even though there are a number of studies on this variable, no information was located on the shape
of the distribution, and relatively little information was located on the upper and lower bounds of the
distribution. Therefore, the value for lb was modeled as an uncertain uniform distribution, as
follows:
lb - PNUM*WUb
WUb - U(min.max) N
min — U(15,20)
max - U(75,85)
3.5 Use }n Main Hww (la)
A number of surveys have been performed of total water use in US households. The table below
summarizes a number of these.
Reference
Total Water Use (L/person/day)
min
Typical
max
Steel and McGhee 1979
75
190-340
380
Bennet and L ins ted 1975
168 '
Witt et al. 1974
161
Ligman et al. 1974
180
EPA 1978
96
161 (154-168)
215
Anderson and Watson 1967
68
166±53 (STD)
261
Kreissl 1978
152
Laak 1974
157
Siegrist et al. 1976
162
A4*W
-------
Reference
Total Water Use (L/person/day)
tnin
Typical
max
Bond et al. 1973
233
Hess et al. 1990
240
Cohen and Wallman 1974
143
210±81 (STD)
384
Partridge et al. 1979
310-439
Nazaroff et al. 1987 combined the data from several studies (comprising a total of 90 individual
houses), and found that the CDF was well-fitted by a lognormal distribution with gin =¦ 189
L/person/day and gsd <°> 1.57. This corresponds to an arithmetic mean and standard deviation of 209
and 99 L/person/day, respectively.
Thus, most studies indicate that typical per capita water use is about 150-250 L/person/day.
However, both Bennet and Lindsted (1975) and Brown and Caldwell (1984) state that water use per
capita depends to some degree on the number of people in the house. Based on this. Brown and
Caldwell stratified their rfara on water use by number of people, and reported the following means
and standard deviations:
N
Number of
Homes
Per Capita Total Water Use
(WUt) (L/person/day)
Mean
STD
1
25
316
90
2
42
266
76
3
33
264
59
4
31
238
55
5
8
216
32
6
1
184
-
A4*Tf~
-------
The authors did not discuss the shape of these distributions, but did provide a graph with
scattergrams. Visual inspection of the graphs suggests that the data are moderately right-skewed,
probably suitable for modeling as a truncated lognormai distribution. These graphs also served to
identify the likely minimum and maximum values for each distribution. Because the number of
homes in each stratum is relatively modest (especially for N - 5 and N » 6), a qf of 25 was chosen
for the first four strata, and a qf of 10 was chose for the last two strata. The resulting values of gm,
gsd, min, max and qf needed to characterize the truncated lognormal distributions are listed below.
N
gm
gsd
mis
max
qf
1
304
1.32
150
560
25
2
256
1.32
130
520
25
3
258
1.23
110
480
25
4
232
1.26
90
440
25
5
214
1.16
70
400
10
6
[214]
[1.16]
[70] -
[400]
10
Based on this, the value for la was calculated as follows:
la - PNUM-WUt, - lb - SFR*Ts*PNUM
WUtj - TLN(gmi,gsdifnuni,maxi)
lnCgmO *- TS(m,.s„qf1)
In-CgsdJ - INVCH(s,,qf|)
In practice, this method for calculating la allows for choosing large values for-SFR and/or lb, while
choosing a small value for total house water use. Thus, occasionally this approach leads to unrealistic
values for la (including values that are negative). Ideally, the solution to this problem would be to
A4-t2
-------
specify a correlation coefficient that describes the degree of correlation between the water use in farh
of the three house compartments. However, since no information was located on the nature or
magnitude of this correlation, the problem of unrealistic combinations of selected compartment
volumes was addressed simply by imposing a "reality check" on the calculated value of la. If the
value of la was smaller than 30% of total water use (PNUM*WUt), then new values were selected for
time in the shower (Ts), shower flow rate (SFR), per capita water use in the bathroom (WUb). and
total per capita water use (WUt), and values were recalculated and retested.
4.0 COMPARTMENT VENTILATION RATES
Ventilation rate (VR) is described either in terms of air changes per hour (ACH), or in terms of air
residence time (RT) (1/min). The residence tins and ventilation rate are related as:
RT - 60/VR
4-1 House Ventilation Rate/Retention Time
McKone 1987 chose a main house residence time of 120 minutes (ventilation rate ¦ 0.5/hr), with a
likely range of 30-240 minutes <0.25/hr-2/hr). The source of these values was not discussed or
referenced.
Grot and Clark (1981) made 1048 measurements in 266 different dwellings located in 14 different
cities across the US. All of the homes were "low income" and relatively old (median age = 45 yrs).
The individual measurements were fit by a lognormal curve with arithmetic geometric mean of
-------
0-86/hr and a gsd of 2.16. The arithmetic mean and standard deviation were 1,12/hr and 0.86/hr,
respectively.
Nero et al."(1983) measured infiltration rates ia 98 different homes. The values ranged from 0.02/hr
to 1,6/hr, but the mean value was not reported. Because of opening doors and windows, total
ventilation is probably about 20% higher than infiltration (Nero 1983).
Grimsrud et a). (1983) measured infiltration rates in 312 homes. These homes were low income
with a median age of less than 10 yrs. The mean value for all homes was 0.63/hr, with a median
(50th percentile) of 0.50/hr. According to Nazaroff et aJ. (1987), these data were moderately-well fit
by a lognormal distribution (gm =» 0.53/hr, gsd » 1.71).
Doyle et al. (1984) calculated air infiltration rates in 58 homes in four different cities. The results
were approximately lognormal in shape, with a gm of 0.8/hr and a gsd of 1.8.
Hess et al. (1990) measured the ventilation rate in 40 homes in Maine using two different.methods.
Based on the first method (decay of SF6), the mean value was 0.55/hr, with a minimum of 0.19/hr
and a maximum of 1,62/hr. Based on the second method (dissipation of radon following water use),
the mean value was 0.76/hr, with a minimum of 0.14/hr and a maximum of 1.33/hr.
Nazaroff et al. (1987) combined the data of Grot and Clark (1981) and Grimsrud et al. (1983),
weighted according to the number of houses in each, Kid obtained a combined^ lognormal distribution
with gm = 0.68/hr and gsd = 2.01. Even though these values are based on two independent surveys
of a large number of homes, both studies investigated only low-income housing, so it is possible that
the data are not fully representative of the US population. Therefore, a qf of 25 was chosen. Based
A4^<
-------
on the minimum and maximum air exchange values reported by Grot and Clark, Grimsrud et ai. and
Hess et al., plausible minimum and maximum values were estimated to be 0.1/hr and 3.5/hr. In
summary, the value of VR, was modeled as:
VRa - TLN(gm,gsd,min,max)
ln(gm) — TS(m,s,qf)
In^gsd) •- INVCH(s.qf)
m = ln(0.68)
s - ln(2.0l)
qf - 25
min * 0.1/hr
max = 3.5/hr
As noted above, the value of RTa (1/min) is simply 60/VRa,
As discussed by Grimsrud, there is a correlation between the effective leakage area of a home and its
size (either surface area or volume). Therefore, it is expected that there should be a correlation
between the size of a home and the ventilation rate for that home. However, analysis of the paired
data provided by Grimsrud on house size and ventilation rate did not reveal any significant correlation
between these variables. Presumably, this is because the effects of weather and house condition are
much more important determinants of air flow than house size. Regardless of *he reason, based on
these data, ventilation rate was modeled as an independent variable (not depending on house size).
* 2 Bathroom Ventilation Rate
AJKtS
-------
Ventilation of the bathroom occurs by two main pathways: 1) simple exchange with air from the main
house, driven mainly by forced air movement from furnaces or air conditioners, and 2) forced air
exhaust via a bathroom fan vented to outdoors. Information located on bathroom ventilation/ air
retention time is summarized below.
Reference
VRb (ACH)
RTb (min)
Comments
McKone 1987
Typical - 2
Range - 1-3
30
20-60
No reference or discussion of the
source of these data
McKone and
Knezovich 1991
3
20
Based on a single experimental model
used by authors. Door closed, fan off
Hopke 1993
1.6
37.5
Based on a single bathroom, fan off,
door open
Giardino et al
1990
1.0, 0.3
60, 200
Door closed, fan off (measurements in
two separate bathrooms)
Wilkes et al 1990
5.5
10.9
Based on Axley 1988. Not stated if
value is measured or assumed, or if
door is open or closed.
Wilkes et al. 1992
2.2
0.8
7.4
27
75
8
Door open, fan off
Door closed, fan off
Door closed, fan on
Based on Axley 1988. Not stated if
values are measured or assumed.
Further information on bathroom ventilation with the door closed and fan on is available from
engineering specification for bathroom exhaust fans. Nominal exhaust rates for different fans
supplied by different manufacturers range from about 40 ftVmin to-160 ft3/min (1100 to 4500 L/min).
with most "mid-range" fans discharging about 70-90 ftJ/min (2000-2500 L/min) (Grainger 1994
General Catalogue). For typically sized bathrooms (e.g., 15,000 L), these fans would produce about
4.4 to 18 ACH (typical - 8-10 ACH).
AJtfftC
-------
Based on these data, air fluxes into and out of the bathroom were modeled separately for three
different conditions:
Condition 1: Door open, fan off (bathroom unoccupied)
RTbl - U(min.max)
min - U(20,30)
max - U(40,50)
Condition 2: Door closed, fan off
RTb2 - U(min,max)
min - U(20,30)
max - U(150,250)
Condition 3: Door closed, fan on
As discussed in Appendix 3, in this condition it is assumed that the exhaust fan rate (EXFR) is the
only source of ventilation in the bathroom. Thus,
RTb3 - VB/EXFR
*
EXFR - TRI(min.max.mode)
min = 1000
max = 5000
-------
mode - U(2000,2500)
No information was located on the fraction of people who turn the bathroom fan on when in the
shower or bathroom. In the absence of data, the liklihood of having the fan on was assumed to be
0.5. Therefore, each individual in the house was assigned at random to either case 2 (fan off) or to
case 3 (fan on), with the liklihood of being assigned to either case equal to 50%.
*•3 Shower Ventilation Rate
Information located on shower ventilation/ air retention time is summarized below.
Reference
VRs (ACH)
RTs (min)
Comments
McKone and
Knezovich 1991
>12
< =» 5
Based on a single
experimental shower used
by authors
Andelman 1985
3
20
Apparently an assumed
value
Wilkes et al. 1992
21
2.9 min
Based on Axley 1988. Not
stated if value is measured
or assumed.
The only pathway for ventilation of the shower is air exchange into the bathroom. The rate of air
mixing depends on the physical structure of the shower (closed stall, tub with curtain, etc.), and is
presumably driven mainly by thermal gradients generated during showering. Based on this, it is
judged to be likely that residence time in the shower is relatively brief, so the assumed value of
Andelman is given little weight compared to the more nearly consistent values of McKone and
Knezovich and Wilkes et al. (Note that Andelman is the senior investigator in the Wilkes et al
study). Therefore, the value of RTs was modeled as:
-------
RTs -
min -
max -
U(min,niax)
U(2.3) ~
U(4,6)
5.0 RADON TRANSFER EFFICIENCY
There are several studies which provide data on the fraction of radon released as a function of type of
water use (shower, bath, toilet, other). The data from these studies are summarized below:
Fixture/Use
Partridge et al. 1979
(Mean±STD)
(N - 11)
Gesell and Priehaid
1980
(N ™ "a number*)
Hess et al. 1982
Hasnand Erchholx
1992
Dishwuher
.98 ±.02
.9
.98*
Shower
.71 ±.02
63
.63'
60-M
Badt
.36 (warm)
.60 (hot)
.47
.3*
Toilet
.24 ±.03 (bowl)
.05 ±.06 (unk)
.30
.3'
Laundry
93 ±02 (cold)
98±.0I (hot)
.90
9»
Cleanint
28
.30-90
V
(a) Measired (no details provided).
(b) "Estimated" (i.e.. not measured).
Nazaroff et al. 1987 noted that for a particular water use there is very little variation in
fractional radon release either within a study (e.g.. Partridge et al.. 1979) or between
studies, and he speculated that variability in fraction released is a very small source of inter-
house variation in exposure to water-borne radon. McKone and Knezovich 1991 reported
A4^KT^
-------
that the distribution of fractional releases of TCE from a shower was 61 ±9.4%. This narrow
variability supports Nazaroff s conclusion.
McKone 1987 cited the dm of Prichard and Gesell (1981) (which his the same data as Gesell
and Prichard 1980) and Hess et al. (1982) and chose the following values for use in his model,
without further discussion or explanation:
Category
Typical
Likely Range
Shower
0.7
0.3-0.7
Toilet
0.3
0.3
Other water
0.6
0.58-0.74
Based on these limited data, the values for the fractional release of radon (designated by "P")
in each room (designated by "i") were modeled as follows:
Pj - U(minj,maXi)
min, - U(0.5,O.6)
max, - U(0.7,0.8)
minfc ~ U(0.15,0.25)
maxb - U(0.35,0.45)
min, - U(0.4,0.5)
-------
max, - U(0.7,0.8)
6.0 UNATTACHED FRACTION (UFRACT)
The unattached fraction depends mainly on the cooccntratioo of aerosol in air and the
attachment rate constant, both of which are highly variable (Kmitson 1988, Phillips et al,
1988). A summary of measured or estimated unattached fractions in homes is provided
below.
Reference
UFRACT (%)
Comments
Knutson 1988
0.7-42
Modeled, not measured
George and Breslin
1980
Mean = 7
Data from 4 houses in New
Jersey
Portsendorfer et al.
1987
6-15
Range observed in "several"
homes
Reineking et al. 1985
Range = 2-15
Data from five different rooms
James 1988
Typical = 5
Range = 1-12
Range based on review of 7
published reports. Stated very
difficult to estimate "typical".
Hopke et al. 1990
Range = 7-40
Value depends mainly on aerosols
present
Reineking and
Porstendorfer 1990
Mean = 9.6
Range = 0.5-77
Value depends mainly on aerosols
present
Vanmarcke et al. 1987
Typical = 10
Range = 0-18
Data from one room over seven
days
M-JAr-
-------
Based on these data, the value for UFRACT was modeled as follows:
UFRACT - BETA(mean,mode,min,max)
mean - U(0.05,0.15)
mode - TRI(min,mean,(min+raean)/2)
min *¦ 0
max » 1
7.0 RADON PROGENY DEPOSITION VELOCITY (DV)
71 Unattached Fraction fDVu)
The deposition velocity of unattached radon progeny is determined mainly by the degree of
air mixing within a room. Knutson (1988) reviewed a number of studies on deposition rate,
and concluded that the average value probably fell within the range of 5-10 m/hr, and
recommended a value of 8 m/hr as the best estimate. The theoretical lower bound (no air
mixing at all) is 0.5 m/hr, and data from several studies suggest that values of 1-4 m/hr may
occur in calm rooms. Studies performed in rooms or chamber with good air mixing yielded
values from 16 to 22 m/hr.
Based on this, the value for DVU (expressed in units of m/min) was modeled as follows:
>4=21"
-------
DVu - (l/60)*U(min,max)
min - U(l,4)
max - U(16,22)
7.2 Attached Fraction (DVa)
The deposition velocity of radon progeny which have become attached to aerosol particles is
dictated both by the size distribution of the particles and by the air mixing rate in the room.
Knutson (1988) reviewed several studies on the deposition rate of various aerosol types, and
concluded that the likely range was from 0.03-0.2 m/hr, with a likely midpoint of about 0.08
m/hr. These values are not very certain, due both to the lack of extensive data and the
expected variability in both particle size distribution and concentration, season, and air mixing
rates. Based on this, the value for DVa (expressed in units of m/min) was modeled as follows:
DVa - (l/60)*U(min,max)
min - U(0.01,0.05)
max - U(0.1,0.3)
>4=2T
-------
8.0
HUMAN ACTIVITY PATTERNS
8.1 Time in Shower (Ts^
The time a person spends in the shower has been discussed previously (see Section 3.2).
8.2 Time in Bathroom After Shower (Tb\
According to EPA's Exposure Assessment Handbook (USEPA, 1989), the time a person
spends in the bathroom is about 4-5 hours/week (34-43 minutes/day). This includes the time
spent bathing (average = 7-8 minutes/day), as well as periodic uses of the bathroom
throughout the day. If the latter totaled about 15 minutes per day, the time spent in the
bathroom after bathing probably averages about 10-20 minutes, with a conceivable range
from near about 1 to about 30 minutes.
On this basis, Tb was modeled as a uniform distribution, as follows:
Tb - U(min,max)
min - U(l,10)
max - U(20,30)
t
8.3 Time Awav from the House (Occupancy Factor. OF)
44*24-
-------
The time a person spends away from the house is characterized by the occupancy factor.
The same variability and uncertainty PDFs were used for the three-compartment model as
described above for the one-compartment approach (see Section 4.L2).
A conflict could occasionally arise if, during the Monte Carlo simulation, an occupancy
factor i§ selected that calls for the person to be away from the house longer than the time
interval between the earliest possible time to leave the house (LHmin, assumed to be 10
minutes after leaving the bathroom after showering) and 12:00 midnight. To avoid this
error, the smallest possible value of OF (OFmin) was calculated as follows;
Leave bathroom (LB) = ES + TB
Earliest time to leave house (LHmin) =» LB + 10
OFmin * LHmin/1440
If the value of OF selected was smaller than OFmin, then OFmin was substituted for the
value selected.
8.3.1 Tunc Leave Horn? (UP
The time a person leaves the house is selected at random, subject to the constraints that the
time must be no earlier than LHmin (see above) and no later than 12:00 midnight minus the
length of time away from the house. That is:
jj^sr
-------
LHmax = OF* 1440
LH ~ U(LHmin, LHmax)
8.3.2 Time Return Hnmr (RH)
The time that a person returns home is simply
RH = LH + 1440(1-OF)
8.4 Breathing Rata (BR)
The USEPA (1989) has collected and tabularized data on breathing rate by humans as a
function of age and activity level. Data for adults (based on groups of 102-595 individuals
catagory) are summarized below. The units are L/min.
Activity
Level
Females
Males
Min
Max
Mean
Min
Max
Mean
Resting
4.2
11.7
5.7
2.3
18.8
12.2
Light
4.2
29.4
8.1
2.3
27.6
13.8
Moderate
20.7
34.2
26.5
14.4
78.0
40.9
Heavy
23.4
114.8
47.9
34.6
183.4
80.0
Similar data are available from Adams (1993), as shown below:
-------
Activity
Level
Females
Males
Mean
STD
Mean
STD
Lying down
7.1
1.5
8.9
2.0
Sitting
7.7
1.9
9.3
1.9
Standing
8.4
2.1
10.7
2.9
Walking
19.2
3.1
22.8
3.8
Moderate activity*
17.4
3.9
24.4
7.4
(a) Housework, hobbies, etc.
Adams did not include an analysis of the shape of the distributions, but inspection of
histograms of the data provided by the author suggests that most distributions are
approximately normal.
For the purposes of this analysis, a single sex- and activity-weighted average PDF was
calculated from the data of Adams (1993). Based on USEPA census data, the sex-weighting
factor (SWF) for males was 0.488 and for females was 0.512. The activity weighting factor
(AWF) was based on the following data provided by EPA (1989):
Activity
Level
Mean Hours
per Day
Percent
- Total
Resting
9.82
48.0
Light
9.82
48.0
Moderate
0.71
3.5
Heavy
0.098
0.5
Total
20.4
[100]
.A<27
-------
The first three activity levels of Adams were categorized as resting or light, which together
account for 96% of the time indoors. Therefore, the AWF for each of the first three levels
was 0.32, while the last two categories were each assigned an AWF value of 0.02. These
weighting factors were then used to calculate the sex- and activity-weighted (SAW) mean and
standard deviation, as follows;
Memuw » E Mean t -SWFi -A WFt
STDUW » ^(STD^SWF^AWF))
The resulting values are:
MeanSAW = 9.1 L/min
STDsaw - 2.0 L/min
The quality factor (qf) selected for evaluation of uncertainty about these parameters is 10.
This low value was chosen mainly because of uncertainty in the accuracy of the weighting
factors selected for combing the distributions. The minimum value was set equal to 2.6,
based on the lowest breathing rate (7.1 L/min) minus three standard deviations (1.5 L/min).
The maximum value was set equal to 46.6, based on the highest breathing (24.4 L/min) plus
three standard deviations (7.4 L/min).
In summary, the value of breating rate was modeled as a truncated normal distribution, as
follows:
-------
PDF,(BR) - TN(mean,std,min,max)
PDFu(mean) *- TS(m,s,qf)
PDFu(std1) - INVCH(s,qf)
m = 9.1
s = 2.0
qf » 10
rain » 2.6
max = 46.6
9.0 SUMMARY OF PDFs
Table 1 summarizes the PDFV ami PDFU types and parameters selected to model the variables
used in the three-compartment model.
-------
TABLE A4-1 SUMMARY OF PDFs
Variable
PDF.
PDF.
Value*
Number of people per
house
PNUM - empnical
NA
1 - .192 4 - .164
2 - 328 3 - .083
3 - .113 6 - .049
Volume of shower
Vi - U(ram.aix)
min - U(a,b)
max - U(c.d)
a - 1000 b - 1300
c - 2300 d - 3000
Volume of bub room
Vb - LNT(gjn.gsd.ain.max)
ln(gtn) *- TS(m.s.qf)
lo'tgri) - INVCH(m.qf)
in - ln(14)
i - It* 1.66)
mia - 4
max - 60
qf - 23
Tool per capit* volume
of house
Vd - LNT(gtn.gsd.raui.nuui)
ln(gmj *- TS(m,i,qf)
IrfCgsd) - (NVCH(m.qf)
m - ln(203.000)
s - lnU.78)
mia - 33.000
max » 1.100.000
qf - 100
VCZ - LNT(gtn.gsd.nun,mai)
ln(gm) — TSfm.s.qf)
lir(gsd) - INVCH(m.qO
re - ln( 144.000)
i - ln<1.74)
min - 30.000
max - 700.000
qf - 100
Vt3 - LNTCgm.gsd.min.isax)
)n(gm) — TSIm.s.qf)
InHgsd) - INVCH(m.qf)
m - ln(99.000)
s - Infl .68)
mm - 23.000
max ~ 430.000
qf - 100
Vt4 - LNT(gm.gsd.min.max)
ln(gm)«- TS(m.s.qf)
InHgtd) - INVCH(m.qf>
m - ln<89.000)
s - ln(1.67>
mia - 20.000
max - 400.000
qf - 100
Vt3 - LNT(gm.gsd.min.max)
Inlgn) «• TS(m.s.qf)
Itr(gsd) •- lNVCH(m.qf)
m - ln(75.000)
i - lnO.70)
min » 13.000
max - 330.000
qf - 100
Vt6 - LNT(gm.gsd,min.max)
in(gm) *- TSIm.i.qO
InHgsd) •- INVCH(m.qf)
m - ln(34.000)
s - IrM 1.78) '
min - 10.000
max - 300.000
qf - 100
Shower tlow rale
SFR - TLN(gm.gsd.min.raaa)
ln(gm) •- TSfm.s.qO
Itr(gsd) - INVCH(m.qf)
m - ln(7.1)
s - 1*1.34)
min - 3
max - 24
qf - 100
Per capita water use in
bathroom
WUb - U(nun.max)
.nun - U(a.b)
max - Ufc.d)
a - 13 b - 20
c - 75 d - 80
A4-3C
-------
Table A4-1 - continued
Variable
PDF,
PDF.
Valuta
Tool per capita wwtr
UIC
WUtl - TLN(|ra,t«l.Biin,Bajil
InCjm) •- TS(ns.i.«jf>
InHfJd) •- tNVCH(m.qf)
m - M30«)
« - liK1.32)
SUB • ISO
mu - 560
qf - 25
WUfi - TLN(fm.gsd.ma,mu>
ln(pa) *- TS(ra.i.qf|
m>K«0-IKVCH(iis.qft
m - ln036)
* - N1.32)
nun * 130
Mi - 520
qf- 23
WTJl3 - TLN(|m.i>d.mm.mu>
latfm) *" TS(m.»,qfi
Wi *) - INVCH(nuqf)
m - M25I)
i - InCl .23)
mia - 110
IMS • 4i0
qf-25
WUt* — TI.Nfgni.gid.ram.max)
liXgm) — TSOn.s.qfl
Irflgsd) «- INVCH(m.qf)
m - ln(2321
t - ta(U«
min - 90
rata «¦ 440 -
qf - 23
WUtS - TLN(im.gid.mm.max)
ln(ftB) — TS(m,i,qf)
lnfl»d) - INVCH(m.itn
m - lnat4)
> - Ml.16)
mia ¦ TO
max - 400
qf - 10
WUt6 - TLN(gro.gsd.mai.niax>
Wis) — TS(!B.»,
-------
Table A4-1 - continued
Variable
PDF,
PDF,
Vahie*
Radon tmufw
effieceocy in mats
bouse
Pa - Ufmia.au)
min - U(a.b)
nu - Lt{c,d)
» - 0.4 b - 0.3
c - 0.7 d - 0.1
Untitir Iwrt fracnoa
UFRACT - Bimean.mode.nun.mix)
mean - U(a.b)
node - TTUftnin. meaiunun+fnetnl/^)
a -0.03 b - 0.15
mm ™ 0
max ~ 1
Deposition velocity of
unattached fraction
DVu - U(min.mui)
min - Ufa.b)
max - Ufc.d)
a - I b - 4
e - 16 d - 22
Deposition velocity of
a cached (ncrion
DVt - U(QUB.UUX)
rub - U(a.b)
max - Ufc.d)
a - 0.01 b - 0.03
c - 0.1 d - 0.3
Time in shower
Ti - TLN{|m.tid.miB.itBui!
Ml®) «- TSfm.i.qf)
trfCgld) - INVCH(m.qf)
m - N6.8)
l « lnfl.fi)
rain - 1
max — 30
qf- 100
Time m bathroom
Tb - U(rmn.mM)
nun - Ufa.b)
max - Ufc.d)
a - 1 b - 10
c - 20 d - 30
Breadunt rate
BR - TWra8an.iM.iffln.nuu)
mean «- TStaM.qf)
id* - INVCHfm.qfl
m - 9.1 1-2.0
min - 2.6 max - 46.6
qf - 10
Occupancy factor
OF - B(mean.mode.mw.ra»)
mean - Ufa.b)
mode - Ufmean.mjjsior U(am.mm\
a - 0.63 b - 0.80
run - 0.33
max ¦ 1.0
-------
APPENDIX 5
UNCERTAINTY IN ORGAN-SPECIFIC CANCER
FATALITY RISK PER UNIT RADIATION DOSE
6*1
-------
* Uncertainty in Organ-Specific Cancer Fatality
Risk per Unit Radiation Dose
To quantify the uncertainty associated with the risk per unit dose estimates used here, a
methodology similar to that employed for assessing the uncertainties in radon risk can be applied
(Puskin 1992). The uncertainty in each site specific risk estimate can be treated as arising from
several independent sources of uncertainty: (1) sampling variability in the epidemiological data; (2)
the variation in risk with time and age; (3) the transport of risk estimates from the Japanese; (4) the
extrapolation to low doses and dose rates; (5) other factors, errors in dosimetry or in medical
ascertainment in the ABSS; (6) for high-LET radiation, uncertainty in RBE. A probability
distribution is assigned to each source of uncertainty and the joint probability distribution calculated
analytically, as was done for radon, or with the aid of Monte Carlo techniques. Necessarily, a
substantial degree of approximation and of subjective judgment are required in assigning the
probability distributions.
A. Sampling Variability
The slope of a dose response curve is ordinarily obtained by performing a linear regression of
excess cancers versus average dose, evaluated over a series of dose intervals. The sampling variation
for the number of excess cancers in each dose interval is governed by the Poisscn distribution; if the
number of excess cancers is not very small, the Poisson distribution is well approximated by a normal
distribution. As a result, with increasing numbers of excess cancers, the uncertainty in the slope will
also approach a normal distribution.
A5-2T
-------
Shimizu et al. (1987, 1990) provide estimates of the average slope, by cancer site, with
associated 90% confidence intervals. These are summarized in Table A4-1. From the table, it can be
seen that, for most sites, the confidence interval limits are distributed nearly symmetrically about the
central estimate of the risk coefficient, as one would expect if the errors are distributed normally
about this value. [The more skewed distributions occur for organs such as esophagus and ovary,
which ordinarily contribute only a small proportion of the total risk from a given exposure.) Hence,
for each site, i, we shall represent the uncertainty due to sampling variation as a normal distribution
with mean (L, + U)(2 and standard deviation (Lt - lf,)/3.Z9. This distribution will, in general, have
a mean displaced slightly (upward) from the maximum likelihood estimate but with the same 901
confidence interval limits obtained from the statistical analysis of the data.
-------
TABLE A5-1
Uncertainties due to sampling variations in the ABSS.
Excess Relative Risk Derived Distribution
Site of'Cancer per Qy* Mean (s.d.)h
Leukemia 5.21 (3.83,7.12) 5.48 (1.00)
All cancers 0.41 (0.32, 0.51) 0.42 (0.06)
except
leukemia
Esophagus 0.58 (0.13,1.24) 0,69 (0.34) Stomach
0.29 (0.09)
Colon 0.85 (0.39,1.45) 0.92(0.32)
Lung 0.63 (0.35,0.97) 0.66(0.19)
Female breast 1.19 (0.56,2.09) 1.33 (0.47)
Ovary 1.33 (0.37,2.86) 1.62 (0.76)
Urinary tract 1.27 (0.53,2.37) 1.45 (0.56)
0.27 (0.14, 0.43)
' Relative risk coefficient and 90% confidence interval from
11 Mean and standard deviation of normal distribution used to
relative risk coefficient (see text).
Shimizu et al. (1990).
characterize the uncertainty in the
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B. Time Projection
A substantia] fraction of the estimated population risk is associated with childhood exposures,
bat there is a-great deal of uncertainly in the estimated risk ton doses to children. First, statistical
uncertainties in the risk coefficients for cancers other than leukemia are generally large for the
youngest age groups among the atomic bomb survivors, since those individuals are just entering the
years of life in which cancers are commonly expressed. Second, there is indication that, for some
types of solid tumors, the excess relative risk may decrease over time for childhood exposures (Little
et al. 1991).
With respect to adult exposures, a temporal fall-off in the excess relative risk of lung cancer
has been observed in radon-exposed underground miners (NAS 1988) and in irradiated spondylitic
patients (Darby et al. t987), but there is no clear indication of such a fall-off in the atomic bomb
surviviors who were over age 20 ATB (Little and Charles 1989). For childhood exposures. Little et
al. (1991) have concluded that there is evidence of a temporal fall-off. Based on an analysis of
observed temporal trends in risk among 4 cohorts of children exposed to radiation, including those
from the ABSS, they estimate that the constant relative risk model for solid tumors may overestimate
the (UK) population risk by 30-45 %.
Another perspective on the uncertainty associated with age and temporal factors can be gained
from the BEIR V report, which treats this uncertainty under "model mis-specification" (NAS 1990, p.
224). From a comparison of risk projections made with alternative age and temporal dependent
models derived from statistical fits to the epidemiological data, the report assigns a GSD of 1.16 and
1 08 to ihe risk about the geometric mean estimates, GM and Gf. for males and females, respectively.
A5^
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Assuming thai the uncertainly is distributed lognormally, these GSD's convert into respective 90%
confidence intervals:
(G„/I.27, 1.27 Gm) and (Gp/1.14, 1.14 GF).
In assigning uncertainties associated with temporal projection, three classes of cancer sites
should be considered:
(1) Sites for which follow-up is essentially complete, with relatively few additional radiation
induced cancers expected past the period of epidemiological follow-up. For this class, which includes
bone sarcomas and leukemia, the uncertainty in lifetime risk associated with temporal projection can
be neglected.
(2) Sites for which a constant relative risk model has been used to project risk beyond the
period of follow-up, but for which the risk coefficients are dependent on the age at exposure. These
sites include stomach, colon, lung, breast, thyroid, and remainder sites. For these sites, most of the
projected lifetime risk is associated with exposures before age 20. As discussed above, the
contribution of childhood exposures is highly uncertain in view of the statistical limitations and
possible decreases in relative risk with time after exposure. For this group of sites, the model
appears more likely to overestimate than to underestimate the population risk. For all of these sites
except colon, we have assigned a range of 0.6-1.0 to the uncertainty factor associated with age and
temporal dependence. For colon, the contribution of childhood exposures to the estimated lifetime
risk appears to be anomalously high; hence, for this organ, we have assigned a larger range of
uncertainty, 0.4-1.0. In all cases, a loguniform distribution will be assumed for the uncertainty.
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(3) Sites for which a constant relative risk projection has been used, but for which the risk
coefficient reflects a single age-averaged value. These sites include esophagus, liver, bladder, kidney,
ovary, and skin. The data available on these sites are generally sketchy and heavily weighted towards
adult exposures. It is plausible that childhood exposures may convey a higher risk than adult
exposures for these sites, as they appear to do for other sites. Consequently, the model used to
project risk may, in this case, tend to understate the population risk. An uncertainty factor between
1.0 and 1.5 will be assigned for these sites; the factor will again be distributed uniformly within this
interval on a logarithmic scale.
C, Transport of Risk Estimates from Japanese
Another major source of uncertainty is over how to apply the results from the analysis of the
Japanese atomic bomb survivors to the estimation of risk in the US population, particularly for cancer
sites which exhibit markedly different baseline rates in the two populations. Reflecting this
uncertainty. EPA has adopted a model for most sites in which the risk coefficients ate a geometric
mean between those obtained using the multiplicative and NIH projection models. In transporting risk
across populations, the multiplicative model presumes that the excess risk will scale with the baseline
cancer rate, whereas the NIH model presumes that the excess risk is fairly independent of differences
in the baseline rate. Viewed from a mechanistic standpoint, the former presumes that radiation risks
act multiplicatively with the other risks for cancer, while the latter presumes that the interaction is
roughly additive.
For the purpose of this analysis, the NIH and multiplicative projections will be used as
uncertainty bounds on the component of uncertainty associated with transporting the risk. In view of
pefT
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the lack of information on bow radiation interacts with other factors affecting carcinogenesis, the
distribution between these two bounds will be taken to be uniform on a Iqgarithmic scale.
D. Low Dose (Dose Rate) Extrapolation
Section to be added.
E. Errors in Dosimetry
Random errors in the individual dose estimates for the atomic bomb survivor population has
been estimated at 25-45% (Jablon 1971, Pierce et al. 1990, Pierce and Vaeth 1991). The net result
of such errors is to overestimate the average dose in the high dose groups (Pierce and Vaeth 1991).
As a result, for a linear fit to the data, the slope of the dose response will be biased low by roughly
10% (Pierce et al. 1990). More significant perhaps, the shape of the dose response will be distorted
towards a convex (downward) curvature; hence, a true linear-quadratic dependence may be distorted
to look linear (Pierce and Vaeth 1991). This possible distortion has been discussed in Section II.B.
and has already been factored into the uncertainty analysis in Section D above.
Measurements of neutron activation products indicate that DS86 may seriously underestimate
neutron doses for Hiroshima survivors, the relative magnitude of the error increasing with distance
from the epicenter (Straume et al. 1992). Using tentative estimates of neutron flux derived by
Straume et al., and assuming a neutron RBE of 20, EPA staff (Geduldig and Puskin, unpublished
results) have calculated that the gamma ray risk estimate may be reduced by about 30% to 50%,
A53T"
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depending on organ; alternatively, if a neutron RfiE of 10 is assumed for total doses of about 100 rad
or more, the reduction in gamma ray risk estimate will be only half as great.
To account for the uncertainty in risk associated with errors in dose estimation, the risk will be
multiplied by a random variable uniformly distributed, on a logarithmic scale, in the interval 0.5-1.1.
F. Uncertainty in Alpha Particle RBE
The NCRP has recently reviewed the laboratory data bearing on the issue of RBE's for high-
LET radiation (NCRP 1990). From an examination of the data on internal emitters, the NCRP
commmittee concludes that: "The effectiveness of alpha emitters is high, relative to beta emitters,
being in the range of 15 to 50 times as effective for the induction of bone sarcomas, liver
chromosome aberrations, and lung cancers. The RBE of alpha emitters tends to increase as the dose
decreases, probably mainly due to the decreased effectiveness per Gy of low LET radiation at low
doses and low dose rates." Also relevant are the findings on external exposures to fission neutrons,
which, because of their comparable LET, are expected to have an RBE similar to that for alpha
particles. For neutrons, a wide range of RBE's have been observed, but if one considers only the
most relevant data on tumorogenesis, the range is about 6 to 60.
Because there is a dearth of cancer sites for which one has detailed epidemiological data
relating to both high and low LET exposures, one cannot generally base estimam of alpha particle
RBE on human data. One apparent exception is leukemia. As discussed elsewhere, the risk of
leukemia induced by internally deposited radium appears to be much lower than what one would
calculate based on low-LET epidemiological data and an RBE of 20. Possibly, the discrepancy can
A$*9-
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be explained in terms of an error in estimating the alpha particle dose to sensitive cells in the bone
marrow. For purposes of our risk assessments, we have treated this as a special case, basing our
high-LET leukemia risk estimates directly on high-LET epidemiological data.
Another exception is the lung, for which there are low-LET data from the AJBSS and high-LET
data on radon exposed underground miners. The latter pertains almost entirely to adult male
exposures. For adult males, the two sets of data are reasonably consistent with an RBE of roughly
10. However, childhood and female exposures among the bomb survivors appear to be associated
with higher relative risks than those for adult males. This is in sharp contrast with the BEIR IV/EPA
radon risk model', which posits no dependence on sex or age at exposure. In conclusion, one cannot,
at this time, properly assess whether or not a single model can be used for calculating the risk of both
low-LET and high-LET (radon) exposures. Unless such a model gains acceptance, one cannot use the
epidemiological data to assign a single RBE value to lung cancer induction.
EPA is generally interested in low dose, low dose rate conditions. Under these conditions, the
low-LET risk is presumed to be reduced by a DDREF, and the alpha particle RBE is increased by
this same factor. The DDREF of 2 adopted here is somewhat lower than what is often observed in
animal experiments. It follows that the RBE's measured determined from low dose extrapolation of
experimental data may be higher than what one might find for humans. Taking this consideration into
account, for solid tumor induction, we assign to the RBE an uncertainty range of 5 to 40 (90%
confidence interval). Within this range the uncertainty is assumed to be distributed lognormally
around the geometric mean of the upper and lower confidence bounds.
For leukemia, the probability distribution for the "RBE" is taken to be uniform (on an
arithmetic scale) in the interval
A>ttf
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ft-2. In part, this distribution reflects uncertainty over the dosimetry-of alpha-emitting bone seekers
and is not meant to imply that high-LET radiation may be inherently less damaging to bone cells than
low-LET radiation.
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