Occurrence Estimation Methodology and Occurrence Findings Report for the Six-Year Review of Existing National Primary Drinking Water Regulations



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                      Occurrence Estimation
                        Methodology and
                   Occurrence Findings Report
                    for the Six-Ye§  R       of
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Off ice of Water
Office of Ground Water and Drinking Water (4607M)
EPA815-D-02-005
www.epa.gov/safewater     *',
March 2002
                                         Printed on Recycled Paper

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                               Disclaimer

  This report is issued in support of the preliminary revise/not revise
  decisions for the Six-Year Review Notice of Intent. It is intended for
  public comment and does not represent final agency policy. EPA expects
  to issue a final version of this report with the publication of the     "  ?
  final notice in 2002, reflecting corrections due to public comment on
  the preliminary notice and the supporting documents, >,
                                                ^ /

  Mention of trade names or commercial products does not constitute
  endorsement or recommendation for use.               ,   ,
Occurrence Estimation Methodology
March 2002

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ACKNOWLEDGMENTS
The compilation and analysis of the data summarized in this report were undertaken by EPA's Office of
Ground Water and Drinking Water (OGWDW) in support of the Six-Year Review of National Primary
Drinking Water Regulations. This effort was directed by Mr. Peter Lassovszky and Dr. Andrew Shulman
ofOGWDW.

We would like to thank the many States and State staff who contributed data sets and valuable advice.
Thank you also to the many public water systems and their staffs who conducted the compliance
monitoring that provided the extensive amount of contaminant occurrence data used in this report.
External expert reviewers also provided constructive comments on earlier drafts of the statistical
methodology used for the contaminant occurrence estimations, ^ •- y; > " \ ";'
EPA also appreciates the technical support provided by The Cadmus Group, Inc., the prime contractor for
this project. Dr. Jonathan Koplos and Dr. George Hallberg served as Cadmus Project Managers in the
provision of support for data management, data quality assurrancexand quality control, statistical model
development and validation, contaminant occurrence analysis, anctteport development. The major
contributions of Dr. Song Qian (in statistical model development and validation), Alison Kotros, and Erin
Hartigan are gratefully acknowledged. -' ^
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                                  TABLE OF CONTENTS

 ACKNOWLEDGMENTS	iii

 TABLES AND FIGURES	,.	v

 APPENDICES	,	vii

 ABBREVIATIONS  	.;	,„.,	viii
                                                                         / /
 EXECUTIVE SUMMARY	'...I..?/.	'.... x

 I.  INTRODUCTION	/	,1
        LA.     Purpose and Scope	'•>-/•	 1
        I.B.     Sources of Data Used for Analysis  	•«„ ,' ,^ ...... „„ .. . 1
        I.C.     Data Analysis	,.:	".	~ . . 2

 II.   DEVELOPING A NATIONAL CROSS-SECTION OF STATES	 2
        II.A.  Pollution Potential Indicators	,. .,	 3
              II.A.l.  Manufacturing Indicators	 3
              II.A.2.  Agricultural Indicators  	 4
        II.B.  Representativeness of the Selected State Data Sets  .....		 5

 III.  INITIAL EIGHT STATE DATA SETS ....;f.	 8
        III.A.  Description of Data	&•'	„	 8
        III.B.  Data Management... 1	 9
        III.C.  Data Quality Issues	fv	I	-~	 10
              III.C.l.  Other Data Use aiid Editing Issues../',..	 11

 IV.  STAGE 1 ANALYSIS	....	....	 12
        IV.A.  Summary of Contaminant Occurrence Ranking Findings	  	 13
        IV.B. Comparison of State Data andURCIS Stage'l Findings	 16

 V.  FULL SIXTEEN STATE DATA SETS AND CROSS-SECTION	 18
        V.A.  Data Use and Editing .;. v	 22
        V.B.  Comparison of 8-State vs. 16-,State National Cross-Sections	 23

 VI.  STAGE 2 ANALYSIS .-...	,	  26
       VI.Ar  Preparation of State Data; for the Stage 2 Analysis	'...  26
       VLB. Previous Occurrence Estimation Methods	  29
       VI.C. General Description of Bayesian Statistics	  30
       VI.D.  Estimating System Mean Concentrations	  31
       VLB.  Estimation of Probabilities of Threshold Exceedance	  32
       VI.F.   Credible Intervals	  32
       VI.G. Using.the Occurrence Probability Estimates to Obtain National Occurrence Estimates
               :.'-• •••'•	  33
       VI.H;  Summary of Occurrence Estimations 	  34
       VLI.   Stage 2 Model Verification  	"...'.'.'.'.'.'.  39
      . VIJ.   Stage 2 Model Validation	..41
             VI.J.I.  Centers for Disease Control and Prevention Fluoridation Census	41
             VI.J.2.  SDWIS Comparison	."	44

VII.  CONCLUSION	  46

References	        48
Occurrence Estimation Methodology
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TABLES AND FIGURES
Table II.B.l. Initial Eight Cross-Section States with Ranking of Pollution Potential Indicators 6

Figure II.B.2. Distribution of State Rankings of Manufacturing Establishments/ Sq. Mile vs.Farm Ag.
Chemical Expenses (Cross-Section States Highlighted) ^ 7

Figure II.B.3. Map of the Initial 8 Cross-Section States 8

Table III.A.1. Initial 8 State Data Sets Used for Analyses 9

Table IV.A.1. Stage 1 Analysis - High Occurrence Contaminants Ranked by MCL for All (Combined)
Surface Water and Ground Water Systems in the Eight Cross-Section States". t -'13
f ~*HT ~ C*~~
Table IV.A.2. Stage 1 Analysis - Low Occurrence Contaminants Ranked by MRL for All (Combined)
Surface Water and Ground Water Systems in the Eight^Cross-Section States 14

Table V.I. Additional State Data Sets Used for Analyses .,.'...':.".. ,\<, 19
•~ / / *.

Table V.2. National Cross-Section States with Ranking of pollution Potential Indicators 20

Figure V.2. Distribution of State Ranking for Manufacturing Establishments/Sq. Mile vs. Farm Ag.
Chemical Expenses (Highlighting Initia| 8 & Additional 8 Cross-Section States) 21
-/•".* j '*"
Figure V.3. Map of the 16 Cross-Section Stales "'. '*,,.* 22

Table V.B.1. Comparison of Stage 1 Analyses for 8-State vs. 16-State National Cross-Sections Based on
the Percent of Systems .. .^,., ;. 23

Table V.B.2. Comparison of Stage 1 Analyses'ibr S-State.vs. 16-State National Cross-Sections Based on
the,Percent of Population Served by Systems 25
** _ L. I S ^
Table VI.A'.l. Contaminant Occurrence Data From the 16-State Cross-Section Used in Stage 2 Analysis
.*..:;...> :\...,. 28
H-"sy " >
Table VI.G.l. Calculating National Estimates of Exceedance 33
Table VLH.1. Comparison o~f Aggregate Stage 1 and Stage 2 Analytical Results Based on the 16-State
National Cross-Section - Percent of Systems and Population Served by Systems Greater than the MCL
"- ;./.':-.' 35

Table VI.H.2. Best Estimate and Range of the Number of Systems Exceeding the MCL in the 16 Cross-
~| * Section StatesaifdNationally 36
, > *'<• \ * . •
Table VT.Hj3. Best Estimate and Range of the Population-Served by Systems Exceeding the MCL in the
^Cross-Section States and Nationally • 38

Table VI.I.1. Stage 2 Comparison of Top Quartile and Bottom Quartile States' Mean Concentration
Values , 39

Table VI. J. 1 .a. Comparison of the National Extrapolations of the Stage 2 Modeled Estimates with the
CDC Fluoridation Census Findings * 42
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 Table VLJ.l.b. Distribution of Fluoridating Systems in the 16 Cross-Section States and the CDC
        Fluoridation Census 1992	 43

 Table VIJ.2.a. Preliminary Comparison of Stage 2 Analytical Findings and SDWIS MCL "Violation
        Information	 46
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                                      APPENDICES


APPENDIX A. Stage 1 Analytical Findings

APPENDIX B. Detailed Description of Bayesian-Based Hierarchical Model
              (Stage 2 Analytical Approach)

APPENDIX C. Stage 2 Analytical Findings

APPENDIX D. Model Bounding Analysis
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                                     ABBREVIATIONS



 l,2-Dibromo-3-chloropropane (DBCP)



 Chemical Abstract Services (CAS)



 Chemical Monitoring Reform (CMR)



 Community Water System (CWS)



 Cumulative Density Function (CDF)



 Environmental Protection Agency (EPA)



 Ethylene Dibromide (EDB)



 File Transfer Protocol (FTP)



 Ground Water (GW)



 Ground Water - Purchased (GWP)



 Ground Water Under Direct Influence (GUDI)  ,



 Ground Water Under Direct Influence - Purchased (GUP)



 Inorganic Chemical (IOC)



 Maximum Contaminant Level (MCL)



 micrograms per liter (ug/L)                     K



 milligrams per liter (mg/L)                   .  -



 Minimum Reporting Level (MRL)



 National Contaminant Occurrence Database (NCOD)



 National Primary Drinking Water Regulations (NPDWRs)



 National Water Quality Assessment Program (NAWQA)



 Non-Transient Non-Community Water System (NTNCWS)



 Office of Ground Water and Drinking Water (OGWDW)



 Percentage of Systems with Exceedances (>MCL)



 Percentage of Systems with Detections (>MRL)



Public Water System (PWS)



Public Water System Identifier (PWSID)
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Safe Drinking Water Act (SDWA)



Safe Drinking Water Information System (SDWIS)




Surface Water (SW)



Surface Water - Purchased (SWP)



Synthetic Organic Chemical (SOC)



Toxics Release Inventory (TRI)



Transient Non-Community Water System (TNCWS)



United States Geological Survey (USGS)



Unregulated Contaminant Information System (URCIS)




Unregulated Contaminant Monitoring Regulation (UCMR)



Volatile Organic Chemical (VOC)
Occurrence Estimation Methodology
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                                    EXECUTIVE SUMMARY
 The 1996 Amendments to the Safe Drinking Water Act require that EPA shall, not less often than every
 six years, review and revise, as appropriate, each national primary drinking water regulation promulgated
 by the Agency.  This report presents an overview of the contaminant occurrence data, data management,
 and statistical methods used to develop national contaminant occurrence estimations generated in support
 of EPA's Six-Year Review of National Primary Drinking Water Regulations. Using the data and
 methods described, estimations of national occurrence and preliminary assessments of exposure are
 derived, evaluated and presented.

 The contaminant occurrence data used are public water system compliance monitoring results reported ta
 and contained in State data sets. A data management approach, consisting of the development of a 16,f
 State cross-section, enables statistical estimations that are indicative of national occurrence of
 contaminants in public drinking water systems. The Safe Drinking Water Act compliance monitoring
 data in the 16-State national cross-section represent more than 13 million analytical results from
 approximately 41,000 public water systems.  Although the 16-State national cross-section is not, in a
 formal sense, statistically representative, the analyses based on the cross^section does indicate a central
 tendency of contaminant occurrence.

 A two stage analytical approach has been developed for this evaluation of the national occurrence of
 regulated contaminants.  The first stage of analysis, referred to as the "Stage 1 analysis," provides a
 straight-forward evaluation of occurrence for all regulated contaminants.  In this Stage 1  analysis, the
 data sources, data quality, and data characteristics were assessed, and the data were used to conduct
 simple and conservative non-parametric assessments for a broad evaluation of contaminant occurrence.

 The subsequent "Stage 2 analysis" is a more  rigorous parametric statistical estimation based on
 probabilistic modeling. The Stage 2 analyses enables estimations of the national number of public
 drinking water systems, and the population served by those systems, that have an estimated mean
 concentration (of a particular subject contaminant) that exceeds a specified threshold concentration of
 interest. The Stage 2 analyses yield detailed, stratifjed-(assessed according to source water type and
 system size) occurrence estimations using a B4yes&n-based hierarchical model estimation method.  This
 method provides estimates of numbers of systemsfand population served by those systems, with system
 mean concentrations exceeding specified contaminant threshold concentrations, and includes quantified
 error for the estimation procedures.

 In the  process of developing this two stage analytical approach for the Six-Year Review, the full
 approach was peer-reviewed, assessed relative to another significant drinking water contaminant
 occurrence estimation method, and evaluated with synthetic (simulated) data sets designed to assess the
 log-normal and constant variance  assumptions made at the system level regarding the national
 distribution of system means. Assessments suggest the Bayesian-based hierarchical model and the 16-
 State national cross-section of compliance'monitoring data used for the Six-"Year Review occurrence
 estimations are appropriate.
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I.   INTRODUCTION

This report presents a detailed review of the contaminant occurrence data used and the statistical methods
developed to estimate regulated contaminant occurrence in public drinking water systems. These
regulated contaminant occurrence estimates are generated in support of the Environmental Protection
Agency's Six-Year Review of National Primary Drinking Water Regulations (NPDWRs). This "Six-
Year Review" assesses the potential revision of regulations for regulated contaminants. The contaminant
occurrence data used for the Six-Year Review's statistical estimations are Safe Drinkingjpfer Act
(SDWA) compliance monitoring data (documenting occurrence of regulated contaminants in public
drinking water systems).  Using the data and statistical methods described, estimations of national
occurrence and preliminary assessments of exposure are derived, evaluated, described and presented.
                                                                        - -    «
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  I.C.
Data Analysis
 A two stage analytical approach has been developed for this evaluation of the national occurrence of
 regulated contaminants. The first stage ("Stage 1") analysis provides a straight-forward evaluation of
 occurrence for all regulated contaminants. In. the Stage 1 analysis, the compliance monitoring analytical
 results data for all regulated contaminants for the cross-section states were compiled in contaminant-
 specific data sets. (The quality of these data were assessed in extensive and comprehensive detail.) Then,
 for each contaminant, these analytical occurrence data were used to simply count the percent of public
 water systems that recorded at least one analytical result that exceeds a specified threshold'
 concentration. With these results, general assessments such as relative rankings of the contaminants'
 occurrence provides a broad characterization of contaminant occurrence. The Stage-1 analyses generate
 occurrence estimates that are clear and easy to understand, were developed through rudimentary
 analytical techniques, and provide conservative estimates of occurrence. (Stage 1 analysis methods are;:
 described in more detail in below in Section IV.)

 In part based on the findings of the Stage  1 analysis, EPA selected a set of contaminants for which more
 rigorous parametric statistical estimations, the Stage 2 analyses, were warranted as a next step.  In the
 Stage 2 approach, estimates can be made for the number of pwblie drinking water systems nationally and
 the population served by those systems, that are expected to have a particular mean contaminant
 concentration present at levels exceeding any specified threshold (or thresholds) of concern to EPA.  The
 Stage 2 analyses yield detailed, stratified occurrence estimations, employ a  Bayesian-based hierarchical
 model estimation method, provide estimates of numbers of systems and population served by those
 systems with system mean concentrations exceeding specified contaminant threshold concentrations, and
 include quantified error for the estimation procedures. (The Stage 2 analysis is described in more detail
 below in Section VI.)


 H.  DEVELOPING A NATIONAL GROSS-SECT ION OF STATES

 Currently, there is no complete analytical record of contaminants in drinking water from public water
 systems collected under SDWA mat can be processed for a comprehensive national overview of
 occurrence and exposure.  EPA's Safe Drinking Water Information System (SDWIS) maintains a variety
 of water system inventory and operation information^ as well as compliance program information.  For
 most contaminants, the only analytical results filed in SDWIS are those related to violations of a
 Maximum Contaminant Level (MCL). The analytical results from monitoring of the Phase rule
 chemicals, and most other contaminants, are stored in individual State databases. In the past, there has
 been no feasible way to access these data to construct a national sample except through  analyzing data
 sets from the individual States.

 EPA previously completed a study reviewing the occurrence of regulated contaminants in public drinking
 water systems using  data sets voluntarily provided by eight States. These data used in the development
 of an initial analysis  of a national cross-section of contaminant occurrence.  The results of this prior
 work, and the report  generated (A Review of Contaminant Occurrence in Public Water Systems, EPA
 #816-R-99-006, referred to as the "CMR Report"), have been widely reviewed by EPA stakeholders and
 were also peer-reviewed. This report and study approach have generated wide and very positive support
 by stakeholders and peer-reviewers alike.

 Data sets from eight States were selected for a detailed national cross-section analysis in the CMR
 Report. For the analyses in the CMR Report, eight States were selected for use in a national analysis as
 providing the best data quality and completeness, and for providing a balanced national cross-section of
 occurrence data using a relative ranking of States based on pollution potential and geographic coverage.
 The data sets from these same eight States provide the basis for analyses conducted for this current
report. Described in the following sections are the evaluations and procedure used in selecting the eight
 initial cross-section States that together provide contaminant occurrence data compiled to be indicative
(representative) of contaminant occurrence nationally.
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II.A.  Pollution Potential Indicators                    .

Many past EPA and USGS studies have shown that some simple measures, such as population (or
population density) are closely associated with pollution1. This is intuitively (as well as empirically)
apparent, since it is human activity and its related land use -be it manufacturing or agriculture- that is the
source of most pollutants, particularly the organic chemicals.  In the CMR Report, various demographic
and other factors were evaluated as independent measures or indicators of pollution potential.

More than thirty-five different factors are potentially useful as indicators of each State 'sjgjollution
potential were considered for the CMR analyses.  The factors ranged from Census data on
manufacturing, agriculture, and population density, to indices such as EPA's Section 106 allocation
factors or the 1991-1992 Green Index: A  State by State Guide to the Nation"? Environmental Health
(prepared by the Institute for Southern Studies) (Hall and Kerr,'l993). Two methods -were considered for
evaluating the States' comparable pollution potential. The firsfwas the development of a singular
numerical index, incorporating factors such as manufacturing in the StateJ total pounds of chemicajs ,
released, and pesticides used, into a comprehensive ranking for each State. However, such a ranking for
all sources requires various factors to be  weighted, and the meaning of the resultant number can be
difficult to understand, as well as argumentative.

A second, simpler method, evaluating the pollution potential of the States., was adopted for the CMR
analyses. The primary factors used indicated the potential pollution from manufacturing and agriculture
in each State.  States were then ranked from 1 to 50 for each factor.  This method does not, of course,
avoid all of the problems discussed above, but it does provide a.simple, practical evaluation of the range
of pollution potential conditions represented by the States.^ *

In general, manufacturing/industrial activities (typically associated withfpopulation density) are
considered the major sources of many VOCs (degreasers, solvents, petroleum compounds). Most SOCs
are pesticides, and agriculture is the  largedbuser of these compounds.  While lOCs can have various uses
in manufacturing, they also occur natu|^|Jy Ambient concentrations of lOCs also can be enhanced by
mining or other diffuse activities. Njjtipal geologic sources of lOCs were not directly considered in the
assessment for representativeness, jlJpart because whole States needed to be evaluated and such sources
are often localized. However, by including geographic or spatial coverage across the United States as a
factor  (e.g., from New Jersey to Montana), a range ofgeologic conditions (as well as a range of
hydrogeologic tind climatic variability) were inherently included in this cross-section development.

n.A.l.  Manufacturing Indicators  ,,        .

Numerous factorcwere considered as potential  indicators of manufacturing-related pollution, including
EPA's Toxics Release Inventory (TRI) (including total releases, releases per square mile, and releases
excludingldr releases), the number of manufacturing establishments, the number of manufacturing
establishments per square mile, the number of manufacturing employees, the value added by
manufacturers, and the value added per capita.  This  information was taken directly from the 1995
Annual Survey ofMamifacja-es(USDOC, 1997), the 1992 Census of Manufactures (USDOC, 1996), and
the 1995 Toxics Release jfrtventory (USEPA, 2001). All factors  were each considered in terms of their
inherent value as pollution potential indicators, their range  and variance (in providing a relative ranking
of the  States), and their inter-relationships.

The total TRT releases per square mile, number of manufacturing establishments per square mile, and
value added per capita were considered the three most useful indicators. The TRI was considered useful
         For example, the most recent report is Squillace et al, 1999.


        2 Data were analyzed on a Statewide basis so any determination of representativeness was based on whether the States, for which
information was available, were representative of the nation as a whole. There are problems, of course, with using States (large, diverse entities)
to determine representativeness; however, it was not practical to break the data down any further.


Occurrence Estimation Methodology                    3                                       March 2002
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 because it is a measure of how many pounds of toxic chemicals are released within the State.  While
 there are problems with the TRI (e.g., some inconsistent release estimation techniques; omission of many
 small establishments, or those with releases below specified thresholds), it is valid to use as a direct
 indicator of potential pollutants released. The number of manufacturing establishments takes into
 account how many factories are actually engaged in manufacturing and thus how many establishments
 potentially contribute to pollution.  By breaking down the number of manufacturing establishments per
 square mile, the size of the State is also taken into account.  The final factor that was considered to be
 viable was the value added by manufacturers per capita. Initially this seemed to be a well-suited measure
 because of the presumed correlation between value added and the level of production (anjfiiy-product
 pollution) within the State. The problem with this measure (and also with the measure of number of
 manufacturing establishments per square mile), is that it does not take into account the Variation in
 pollution released by different industries. For example, an industry that adds a lot of value to a product
 may cause little pollution while another industry that does not add much value may contribute more
 pollution.                                                              """""  ,, '  ,~~

 The data clearly showed a close correlation between the number of manufacturing establishments per
 square mile and the population density in each State, as well as a clear finear association with the total
 TRI pounds released/square mile, number of manufacturing employees, and total value added  Hence,
 the number of manufacturing establishments per square mile was used as the primary indicator because it
 is a simple measure of how many establishments are actually engaged in manufacturing and thus are
 potentially polluting sources of drinking water. The TRI total pounds released per square mile was used
 as a secondary factor in determining representativeness.. Squillace et al. (199,9) found a significant
 correlation between VOC occurrence in ambient ground water and population, density in a USGS
 national NAWQA study. As noted,  population density, and manufacturing density are highly correlated.
 Manufacturing density and TRI data were used in this ranking because they were considered more direct
 measures of pollution potential for this study./-;-

 H.A.2.  Agricultural Indicators

 There is no complete measure of pesticide usage by States that is readily available. Thus, a variety of
 factors were considered to assess potential organip chemical pollution from agriculture in each State.
 These included the percent of the State's population;?th|ps classified as rural, the percent of land in the
 State that is crop land, the percent of land that is grassland pasture and rangeland (a possible inverse
 indicator), and total farm agricultural chemical expenses. Like the manufacturing factors, these
 agricultural variables were considered in terms of their value in indicating potential sources of pollution
 and were plotted against one another to determine how closely they are correlated.

 Of these factors, total farm agricultural chemical expenses was considered to be the best  indicator of
 potential pollution. The percent of the State's population that lives in rural areas does not necessarily
 relate to agricultural chemical use or crop land. There is, of course, a correlation between crop land and
 agricultural chemical use. However, there are notable exceptions such as Florida and California which
 use a large amount of agricultural chemicals despite having more limited crop land area.  While there are
 some incomplete surveys of pesticide use, the 1992 Census of Agriculture (USDOC, 1994) measure of
 dollars spent on  agricultural chemicals was a more consistent and complete measure.

 In summary, three specific measures were selected as reasonable indicators of pollution potential. These
 measures, the number of manufacturing facilities per square mile (to reflect the range of potential VOC
 occurrence), total expenditures on farm agricultural chemicals (to reflect the range of potential SOC
 occurrence), and Toxics Release Inventory (TRI) releases (in total pounds) per square mile (to reflect the
releases of any type of chemical into the environment) were used to assess the pollution potential
characteristics of the States. Additionally, in the development of a nationally representative group of
States (discussed in the following section), a geographic distribution of States is also considered (to
reflect the range of hydrologic and climatic conditions, and geologically-influenced, potential IOC
occurrence).
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n.B.   Representativeness of the Selected State Data Sets

Most of the data used in this review were provided voluntarily by States. Obviously, constructing a
"representative" sample from such data can be problematic, so additional data were requested from a few
States to broaden the spatial coverage of the analysis. In all, 14 States originally provided data for
review. While 14 of 50 States is a substantial sample, it is not necessarily representative. While the data
from all these 14 States could have simply been aggregated to compute a composite occurrence value for
a contaminant, the resulting group of States would have significantly over-represented Midwestern
"Cornbelt" States.  (The sample would contain Kansas, Missouri, Iowa, Illinois, Indiana, and Ohio,
accounting for over 40% of the 14 States represented. These six cornbelt States use a relatively large
amount of row-crop herbicides relative to non-agricultural States, so for the .group of,14 States the
resulting "pollution potentiaP'for agricultural chemicals would be'bver-represented). Hence, various
means were evaluated to enable the construction of a grouping of'the available State data sets that would
provide a reasonable first view of national occurrence based on a representative cross-section of States.
                                '..                                    -V           '
As described in the previous section, two broad factors were^considered in the assessment of a nationally
representative compilation of State data sets:  geographic or spatial diversity, and pollution potential.
Consideration of States that collectively provide a geographic diversity was one means by which to
include contaminant occurrence data from the wide, and national., range of climatic and hydrologic
conditions across the United States. The representative group of State data sets was also selected to
represent the range of pollution potential (reflecting the likely range'ofMglt, medium, and low
contaminant occurrence) across the various regions and States of the United States,
                                                    / i                 "'  *
The 50 States' pollution potential indicators (described above) were ranked from highest to lowest.
These ranked lists of States were then divided into four qiiartiles'. The rankings were reviewed to assess
if States could be selected in approximate balance from each quarfile/~The primary ranking indicator was
the number of manufacturing establishmen^per squar^mile, but total farm agricultural expenditures and
TR1 releases were also considered to contifpute furthjf to insuring that the occurrence data from the
selected States were, collectively, reprjleiitative or indicative of national occurrence. This cross-section
selection process was used to selectthe  initial 8 State cross-section, and the compliance monitoring data
from these initial 8 cross-section States provides a broad distribution geographically and across the
pollution potential rankings.     -              ')t    "'

The quartile division of thelStates selected to approximate the national cross-section are summarized in
Table ILB.L/Ttfe compliance monitoring contaminant occurrence data from these eight States
collectively provided-balanced cross-section, based on relative rankings for pollution potential (i.e., the
potential for contaminant occurrence)3geographic coverage, and data quality and completeness.  The
eight initial cross^section States represent over 25% of the U.S.  population using PWSs, and over 20%
of the PWSs nationally. „ ^
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 Table II.B.1.  Initial Eight Cross-Section States with Ranking of Pollution Potential Indicators
Quartiles
for Rank-Order of
AH States Based on
Manufacturing Ranking
1
2
' 3
4
Initial Eight
States in
National Cross-
Section
NJ
IL
CA
MI
AL
OR
NM
MT
_» „ ** ,. *~ ' *, ' "*
f '~~ National Ranking of ^ - 4,0^-"^ '
Pollution l*otential Indicators ' , " ' ~"
Manufacturing*
s'
2
10
11
13
25
34
44
48
/v
^AgrUmttiur^
•* >54N
37
2
*:':/h 1
IS
26
22
40
34
1 -* * "
^ TRlRaiaV "
•-^ * J «
8x
11
38
16
7
39
40
34
 1) the number of manufacturing facilities per square mile, 2)' total expenditures on farm agricultural chemicals, and 3) "Bxics Release Inventory
 (TR1) releases (in total pounds) per square mile. For more detailed de'scription of thedevelopment of the national cross-section and of the
 rankings, sec .4 Review ofContaminanl Occurrence in Public Wat/r'Systems (EgA., 1999; EPA #816-R-99-006).
 Different presentations of the pollution potential rankings, distribution and representative nature of the
 States used in the occurrence analyses are illustrated in Figures ,11.6.2 and II.B.3. The dual assessment of
 manufacturing and agriculture pollution potential indicators shown in Figure II.B.2. illustrate the
 balanced distribution of the 8 cross-section States across the fpur quartiles of both of those indicators.
 The map presented in Figure II.B.3 shows the geographic  distribution of the cross-section  States. The
 distribution across pollution potential quartiles (Figure ILB. 2) and geographically (Figure  II.B.3)
 suggests that the cross-section States should provide a representative indication of the potential range and
 occurrence of VOC,  SOC, and IOC contamination in PWSs nationally.
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March 2002
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Figure ELB.2. Distribution of State Rankings of Manufacturing Establishments/ Sq. Mile vs.
FarmAg.  Chemical Expenses (Cross-Section States Highlighted)

                        Ranking of the No. of Manufacturing Establishments/ Sq. Mile
LOW ' TC
GA-
IL -










MI -


OR -


AL -






MT -


NJ -

KM -










1















25






















50





O


0




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o
o







•




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o
0
c


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o

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o

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o

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•


o



o.

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o






5 raa






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ft


o

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o





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-LOW
50 25 1
MT MM OR AL MI CA IL NJ
^ Cross-Section States
o All Other States
                                                                                   £.
                                                                                   CL<


                                                                                   i2
Occurrence Estimation Methodology
March 2002
-------
 Figure H.B.3. Map of the Initial 8 Cross-Section States
                                                         F^t Wtial 8-SWe CJoss-Section
                                                         I  I States, notifldu&dm doss-Section
 The data from these eight cross-section States were used to compute aggregate occurrence values (i.e.,
 the percentage of water systems that had a detection of contaminant X) as an approximation of national
 occurrence. While the data from the cross-section States cannot be stated to be "statistically
 representative," their distribution should provide a clear indication of central tendency.


 m.   INITIAL EIGHT STATE DATA SETS

 The group of eight State data sets used for analysis in this report reflects a national cross-section of
 States that is indicative (though not strictly statistically representative) of national contaminant
 occurrence. Table 111.A.I provides a general description of monitoring data provided by these eight
 States (number of records, time period of data^ etc.).  Details describing general data quality are
 discussed in Sections III.A., III.B., and III.C.

 III.A.  Description of Data

 The initial eight State data sets are comprised of SDWA compliance monitoring data from public
 drinking water systems. As summarized in Table III.A.1, these data represent approximately 10 million .
 analytical results from nearly 22,000 public water systems. In most cases, the initial State data sets
 contained additional data that were not included in analyses either because they were not appropriate or
 because they posed various data quality problems (e.g., invalid PWSID or contaminant codes, missing
 significant data elements such as source water type or system type) that prevented analysis of adequate
 quality, specificity, or accuracy.

Various State data sets included data from  different time periods (see Table III.A.1).  However, the
majority of data are from 1993 and later (which coincides with the beginning of Phase II/V monitoring).
Initial screening of the data showed that most data quality problems were in pre-1993 data. Therefore, in
some of the data sets, results gathered before 1993 were eliminated from these analyses. More than 80%
of all data utilized in this report are from 1993 or later; this proportion is even greater for most synthetic
organic chemicals (SOCs). More than 92% of all data used for this analysis are from 1990 or later.
Occurrence Estimation Methodology
March 2002
-------
Therefore, only about 8% of the total records are for years prior to 1990. Beyond these generalities,
though, the amount of problematic data was quite small in the State data sets selected for use in the cross-
section, and there was no apparent or particular systemic data problem. Therefore, all data collected
prior to 1993 used for this analysis that met the necessary data quality conditions for this analysis were
retained.  Based on these considerations, we felt that retaining these results would not compromise the
consistency of the data.

The State data sets represent State primacy agency SDWA monitoring results as provided by the States.
The data represent the analytical results for Non-Purchased Community Water Systems Jpf'Ss) and
Non-Purchased Non-Transient Non-Community Water Systems (NTNCWSs) mat  are required to monitor
for the Phase II/V chemicals. Some States included data from Transient Non:e 'J*4&fi."?}**"/"-0' -^ 	 ~.~".v.,~~
i i ** ~" " w
-708,569
/'' 3,89?,'362
2,967,946
„ 685,721 /
,r 276,675
980S915
266,262
'" ' 169,521
9,952,971
Air*"^," t£
s-j-'i v ;' " ~£r
-m^ft&rvy^fs
* /Jlepresenjtwl "^ ,.
" - 731- "
6,414
- 1,392
3,252
1,786
4,503
1,299
2,345
21,722
•> v-.*- *
* * - 
-------
 For the most part, the States that volunteered data did not reorganize or reformat data, but simply
 transmitted the data in whatever manner was easiest. Data were transferred using three main media: file
 transfer protocol (FTP), e-mail, and diskettes (including zip-disks or CD-ROM). These transfers were of
 very large databases, often several megabytes in size, and transmission was often complicated. The data
 were received in a number of file types, including spreadsheet, database, and image files. Many of the
 data sets were received "as is" and had not been formatted by the State in any way.  For example, while
 the Phase II/V compliance data from 1993-1995 were of greatest interest, in many cases it was easier for
 the State to simply transmit their entire data set, which generally contained information on all chemical
 contaminants (in addition to the Phase II/V), over a greater span of years.              .

 After receipt, an initial review of the information in each data set was performed. Each data set was
 unique in format, layout, custom codes, and data element usage. In most cases, the data were not
 accompanied by a protocol outlining each variable. In every instance, follow-up with a State contact was
 necessary to decipher variable headings or contaminant codes,  When all variables were understood, a
 formatting plan was developed for the data.  Nearly all of the data sets required some type of formatting
 to facilitate analysis. Data formatting problems varied from one data set to another.

 All statistical analyses were conducted in SAS® statistical software. Data formatting problems were
 corrected in Microsoft® Excel with the aid of specialized programs written in Visual Basic® or were
 corrected directly in SAS® before the analysis began3. Data management and formatting was the most
 time consuming and labor intensive part of the data analysis: Each data'set presented unique challenges.
 While analysis of the data was consistent from one data set to another, each data set required some
 unique editing and filtering because of differences among basic data elements.

 IILC.   Data Quality Issues

 There are numerous data quality issues inherent to a study where very large data sets of differing format
 and quality are assembled from many States to be used to characterize contaminant occurrence in the
 nation's public water systems. The quality and dependability o|the data used in the contaminant
 occurrence analyses directly affect the quality andjxiependabjlit^ of the results of the analyses conducted.
 Therefore, many of the data quality issues are reviewed in detail below as a preface to understanding the
 analytical results and the processes required before theSanalytical results could be generated.

 This study only used data from State primacy agencies-official data from the regulated drinking water
 program. All such analytical results are-generated by laboratories that are certified for drinking water
 programs, which assumes the use of various quality-assurance and quality control procedures. Certainly
 data problems exist, but efforts have been taken to reduce the problems and increase the dependability
 and quality of the State occurrence data used in these analyses.

 Every State data set reviewed^ for this study contained unique data elements or unique treatment of
 common elements. Even after initial screening and conversion to uniform formats and data set structure,
 unique factors were always uncovered during data analysis. Many of the confounding factors were
 resolved only through direct consultation with the States.  As a general rule, when errors or ambiguities
 inivarious data elements could not be resolved, those particular data elements were not included in the
 analyses to avoid problematic results or results based on data of questionable quality.  This data quality
 measure eliminated relatively very few observations (compared to the thousands of analytical results
 included in the data sets).

 Each data set was reviewed to ensure it contained the basic data elements (data fields) necessary to
 conduct a consistent analysis for this study. These elements were reviewed with State (data source)
 contacts both before and after data were received to ensure consistent and appropriate interpretations.
 While the presence of such elements enables the various data sets to be analyzed in a similar manner,
         SAS is a registered trademark of the SAS Institute, Inc. Excel and Visual Basic are trademarks of the Microsoft Corporation.


Occurrence Estimation Methodology                    10                                      March 2002
-------
each also may be used in unique ways by the individual States/sources. A few key issues are summarized
below. For a complete summary of data editing, please refer to the First Stage Occurrence and Exposure
Report for Six-Year Review (Cadmus, 2000).

Any issues within the analytical results data elements affect fundamental data processing procedures
before any statistical processing can even begin. Very few databases contained the Minimum Reporting
Level (MRL) field for a contaminant/method combination.  (The Minimum Reporting Level is the lowest
level that can be reliably achieved within specified limits of precision and accuracy underjputine
laboratory operating conditions.) The actual analytical results generally comprise multiplijfields, and one
critical component in such databases is how analytical results with values that are less than the MRL are
recorded.  The State data sets vary widely in how these "less than the MRL" values (sometimes referred
to as "non-detections" or "no-detects") are recorded. Some record a "<" symbol in Ojie field and then the
actual MRL concentration value in a corresponding field while others simply enter zero in the results
field. Other States record an "ND" (non-detection/no detect) or some other code*and>many indicate a >
mixed usage that required careful editing and attention to detail to correctly resolve., -  ,

System and sample data elements also required some time-consuming editing. Many States data sets
contained no, or only incomplete, source water type and population records. (Both of these'data elements
are essential for these analyses.) When these data elements were not reported, the data  set was  linked
with the Needs Survey sample frame which provided the source water type'and population information
(as linked by common PWSID) for many PWSs. However, information for all^systems could not always
be determined from the Needs Survey.  Observations whose,spurce water type could not be determined
were not included in the analysis.                         },              '
                                                          \
III.C.1.  Other Data Use and Editing Issues

When computing basic occurrence statistics, such as the number or  percent of samples or systems with
detections of a given contaminant, the value (or concentration) of the Minimum Reporting Level (MRL)
can have important consequences.  For example, the lower the MRL, the greater the number of
detections. Multiple MRLs arise because of many reasons. Improvement in analytical methods over
time can result in a lowering of the1 MRL.  Within reason,, MRLs can even vary from laboratory to
laboratory using the same method, can vary with sariipje batch, etc.  There can be more dramatic
variation when different methods are used  for thejsarneicbntaminant.  Within the drinking water program,
methods have,become well standardized so this was not a major issue for this study, particularly for the
SOCs and VOCs, However, the use of multiple MRLs within a State was not uncommon.

Another general data quality issue that can affect a large-scale summary of results is the different
sampling schedules that may be used by different PWSs.  A PWS with a known contaminant problem
usually has. to sample more frequently than a PWS that has never detected the contaminant. Obviously,
the results of a simple computation of the percentage of samples with detections (or other statistics) can
be skewed by the more frequent sampling results reported by the contaminated site. Therefore, this
analysis is focused on occurrence at the system level (rather than on a total sample basis), which avoids
the skewness inherent in the sample data, particularly over the multi-year period covered.

Systems sampling schedules vary, generally ranging from annually to monthly by contaminant. Data are
generally available for one sample monthly per system for lOCs. The range of sampling frequencies for
IOC records for all systems is between  1 and more than 2,000 samples per month. Data are generally
available for three samples per month per system for SOCs.  The range of sampling frequencies for SOC
records for all systems is between 1 and more than 1,600 samples per month.  Data are generally
available for four samples per month per system for VOCs. The range of sampling frequencies for VOC
records for all systems is between 1 and more than 24,000 samples per month. The reduced number of
systems sampling for SOC data, as compared to lOCs and VOCs, may relate to state waivers for
pesticides and herbicides.
Occurrence Estimation Methodology
11
                                       March 2002
-------
 Also, as noted above, the data used in this analysis were limited to only those data with confirmed water
 source and sampling type information. Only standard SD\VA compliance samples were used; "special"
 samples, or "investigation" samples (investigating a contaminant problem that would bias results), or
 samples of unknown type were not used in the analysis.  Various quality control and review checks were
 made of the results, including review by the States providing the data.  Many of the most problematic
 data quality problems encountered occurred with older data (especially, pre-1990 or 1993). In some
 cases, as noted, these were simply eliminated from the analysis.

 All of these data management and editing procedures were performed to make the results as reliable and
 consistent as possible, and to ensure that they clearly were standard SDWA compliance samples. Also,
 elimination of data with inconsistent elements helps to ensure that the analysisls relatively repeatable,'
 for future consideration and applications of the data.
                                                           ' «X ^         V ~ y                    ^

 IV.  STAGE 1 ANALYSIS                                                               ,  f
                                                                    f                    - - j-'^:'""'
 The initial step in estimating the occurrence of regulated contaminants, the Stage 1 analysis, develops
 general occurrence assessments which are more straight-forward"and conservative than the subsequent
 Stage 2 (full probability) analysis. The Stage 1 analyses were conducted according to source water type,
 therefore separately for surface water systems, ground water systems, and then for all (surface and
 ground water) systems combined.  The analyses were also grouped according to general contaminant
 groupings (lOCs, SOCs, and VOCs). Stage  1 analyses were conducted on the compliance monitoring
 data sets from the initial eight cross-section States at the system-level (not sample-level).  The initial
 eight cross-section States, which in aggregate are indicative of national occurrence, are Alabama,
 California, Illinois, Michigan, Montana, New Jersey, NewMekico, and Oregon.

 Stage 1 analysis provides a conservative assessment of occurrence by simply counting (then calculating
 the percentages of) public water systems (and total population served by public water systems) with at
 least one analytical result that exceeds a concentration equal to the MRL, V2 MCL, and the MCL for each
 particular contaminant.  These Stage 1 analyses are essentially based, therefore, on the single maximum
 analytical value recorded at each public water System.  Assessed relative to MCLs, which reflect public
 health considerations for long-term exposure to contaiiMnanis in drinking water, the Stage 1 analysis is
 conservative -cautious regarding public health confceetiisi- in the sense that they are descriptive statistics
 based on peak, rather than long-term mean, concentrations of contaminants.

 Using these findings, the contaminants were then ranked, from highest to lowest, based on the percentage
 of systems with at least one analytical result  greater than the MRL, V2 MCL, and the MCL for each
 particular contaminant.  (These rankings were conducted separately for the percent of systems and for the
 population served by those systems.) There are inherent vulnerability, occurrence pattern, and some
 regulatory .differences between surface water-supplied and ground water-supplied PWSs, so occurrence
 rankings were conducted separately according to source water type, for surface water (SW) systems and
 ground water (GW) systems. Contaminant occurrence rankings were also conducted separately for three
 general contaminant groupings: Inorganic Chemicals (lOCs), Synthetic Organic Chemicals (SOCs), and
 Volatile Organic Chemicals (VOCs). The contaminant group classifications relate partly to the
 contaminants' sources, fate, and transport, to their chemical properties and general methods of laboratory
 analyses, and to regulatory requirements that vary somewhat according to these contaminant groupings.
 For IOC occurrence,rankings, arsenic was not evaluated since it is being evaluated and addressed
 separately through the new arsenic rule. There were too few data to evaluate for asbestos (an IOC),
 nitrate/nitrite (lOCs), and dioxin (an SOC). Therefore, these contaminants were also excluded from all
 occurrence rankings.

The "highest ranking contaminants" were defined as being the contaminants which occur in the highest
percentage of public water systems (based on at least one analytical result) at a concentration greater than
the MCL ("% > MCL"). The "lowest ranking concentrations" were defined as the contaminants which
occur in the lowest percentage of public water systems at any concentration greater than the Minimum
Occurrence Estimation Methodology
12
                                                                                      March 2002
-------
Reporting Level ("% > MRL"). The high to low occurrence rank-ordering list of contaminants was then
divided into quartiles.  The "top quartile contaminants" were the upper 25% of the highest occurrence
contaminants, and the "bottom quartile contaminants" were the lower 25% of the lowest occurrence
contaminants. (It should be noted that the different contaminant groups -IOC, SOC, and VOC- have
different total numbers of contaminants so the respective quartiles contain different numbers of
contaminants.)

These rankings served to develop an overview pattern of high, medium, or low occurrenceijpr each
contaminant,  as well as to identify each contaminant's occurrence relative to the other contaminants.
Similar estimates based on the population served by PWSs provides a "Stage 1" preliminary
characteristic of exposure potential.                                        '**,"

There are additional, more involved statistical methods that can be applied to analyze limited data, such]
as those comprising the cross-section State data sets. However, for these initial  analyses, a simple    f
approach was developed to be clear and repeatable, resulting in aggregate numbers-that could be easily
understood, and that would rank the occurrence of the contaminants, from high  (frequent occurrence at
levels greater than the MCL) to low (infrequent occurrence at any level greater than the MRL).

IVA.  Summary of Contaminant Occurrence Ranking Findings,  "

Table IV.A. 1. lists the Stage 1 analysis "high occurrence" 6ohtaminants, as based on the percent of
systems and population served by all systems (ground and surface) with at least one analytical result
greater than the MCL. The percent systems and percent population "> MCLMndicates the proportion of
all cross-section State  public water supply systems^? population-served by systems with any analytical
results exceeding the concentration value of theJMCL. (Note; This does npt necessarily indicate an MCL
violation.  An MCL violation occurs when tlieMCL is exceeded by the average results from four
consecutive quarterly confirmation samples as required By the priraacy^States.)  Most contaminants
ranked as high occurrence based on the percent systems were also ranked as high occurrence based on
the percent population served. These contaminants are indicate^ in italics in the table.
Table IV.A.l.s.Stage 1 Analysis - High Occurrence Contaminants Ranked by MCL
(Combined)"§prface WaterTand Ground Water Systems in the Eight Cross-Section
                                for AH
                                States
Contaminant
(MCl/iu rag/L)
Percent Contaminant
SMCL (MCL in mg/L)
Percent
Pop. Served
by Systems
>MCL
v ~" > Inorganic Chemicals "
f **~
Fluoride (4.0) i~^
Cadmium (0.005)
Thallium (0.002) ,'
1.41%
0.69%
0.45%
Fluoride (4.0)
Chromium (0.1)
Cadmium (0.005)
7.31%
1.06%
0.54%
/ Synthetic Organic Chemicals b
Bis(2-eihylhexyl)phthatate c (0.006)
I,2~Dibromd,-3-chloropropane (0.0002)
Atrazine (0.003)
Ethylene Dibromide (0.00005)
Undone (0.0002)
Toxaphene (0.004)
2.17%
1.95%
0.94%
0.92%
0.11%
-• 0.09%
Ethylene Dibromide (0.00005)
l,2-Dibromo-3-chloropropane (0.0002)
Bis(2-ethylhexyl)phthalate c (0.006)
Atrazine (0.003)
Undone (0.0002)
PCBs (0.0005)
17.17%
16.07%
2.74%
1.39%
0.86%
0.49%
Occurrence Estimation Methodology
13
March 2002
-------
Contaminant
(MCL in mg/L)
PCBs (0.0005)
Percent
Systems
>MCL
0.08%
Contaminant
(MCL in mg/L)
Endrin (0.002)
Percent
Pop. Served
by Systems
>MCL
0.35%
Volatile Organic Chemicals
Tetrachloroethylene (0.005)
Trichloroethylene (0.005)
Dichloromethaned (0.005)
1,1-Dichloroethylene (0.007)
Carbon Tetrachloride (0.005)
Benzene (0.005)
1.18%
0.94%
0.74%
0.25%
0.24%
0.23%
Tetrachloroethylene (0.005)
Trichloroethylene (0.005)
Dichloromethane? (0.005)
l,2-Dichloroeth;ihe (0.005) •*
1,1-Dichloroethylene (0.007) , .
Carbon Tetrachloride (0.005)
22.24%
21.11%
15.00%
14.09% «
13.59%'!"
12.44%
 a) Too few data to evaluate asbestos. Arsenic was not evaluated, b) 'Bo few data to evaluate dioxin Generally Phase II/V compliance
 monitoring data sets wereused and these contained too few data to evaluate nitrate/nitrite   c) The high occurrences of phthalate are, in part,
 considered false positives related to sample contamination by plastics and laboratory analytical problems  d) The high occurrences of
 dichloromcthane are, in part, considered to be false positives related to laboratory analytical problems.
 Contaminants in italics are in top rank category for both percent system and percent population measures
 Rankings are based on data from the eight cross-section States of AL, CA, IL; MI; MTNJ, NM, and OR,


 Table IV.A.2. lists the Stage 1 analysis "low occurrence" Contaminants, as based on the proportion of all
 cross-section State systems or population-served by systems with at least one analytical result exceeding
 the concentration value of the Minimum Reporting Level (MRL). (Note that the contaminant
 concentration value of a minimum reporting level is a characteristic of the analytical method employed to
 conduct the laboratory analysis for any particular contaminant/'The actual analytical concentration of an
 MRL, therefore, generally differs for different contaminants. There can also be several different
 approved analytical methods for analysis of the same contaminant, and therefore, multiple MRLs for
 even a single contaminant.  Given this, the occurrence Measures presented in Table IV.A.2 are relative to
 the variable MRLs, with each MRL representing tha  lowest level that can be reliably achieved within
 specified limits of precision and accuracy under routine laboratory operating conditions.) Most
 contaminants ranked as low occurrence based on the percent systems were also ranked as low occurrence
 based on the percent population served. These contaminants are indicated in italics.
Table IV.A.2. Stage 1 Analysis - Low Occurrence Contaminants Ranked by MRL for AH
(Combined) Surface Water and Ground Water Systems in the Eight Cross-Section States
Contaminant
(MCL in mg/L)
Percent
Systems
>MRL
Contaminant
(MCL in mg/L)
Percent
Pop. Served
by Systems
>MRL
.Inorganic Chemicals *
rAntimony (0.006)
Cyanide (0;2)
Beryllium (0.004)
3.24%
2.38%
2.10%
Cyanide (0.2)
Beryllium (0.004)
Thallium (0.002)
3.35% •
3.24%
2.29%
Synthetic Organic Chemicals b
PCBs (0.0005)
Carbofiiran (0.003)
0.20%
0.16%
PCBs (0.0005)
Heptachlor (0.0004)
0.57%
0.34%
Occurrence Estimation Methodology
14
                                                                                             March 2002
-------
Contaminant
(MCL in mg/L)
Carbofuran (0.04)
Glyphosate (0.7)
Oxamyl (0.2)
Chlordane (0.002)
Hexachlorobenzene (0.001)
Percent
Systems
>MRL
0.11%
0.10%
0.09%
0.05%
0.04%
Contaminant
(MCL in mg/L)
Heptachlor Epoxide (0.0002)
Oxamyl (0.2)
Hexachlorobenzene (0.001)
Glyphosate (0 7) >H
Chlordane (0,002) ~~" "
Percent
Pop. Served
by Systems
>MRL
0.16%
0.10%
0.09%
0.02%
0.01%
Volatile Organic Chemicals ^ ^
1,2-DichIoropropane (0.005)
1,2,4-Trichlorobenzene (0.07)
1,1,2-Trichloroethane (0.005)
trans- 1,2-DichloroethyIene (0.1)
Vinyl Chloride (0.002)
1.12% .
1.08%
1.00%
0.80%
0.64%
1,4-Dichlorobenzene (0.075) "• * „
o-Dichlorobenzene (0.6)
Vinyl Chloride (0.002)
1,2,4-Trichlorobenzene (0 07)
Styrene (0 1)
6.50%,..JF
, 5.28%^
- 4:92%
2.76%
2.69%
a) Too few data to evaluate asbestos. Arsenic was not evaluated b) "Bo few data to evaluate dioxin Generally Phase II/V compliance
monitoring data sets wereused and these contained too few data to evaluate nitrate/nitrite           ,
Contaminants in italics are in bottom rank category for both percent system and percent population measures
Rankings are based on data from the eight cross-section States of AL, CA, IL, MI, MTNJ, MM, and OR


Stage 1  analyses were also generated separately by ground and sfffade source water type. Contaminants
were ranked based on the proportion o£systems (and populatiorifserved by systems) with any analytical
results greater than the MCL, '/2 MCL,  and MRL for each sour§6 water type. The same lists of high and
low occurrence contaminants (included in Tables IV.A.1 andtfV.A.2) were determined by all the ranking
approaches (i,e., ground water.r|mking, surface water ranking, or combined ground and surface water
approach and a presentation of the complete Stage 1 analytical findings, please refer to the report titled
First Stage Occurrence andExposure'Reportfor Six-Year Review (Cadmus, 2000).

Fluoride was consistently ranked as the highest occurrence IOC on most or all of the various ranking
approaches. Chromium and jcadmium were also consistently ranked high in many of the ranking
approaches. Antimony and mercuryswere occasionally ranked with high occurrence.

For low occurrence of lOCs, beryllium was the most consistent contaminant of low ranking occurrence.
Antiinony, cyanide and thallium were also commonly ranked as low occurrence contaminants on the
various ranking approaches.

Note;tiiere are seemingly contradictory occurrence findings for antimony since it occurs on both the high
oc,currencejist( (based on percent of analytical results above the MCL) and low occurrence list (based on .
percent of analytical results above the MRL). These two occurrence measures can be simultaneous and
are valid.rln me case of antimony, the MCL is relatively close to the MRL, so when an analytical
concentration is detected for antimony (above the MRL), the detection is more likely to also be above the
MCL.  Antimony is detected relatively infrequently compared to other lOCs; its presence is infrequently
identified above the MRL making it a "low occurrence contaminant." Yet on those few occasions when
antimony is detected, it is often detected at concentrations greater than the MCL. A large proportion of
antimony results exceed its MCL, relative to the other lOCs' detections exceeding their respective
MCLs. By this measure, antimony is also considered a "high occurrence contaminant." This apparent
occurrence contradiction is also possible present in the findings for several other contaminants (e.g., the
Occurrence Estimation Methodology
15
March 2002
-------
 VOC vinyl chloride). These subtly differences in occurrence measures must be noted when considering
 what type of occurrence assessment and conclusions are to be made.

 Ethylene dibromide (EDB), l,2-dibromo-3-chloropropane (DBCP), and bis(2-ethylhexyl)phthalate
 (DEHP) were consistently ranked as the highest occurrence SOCs on most or all of the ranking
 approaches. The next most frequent contaminant was atrazine, which was ranked high in many of the
 ranking approaches.  (Atrazine occurrence is being considered separately under other occurrence and
 exposure analyses.) This was followed by benzo[a]pyrene, diquat, and endrin, which were^occasionally
 ranked with high occurrence. The high occurrences of phthalate are, in part, considered false positives
 related to sample contamination by plastics and laboratory analytical problems4,

 Carbofuran, glyphosate, chlordane, oxamyl, hexachlorocyclopentadiene, carSofuran, hexachlorobenzene,
 and PCBs were consistently ranked as the lowest occurrence SOCs.         " -

 Dichloromethane, tetrachloroethylene, and trichloroethylene were consistently ranked as the highest;'
 occurrence VOCs on most or all of the separate ranking approaches. The next most frequeht'contaminant
 was 1,1-dichloroethylene which was ranked high in many of the ranking approaches. This was followed
 by carbon tetrachloride, 1,1,1-trichloroethane, and, to a lessor degree, yinyl chloride and 1,4-
 dichlorobenzene, which were occasionally ranked with high occurrence. Note that the high  occurrences
 of dichloromethane are, in part, considered false positives related to laboratory analytical problems.

 For low occurrence of VOCs, 1,2-dichloropropane, l,24^trichlorobenzene,;ymyl chloride, styrene, and
 o-dichlorobenzene were the most consistent contaminants of low rank occurrence based on the various
 ranking approaches.
                                                      -  i j

 IV.B.  Comparison of State Data and URCIS Stage 1 Findings

 As an additional evaluation of the national "representativeness"'of the initial eight cross-section States,
 occurrence analyses from the cross-section States'/yvere compared to similar occurrence analyses
 aggregated from another cross-section of compliance monitoring data - the Unregulated Contaminant
 Information System (URCIS) 24-State Cross-Section. The URCIS data set includes information on sixty
 regulated and unregulated VOCsy and two regulated SJDCJs from a total of 40 U.S. States or Territories.
 (A group of 24 URCIS States was selected from tjiejUJlCIS database, using the same cross-section
 development approach described in Section II.) The majority of the data are from the first round of
 required unregulated contaminant monitoring from 1987 through 1992. It is important to note that
 because of the age of the data, in relation to rapid improvements made in data processing systems, the
 quality of data received by EPA for URCIS is highly variable.

 The URCIS data are from an earlier time period than are the data for this current study (which mostly
 date from 1993 to 1997). The URCIS data also are largely limited to occurrence monitoring results for
 volatile organic chemicals (VOCs). Nonetheless, in aggregation and for (non-parametric) rank order
 determination of highest and lowest occurrence of VOC contaminants, the comparison to the URCIS data
 provides an additional evaluation of the  use of the cross-section States for broad occurrence  assessments
 indicative of national occurrence.  The comparison is qualitative, but still provides information for
 comparative assessments of, for example, the relative occurrence of the different VOCs across different
 time periods and different (yet presumably nationally-balanced) cross-sections of States.

 URCIS VOC occurrence findings were ranked according to systems and population served, and then
 compared to the initial eight cross-section State data occurrence findings for VOCs. A general summary
 of the determined high and low occurrence contaminants based on these rankings is described below.
         The false positive issue was informally evaluated. The issue was discussed with several national laboratories, and available State
occurrence data was evaluated over time. The opinions of the laboratory staff contacted corresponded to the evaluation of the occurrence data;
there appears to be no distinct time period or date after which occurrence data on phthalates can clearly be considered free of false positives.
Occurrence Estimation Methodology
16
                                                                                        March 2002
-------
For a detailed description of the URCIS rankings, please refer to Section 4.5, in First Stage Occurrence
an d Exposure Report for Six-Year Review (Cadmus, 2000).

High and low contaminant occurrence rankings, based on the number of systems and population served,
were conducted separately for surface water-supplied and ground water-supplied systems using URCIS
Round 1 data from a group of 24 States.  Generally, there was agreement between the findings of high
and low occurrence contaminants for both systems and population served rankings and for surface and
ground water systems. The URCIS rankings were also in general agreement with the rankjigs of the
eight cross-section States' data. Again, please note that the high occurrences of dichloromethane are, in
part, considered false positives related to analytical problems.              ,.-
                                                                      s"~   './
The high occurrence VOCs common to both surface and ground water systeniSxranked by the proportion
of systems with at least one analytical result greater than the MCL Xvere 1,1 -diehlorqethylene,         Jp=
dichloromethane, tetrachloroethylene, and trichloroethylene. The low occurrence VOCs common to frcjffi
surface and ground water systems ranked by proportion of systems were vinyl chloride,'  ^ "
o-dichlorobenzene, and 1,2,4-trichlorobenzene.            /,                          -i,

Based on the proportion of population served by systems with-af least one analytical result'greater than
the MCL, the high occurrence VOCs common to both surface and ground water systems were
 1,1-dichloroethylene,  dichloromethane, tetrachloroethylene., and trichloroethylene.  The low occurrence
VOCs common to both surface and ground water systems ranked by population served were styrene and
 1,2,4- trichlorobenzene.                               _, ,            -      ^
                                                <*     r,  -f..             ^.
As an additional comparison, tetrachloroethylene-Stage l MRL) for
both cross-sections.
 Occurrence Estimation Methodology
                                                17
March 2002
-------
  Table IVJB.l.  Stage 1 Analysis Comparison of Tetrachloroethylene Occurrence in Different
  Cross-Sections
Source Water
Type
Ground Water

Surface Water
Threshold
MCL
'/2MCL
MRL
Percent of Systems
Exceeding Threshold
Initial 8-State
Cross-Section
1.2%
1.9%
4.5%
URCIS 24-State
Cross-Section
0.9%
1.5%
3.4%
Percent of Population Served by
Systems Exceeding Threshold
Initial 8-State
Cross-Section
32.1%
37.3%
467%
URCIS 24-State
Cross-Section
' ,17>/o
25.3%
33.7%
'
MCL
1AMCL
MRL
1.7%
2.9%
8.7%
0.7% '
1.0%
2.7%'
3.2%
4.9%
, 29.0%
2.1%
3.5%
17.5%
 The MCL for tetrachloroethylene is 0.005 mg/L. One-half the MCL is 0.0025 ing/I, The Minimum Reporting Level (MRL) is variable.


 V.  FULL SIXTEEN STATE DATA SETS AND CROSS-SECTION

 The coverage suggests that the initial eight cross-section State data sets are indicative of national
 occurrence and the aggregate size of the data sets is substantial (representing approximately 10 million
 analytical results from nearly 22,000 PWSs). Nonetheless, the addition of data from other States would
 contribute to more nationally representative occurrence analyses and greater confidence in the
 conclusions derived from the analyses.                  •

 Consideration was first made regarding the expanded use of State data sets that were already in hand
 (i.e., the 6 out of the 14 data sets not used in the initial 8-State cross-section). For example, Indiana's
 data set had been previously volunteered, and was available for use. The data set, which is quite
 complete and of satisfactory quality, was carefully considered for addition to the national cross-section
 (as long as other State data sets were added from other quartiles for balance).

 While other State data that'was in hand were used in some of the non-parametric descriptive statistics for
 the CMR Report (such as determination of range of contaminant occurrence), most were.not usable for
 expanding the national cross-section of State data. For instance, Iowa had a adequate and complete data
 set , but using Iowa data would over-represent the Midwestern "Cornbelt" states, with Illinois and
 possibly Indiana already included in the national cross-section of State data. Other data sets that were in-
 hand (those from Kansas, Massachusetts, Missouri, and Ohio) were seriously incomplete, biased, or not
 functionally suitable for expanding the national cross-section.  The acquisition  of additional State data
 sets to expand the national cross-section in a balanced and representative way was conducted using the
 same pollution potential quartile distribution and geographic diversity criteria that were used to develop
 the balanced and representative initial (8-State) cross-section. (As with the selection of the initial 8
 cross-section states, consideration of the additional cross-section  states was  based primarily on the
 ranking indicator of the number of manufacturing establishments per square mile, but total farm
          For the CMR Report, contaminant occurrence results from Iowa were included, but the Iowa data set was not directly used.  Iowa
has a published report that provided the necessary occurrence figures, which provided occurrence information without conducting additional
analyses.  Therefore, the actual Iowa data set has not yet been procured, but likely could be, if necessary.

Occurrence Estimation Methodology                    18                                       March 2002
-------
agricultural expenditures and TRI releases were also considered to insure that the occurrence data from
the selected States were, collectively, representative or indicative of national occurrence.)

Maintaining a geographic balance, to the extent possible, also contributes to an aggregate data set that is
more representative of the variety of geographic conditions present nationally. Regarding this balance,
further representation from the New England area, the southeast and south-central States would
contribute to balancing an expanded national coverage. Based on the consideration of States' pollution
potential rankings, how they best fit into the quartile distribution, and how their spatial or geographic
coverage contributed to a representative national cross-section of States, the suggested Stales considered
for addition to the national cross-section contaminant occurrence data set weref -
                                                                        ;•        *
        Quartile 1) Rhode Island, Pennsylvania, Florida;          „.„     '•'"   }  ^"
        Quartile 2) Indiana, New Hampshire, Tennessee, South Carolina, Vermont;
        Quartile 3) Kentucky, Minnesota, Texas, Mississippi, West Virginia, Oklahoma:; and
        Quartile 4) Utah, Nebraska, South Dakota.                     J'        ^-   , -/.
                                                                      *           \            /
As new State data sets were added to the initial group of eigh't cross-section States, the data sets were
added in specific groups to further build the cross-section sample in a^balanced manner. Based on data
availability and quality, the additional group of eight States added to the cross-section were: Florida-
Quartile 1; Indiana, South Carolina, and Vermont - Quartile 2; Kentucky, and Texas -  Quartile 3;
Nebraska, and South Dakota - Quartile 4. A summary of these additional, eight State  data sets is
presented in Table V. 1.                                               ,      *'r -"*
                                                   '      >            * _. "
                                                             "^
Table V.I.  Additional State Data Sets Used for-Analysest      "'     >
' ",4 /t? * '"- *••
* -r, rw6?- i
•:^ state- ' ,ff
«* * ^ <. "** ,
Florida
Indiana
Kentucky
Nebraska
South Carolina
South Dakota
Texas
Vermont
Total
-' CoiatoniftiaiitGwW'''
, 'f ,&ei»rcsente^~, '^
lOCs, SOCs, VOCs
lOCs, SOCs, VOCs, O
lOCs, SOCs, VOCs, O ,
IQCvSOCs, VOCs
lOCs, SOCs -VOC$,^
lOCs, SOCs, VOCs
lOCs, SOCs, VOCs
lOCs. SOCs, VOCs, 0
lOCs, SOCs, VOCs, 0
''^tttnber.oE*' ""„
^AwaryifejJ Results
< •*>/'
713,543/"
257,428
; » 177,070
189,959
501,286
55,526
947,615
248,438
3,090,865
Nttm'bc^tfflWSsr*
, * Jtepresente
-• Tm&Vf»M% ^,
-~^l"^ ^,'4
1993-1997
1982-1997
1993-1997
1993-1999
1989-2000
1990-2000
1990-2000
1987-2000
1982-2000
 1) lOCs = the 13 regulated inoigatte chemicals; SOCs = the 30 regulated synthetic oganic chemicals; VOCs = the 21 regulated volatile oganic
 chemicals, O = Other regulated or unregulated chemicals.
 2) iData from 1999 and 20QO were excluded from analysis. Most data sets contained complete data only through 1998.
    ' ,,          *
           /
 Table V.2.  shows quartile rankings for the 16 States contained in the national cross-section. Figure V.2.
 shows the distribution of the initial eight cross-section States along with additional eight cross-section
 States. The distribution  is broad and relatively uniform across all quartiles of the manufacturing and
 agriculture pollution potential indicators (note that the manufacturing pollution potential indicator was
 the primary ranking factor with agricultural and TRI indicators considered in a secondary sense). Figure
 V.3.  is a map illustrating the geographic distribution of the initial eight cross-section States, as well as
 the additional eight cross-section States
 Occurrence Estimation Methodology
                                                  19
March 2002
-------
 Table V.2. National Cross-Section States with Ranking of Pollution Potential Indicators
Quartiles
for Rank-Order of
AH States Based on
Manufacturing Ranking
1
2
3
4

Stales in
Mtial
8-StatC
National
CrossV-,
Section
NJ
IL
CA
MI
AL

OR

NM
MX
National Ranking of
Pollution Potential Indicators,
Manu-
facturing1
2
10
11
13
25

34

44 .
48
Agri-
culture
37
2
1
18
26

22

40
34
< rrar «.
KeI&W'r
8
11
38
16 ,
7
f
39

40
34
States in
Additional,
> 8-St*fer
National ,
Cross-* '
Section
FL


IN
SC
VT
KY
TX
NTS
SD
,^ ,'- National Ranking of ,/>
/" Pollution Potential Indicators
-^
' Mann-
facturing'
*&>

-
15
21
,23
- 27
30
42
45
^Agr^"'
culture*
•Tff,
4

'•
7
32
47
27
6
9
21
&t&
^efeascsf*
13

i'i ,.?;
" 6
10
45
21
20
41
49
Occurrence Estimation Methodology
20
                                                                                          March 2002
-------
Figure V.2. Distribution of State Ranking for Manufacturing Establishments/ Sq. Mile vs. Farm
Ag.  Chemical Expenses (Highlighting Initial 8 & Additional 8 Cross-Section States)
                                Ranking of the No. of Manufacturing Establishments/ Sq. Mile


FL -
HE -





SD -


KY -

SC -











VT -


CA -
IL -






MI -
OR -

AL -




MT -

NJ -

NM -








1










25
















50



^

o
o


^






•



4h
o
0


o


o

o




0
o
o
«
o
o
30
,

^
^f
w

o

o _
° 0

o
(

o
V


• o








' o


^
'

o








o
o



o

9
o


o

o


o




s
iM"
•eS


• g
<
G
- TO g
3
E^
0

o











-LOW
25 1
	 1 	 1 	 -T- i iii i
MT NM OR AL MI CA IL NJ



SD ME
^ Initial S-State Cross-Section
^ Additional 8-State Cross-Section
O AH Other States
TX KY VT SC IN FL


 Occurrence Estimation Methodology
                                                21
March 2002
-------
  Figure V.3. Map of the 16 Cross-Section States
                                                           3 Initial 8-Stete Cross-Section
5                                                            Additional Rotate doss-Section
                                                            States not incfaded taCrflss-Section
                                                                   *n&S.  * «,«?,.
 VIA.   Data Use and Editing            £'<'•'       ,,       ~   _  J/    •

 Similar to the initial eight cross-section States, a considerable amount of data editing was necessary for
 the additional eight cross-section States.  Each data set was reviewed to ensure it contained the basic data
 elements necessary to conduct a consistent analysis for this study. These elements were reviewed with
 State contacts to ensure consistent ;aBd appropriate interpretations.  Once data quality issues were
 resolved, each data set was converted into a consistent format.

 A common data quality issue of the additional eight States related to data that appeared to have been
 recorded or mislabeled in incorrect units. In many State databases, analytical results are presented as
 integers in one column with a corresponding column to identify how many decimal points are associated
 with that integer (analytical result).  Sinceihese data are often hard-entered by a data entry person  there
 is a large potential for error. If the "decimal point" column is incorrectly entered (even off by one) the
 analytical results are recorded in the data set in the wrong units. In many cases, detailed double-checking
 with the analytical results for similar contaminants in other States showed that the analytical results
 appeared to be incorrect (either too low or too high) by a constant factor of 1,000. The interpretation was
 that the data were (mistakenly) recorded in ug/L in the database, but actually  represented data in mg/L
 (or vice versa).  These data corrections were somewhat straightforward after identifying reviewing and
 cross-checking the analytical results.  The criteria for excluding outliers included evaluating the data on
 an individual  basis. Other data that appeared to be in incorrect units, but were not off by the typical
 factor of 1,000, were either left in the database or excluded from analysis, depending on how much of an
 outlier it was.

 Values evaluated were both high and low value outliers, therefore by removing incorrect values both
 large and small questionable values were removed. Because this analysis is focused on occurrence at the
 system  level (calculating a mean concentration value for each system for a given contaminant)  rather
than on a total sample basis, we were able to avoid the skewness inherent in the sample data  Therefore
 it is believed that the small amount of outlier data that may remain in the database does not influence the
final estimates Less than 0.02% of the total number records were identified as analytical results recorded
Occurrence Estimation Methodology
22
                                                                                        March 2002
-------
in the incorrect units. Less than 0.25% of the analytical results were identified and changed to non-
detections. Of the total number of records excluded from analysis, only 0.002% of the total data were
removed as suspected or confirmed outliers.

V.B.  Comparison of 8-State vs. 16-State National Cross-Sections

To further evaluate the representativeness of the cross-section, occurrence analyses from the 8-State
cross-section were compared to occurrence analyses from the 16-State cross-section. For the group of 30
contaminants to be analyzed with Stage 2 (Stage 2 analyses are described in detail in Section VI.A), the
percent of systems (and population  served by systems) with at least one analytical result greater than the
MCL and MRL in the eight States were compared to the same measures for the 16-State cross-section.
The 8-State and 16-State Stage 1 findings were quite similar.  Generally, thes contaminants found with
high, medium or low relative occurrence based on the 8-State data sets Stage 1 analyses were the same j?
contaminants with high, medium or low occurrence, respectively, based on the 16-State'data set.  The ^f
ranking from highest to lowest occurrence was not identical in'the 8-State arid 16-State data sets bitt^/or
this simple non-parametric evaluation, the dissimilarities were small. '               ~ „    _ "

Table V.B.1 compares the 8-State and 16-State cross-sections based,oh the percent of systems. The
percentages are generally consistent between the two cross-sections. For the most part,  the proportion of
systems with analytical detections (i.e.,  "% Systems > MRL") is higher for the 8-State cross-section than
the 16-State cross-section. With the exception of the lOCs -and a few SOCs, tfie proportion of systems
with at least one analytical result greater than the MCL (i.e., "% Systems > MCL") is also higher for the
8-State cross-section than the 16-State cross-section.

The greatest discrepancy between the 8-State and 16-State proportion of systems  with analytical
detections is seen in the contaminant mercury,. The 16-State percentage of systems with analytical
detection of mercury is slightly greater thariplS timesjthe 8-State percentage of systems with analytical
detection of mercury. Based on the propoif Ion of systems with at/fleast one analytical result greater than
the MCL, the greatest discrepancy beg|ien the 8-State and 16-State cross-section is seen in the
contaminant chromium. The percen|igVbf systems in the 8 Steles with at least one analytical result
greater than the MCL for chromium is approximately 5 times the percentage of systems in the 16 States
with at least one analytical result greater than the MCL for chromium.
Table V.B.1. Comparison of Stage 1 Analyses for 8-State vs. 16-State National Cross-Sections
Based on the'Percenfcof Systems"  s, >
Contaminant
£
MCL
(mg/L)
% Systems > MRL
8 States
16 States
IOCS
Beryllium 4!
Chromium f \
Fluoride „ *''
Mercury
Thallium
; 0.004
0.1
4
0.002
0.002
2.10%
13.0%
73.8%
4.90%
3.41%
3.32%
18.3%
83.8%
17.3%
4.22%
% Systems > MCL
8 States
16 States

0.520%
0.620%
3.90%
0.850%
1.33%
0.217%
0.127%
1.28%
0.263%
0.679%
SOCs
Alachlor
Bis(2rethylhexyl)phthalate
0.002
0.006
0.900%
12.1%
0.670%
12.5%
0.0500%
2.17%
0.0420%
2.20%
Occurrence Estimation Methodology
23
                                                                                        March 2002
-------
Contaminant
Carbofuran
Chlordane
l,2-Dibromo-3-
Diquat
Glyphosate
Heptachlor
Hcptachlor Epoxide
Hcxachlorobenzene
Hcxachlorocyclopentadiene
Oxamyl
Picloram
Simazine
Toxaphene

Benzene
Carbon Tetrachloride
1 ,4-Dichlorobenzene
1 ,2-Dichloroethane
1 , 1 -Dichloroethy lene
Dichlorometliane
1 ,2-Dichloropropane
Tctrachloroethylene
1 , 1 ,2-Trichloroethane
Trichloroethylene
MCL
(mg/L)
0.04
0.002
0.0002
0.02
0.7
0.0004
• 0.0002
0.001
0.05
0.2
0.5
0.004.
0.003
% Systems > MRL
8 States
0.110%
0.0500%
2.86%
1.06%
0.100%
0.220%
0.210%
0.0400%
0.910%
0.0900%
0.850%
2.81%
0.160% ~~
16 States
0.0600%
0.120%
1.61%
0.490%
0.100%
0.0800%
0,0900%
0,0900%
0.890%
0.0800%'
0.410%
' 1.80%
0.0800%
% Systems > MCL
8 States
0.000%
0.000%
1.95%
0.0600%
0.000%
0.0200% ,
• 0.0300%
0.000%
0.000%
0.000%
0.000%
0.0900%
0:0200%
VOCs '''"
0.005
0.005
0.075
0.005
0.007
0.005
0.005
0.005
0.005
0.005
' 1,54%
2.06%
2.26%
1.53%
2.03% .-'.... ,
11.8%
1.12%
'4.63%
1.00%
3.55%
1.31%
1.99%
1.76%
1.31%
1.58%
8.59%
0.670%
3.36%
0.620%
2.61%
0.235%
0.240%
0.000%
0.160%
0.301%
0.740%
0.130%
1.18%
0.0700%
0.940%
16 States
0.000%
0.0150%
0.912%
0.0220%
0.000%
0.00700% /,'
0.028% ,
, 0.00700%
' ' -'0.000%
0.000%
0.000%
0.0550%
0.00700%

0.189%
0.204%
0.000%
0.126%
0.236%
0.669%
0.0680%
0.778%
0.0400%
0.647%
Note: All percentages are shown to three significant figures.


Table V.B.2 compares the 8-State and 16-State cross-sections based on the percent of population served
by systems, The percentages are generally consistent between the two cross-sections.  For the lOCs, the
proportion of population served by systems "> MRL" is always smaller for the 8-State cross-section'than
the 16-State cross-section. However, the proportion of population served by systems "> MCL" is
generally larger for the 8-State cross-section than the 16-State cross-section for the lOCs.  For the SOCs
the proportion of population served by systems "> MRL" and "> MCL" is generally higher for the 8-   '
State cross-section than the 16-State cross-section. For the VOCs, the proportion of population served by
systems "> MRL" and "> MCL" is always higher for the 8-State cross-section than the 16-State cross-
section.
Occurrence Estimation Methodology
24
                                                                                        March 2002
-------
The greatest discrepancy between the 8-State and 16-State proportion of population served by systems
with analytical detections is seen in the contaminant chlordane.  The 16-State percentage of systems with
analytical detection of chlordane is about 16 times the 8-State percentage of systems with analytical
detection of chlordane. Based on the proportion of systems with at least one analytical result greater than
the MCL, the greatest discrepancy between the 8-State and 16^-State cross-section is seen in the
contaminant beryllium.  The percentage of systems in the 16 States with at least one analytical result
greater than the MCL for beryllium is more than 12 times the percentage of systems in the 8 States with
at least one analytical result greater than the MCL for beryllium.                      ^
Table V.B.2. Comparison of Stage 1 Analyses for 8-State vs. 16-State National Cross-Sections
Based on the Percent of Population Served by Systems         ,
Contaminant
MCL
(mg/L)
% Population Served by Systems >
MRL
8 States
Instates
% Population Served by Systems
8 States
16 States
IOCS
Beryllium
Chromium
Fluoride
Mercury
Thallium

Alachlor
Bis(2-ethylhexyl)phthalate
Carbofuran
Chlordane .'" , .
l,2-Dibromo-3- ,
Diquat J*f ' _,"
Glyphosate ^ 1~
Heptachlof
HepMchlor Epoxide
Hexachlorobenzene
Hexachlorocyclopentadiene
Oxainyi - "',
Piclorain ~"
Simazine"'
Toxaphene
0.004
0.1
4
0.002
0.002
3.24%
25.4%
96.2%
5.58%
2.29%
sots
0.002
0.006J? *
0.04- -
0.002
0.0002
0.02 ,
* 0.7
. - 0,0004
0,0002
0.001
0.05
0.2
0.5
0.004
0.003

Benzene
Carbon Tetrachloride
0.005
0.005
1.31%;'
32.6%
0.940%.*
0.0100%
„ 18.2%
' 0.980%
0.0200%
0.340%
0.160%
0.0900%
3.54%
0.100%
0.970%
9.51%
1.47%
VOCs
17.4%
19.7%
6.65%
28.7%
~ 969%
21.6%
6.49%
" 0.0500%
" 1.06%
"7.31%
0.410%
0.190%
«v
2 55%
28 0%
0.5400%
0.160%
13.5%
0.760%
0.0400%
0.190%
0.100%
0.330%
2.28%
0.170%
0.580%
11.2%
0.850%

12.0%
14.8%
0.130%
2.74%
0.000%
0.000%
16.1%
0.330%
0.000%
0.0000000699%
0.0300%
0.000%
0.000%
0.000%
0.000%
0.0700%
0.230%
0.621%
0.666%
• 4.56%
0.276%
1.85%

0.259%
3.19%
0.000%
0.0000000477%
11.4%
0.208%
0.000%
0.0000000398%
0,0290%
0.0400%
0.000%
0.000%
0.000%
.0.0470%
0.131%

0.701%
12.4%
0.518%
7.35%
Occurrence Estimation Methodology
25
March2002
-------
Contaminant
1 ,4-Dichlorobenzene
1,2-Dichloroethane
1 , 1 -Dichloroethylene
Dichloromethane
1 ,2-Dichloropropane
Tetrachloroethylene
1,1,2-Trichloroethane
Trichloroethylene
MCL
(mg/L)
0.075
0.005
0.007
0.005
0.005
0.005
0.005
0.005
% Population Served by Systems >
MRL
S States
6.50%
19.3%
24.1%
44.0%
17.9%
36.3%
16.7%
37.3%
16 States
4.38%
12.3%
16.0%
28.6%
11.1% -,
27.2%'
1014%
25.0%
% Population Served by Systems
>MCL
8 States
0.000%
14.1%
13.6%
f5.0%
1.30%".
22.2%
11.8%
21.1% - -
16 States
0.000%
8.40%
' 8.69%
9.50%
1.18%
13.5% •-.
, e.97%^
13:3%
 Note: All percentages are shown to three significant figures.                ,r~

                                                          _t    t
 The occurrence findings in Tables V.B.I and V.B.2 are broadly consistent between the two cross-
 sections regarding contaminant occurrence rankings and "orders of magnitude" values (note there are a
 few possible exceptions).  The 16-State cross-section contains twice as much date as the 8-State cross-
 section while also covering a broader range geographically and across pollution potential indicators.
 Therefore, all additional analyses were conducted on the fljll 16-State cross-section.


 VI.  STAGE 2 ANALYSIS

 The goal of Stage 2 analysis is to estimate the number of PWSs with contaminant mean concentration
 values  greater than a specified threshold for each source water type and system size. Thus, it is necessary
 to calculate amean concentration value for each systen^Jfar a given contaminant. Howevei; it is very
 difficult to calculate a simple arithmetic mearirsince most PWS compliance monitoring analytical
 observations are non-detections. Such concentrations are generally reported as "less than MRL" rather
 than as actual numerical values.  The numerical concentration value of a non-detection lies somewhere
 between zero and the  specified Minimum Reporting Level. (The Minimum Reporting Level represents
 the lowest level that can be reliably achieyectwithin specified limits of precision and accuracy under
 routine laboratory operating conditions.) Historically, three approaches have been commonly used to
 determine the mean of such data: assume non-detection data are equal to zero, assume all non-detection
 data are equal to half the MRL, or assume all non-detection data are equal to the MRL.  An arithmetic
 mean is then calculated using these fabricated numbers together with values above the MRL.  While
 these methods are widely used, they all "introduce a bias and result in erroneous estimates of the mean
 and  standard deviation" (Porter et.  al., as cited in Travis and Land, 1990).  Setting all non-detections
 equal to zero likely underestimates the true analytical value of the sample, and setting all non-detections
 equal to the MRL or halfthe MRL likely over estimates the true analytical value.

 VI. A.   Preparation of State Data for the Stage 2 Analysis

 The  contaminant occurrence rankings (described in Section IV) provided a preliminary means by which
 EPA began to assess the occurrence of regulated contaminants considered for Six-Year Review.  The
 more rigorous Stage 2 analysis was conducted on 30 of these contaminants.  The development of formal
 exposure estimates for these contaminants requires several intermediate data management and analysis
 steps prior to conducting any parametric statistical analyses. A summary of the data editing necessary to
 enable Stage 2 analysis is described below.
Occurrence Estimation Methodology
26
                                                                                       March 2002
-------
As previously noted, no IOC data were originally available from the State of Michigan. As part of the
preparation for Stage 2 analysis, Michigan State data management staff were contacted. Compliance
monitoring data were acquired for fluoride, beryllium, chromium, mercury, and thallium.  The data were
checked and edited for quality, and were added to the cross-section data set.

Once the 16-State cross-section was established (including Michigan IOC data), the data still required
further computational manipulation prior to estimating national occurrence (and exposure). Stage 1
analysis is based on the proportion of systems with at least one analytical result greater thag a specified
threshold.  The complete distribution of the analytical results is not of interest. ff Stage 2 aiplysis,
however, is based on the proportion of systems with a mean concentration value greater tnan a specified
threshold.  The mean concentration value is affected by all observations (including non-detections and
detections less than the specified health threshold). Therefore, each analytical record for each
contaminant had to be checked to prepare the data for Stage 2 analysis.
The distribution of analytical results for all 30 contaminants for each of the 16 states'was^cJosely
reviewed. Many data quality issues appeared that were not discovered id" the first roun^oi; data-quality
review. For example, South Dakota data contained 91 analytical detections for beryllium, "Fifty-six of
these detections were equal to 0.0005. It is very unusual to have such a large proportion (&2°7o) of
analytical detections all equal to the same value. Since 0.0005 mg/L is well below the MCL for
beryllium (0.004 mg/L), these data would not affect Stage 1  analysis, However, so many analytical
results equal to the same concentration value would greatly influence,^ mean concentration value used
in Stage 2 analysis. After consultation with state data management staff in SoutJ^Dakota, it was
determined that these analytical results were actually non-detections.  Apparently; the values were simply
entered into the database at the MRL, and no flag was-included to specify whether the result was a
detection or. non-detection.                  ~r              >

Decisions also had to be made on how to qufmtitatively include non-detection data.  Some states record
the Minimum Reporting Level (MRL) m.me analytical result column and also include a "<" in a
corresponding column to flag the recprcffas^a non-detection. Other states simply include a zero in the
analytical result column to signify a*ncp-detectio0. Although non-detection data were not a concern in
the initial occurrence analyses, meyjpose a problem within Stage 2 analysis where mean concentration
values are estimated for each system.  In order to Estimate a mean concentration value for each system, a
non-zero MRL must be included for all analytical results that were reported either as zero or
alphanumerically as "non-detection** or "ND," etc/ (The method  used to estimate mean concentration
values for eachrsystem is described%i>Section VI.D.) A convention was developed to set all such records
equal to "less-than" the-state's non-zero modal MRL6 wherever possible. For the states that set all non-
detections equal to zero, the non-detections \yefe set equal to "less than" the non-zero modal MRL for all
16 states. (Note:,,TJiis is not the same type of substitution method described in the first paragraph of this
Section. When non-detection values are set equal to the non-zero modal MRL, they are still considered
"less-than" that non-zero modal MRL. The substitution method mentioned early simply set the non-
detection values equal to the MRL, as if that were the true numerical concentration value.)

The final element of the Sjplge 2 data quality analysis is related to the source water type and population
served for each system. |?pr the Stage 2 analysis, it was necessary to define each system in a unique
source water rype/popujtiiiion size strata. Systems using both ground and surface water, and systems
using ground water,uttder direct influence of surface water, were included with surface water data.
Systems with^more than one population  served specified in the original data were included using the
largest population  served value. Because these data management decisions were not conducted for the
Stage 1, analysis, some very slight differences (based on the very few number of systems so affected) may
occur between Stage 1 and Stage 2 findings.
         The "non-zero modal MRL" refers to the most commonly occurring MRL, other than zero, for each contaminant in the 16-State
cross-section data.


Occurrence Estimation Methodology                    27                                      March 2002
-------
 Table VI.A. 1.  describes the occurrence data from the 16-State cross-section data set used for Stage 2
 analysis. For each contaminant, this table includes the Maximum Contaminant Level (MCL)
 concentration values, as well as the total number of analyses, systems, and population served by systems
 that have data represented in the 16 cross-section States. All population numbers were rounded to the
 nearest hundred. This table also lists the range of Minimum Reporting Levels (MRL) concentration
 values used for the convention of substituting for the "non-detection" data.  As illustrated, these values
 ranged from 0 to as high as 100 mg/L.  For the Stage 2 analysis, the non-zero modal MRL (also included
 in Table VI.A.1) was substituted for all non-detection data that were originally equal to zero.
 Table VI.A.1. Contaminant Occurrence Data From the 16-State Cross-Section Used in Stage 2
 Analysis                                                  ,             '  ^
Contaminant

Beryllium
Chromium
Fluoride
Mercury
Thallium

Alachlor
Bis(2-ethylhexyl)phthalate
Carbofuran .
Chlordanc
l,2-Dibromo-3-
Diquat
Glyphosate - i-_ 	 ,»_:
Hcptachlor X
Hcptachlor Epoxide
Hcxachlorobcnzene
Hcxacblorocyclopentadiene
Oxamyl "
Piclomm
Simazfnc" " ''
Toxaphene

Benzene
Carbon Tetrachloridc
Total
Number of
Analyses
Total
Number of
Systems
Total Population
Served by
Systems
MCL
(rag/L)
Non-Eero
Modal MRL
(mg/L)
Range of
• MRLs
(rag/L)
lOCs
47,761
65,437
93,062
64,764
46,959

58,700
41,052
51,994
59,689
98,559:
"-36,443
33,957
. -.57,489 \
; 57,73;1 "'
,;, 52,931
52,614
47,664
46,323
68,176
52,429

188,811
182,944
18,933
19,695
20,803
18,995
17,972'
104,573,700
105,380,000
' 107,075,700
105,096.700
104-291,600
0004
0.1
4
0.002 '/
0002
0.001
, 0.01
0.1
0.001
0.001
0-1
0-5
0-100
0-0.5
0-2.2
SOCs
14,330 4
9,418
13,925 '•:•:::,
13,184
.14,042
9,159
/7,862
14,245
14,133 .
14,011
13,922
13,157
12,907
14,533
13,805
/ 95,678,600,;
78,293,000
^94;338,000
97,459,900
87,727,200
73,602,900
70,081,900
96,563,400
96,222,900
94,035,300
93,429,200
92,345,800
93,235,500
98,178,100
95,108,100
0.002
0.006
0.04
0.002
0.0002
0.02
0.7
0.0004
0.0002
0.001
0.05
0.2
0.5
0.004
0.003
0.0002
0.0006
0.0009
0.0002 '
0.00002
0.0004
0.006
0.00004
0.00002
0.0001
0.005
0.002
0.0001
0.001
0.001
VOCs
23,266
23,028
110,866,600
110,605,500
0.005
0.005
0.0005
0.0005
0-0.2
0-0.2
0-0.9
0 - 0:2
0-0.5
0-0.4
0-6
0-0.1
0-0.1
0-0.1
0-0.1
0-2
0-0.2
0-0.1
0-2.2

0-0.5
0-0.5
Occurrence Estimation Methodology
28
                                                                                      March 2002
-------
Contaminant
1 ,4-DichIorobenzene
1 ,2-Dichloroethane
1 , 1 -Dichloroethy lene
Dichloromethane
1 ,2-Dichloropropane
Tetrachloroethylene
1 , 1 ,2-Trichloroethane
Trichloroethylene
Total
Number of
Analyses
123,229
180,631
170,411
170,899
180,920
195,239
173,927
201,235 ^
Total
Number of
Systems
18,961
23,038
19^01
21,530
21,988
22,362
22,284
23,035
Total Population
Served by
Systems
72,994,500
110,794,100
106,607,600
110,146,100
110,450,100 ~
110,557,800
110,366,500
110,612,900
MCL
(mg/L)
0.075
0.005
0.007
0.005
0 005
0.005
0005
0005
Non-Zero
Modal MRL
(mg/L)
0.0005
0.0005
0.0005 If
00005
' 0 0005
/ 00005
* 0.0005
0 000| ,
Range of
MRLs
(mg/L)
0-0.5
0-1
0-0.5
0 - 0.62
0-0.5
0-0.5 /
0-0.5'
0-05
The reduced number of systems sampling for SOC data, as compared to lOCs and VOCi, may relate to state waivers for pesticides and
herbicides.                                                    '


VLB.  Previous Occurrence Estimation Methods

In the past, several estimation procedures have been implemented to estimate system mean
concentrations when non-detecjion data are present. Each method has a unique way of handling non-
detection data, characterizing the data's distribution, and generating occurrence estimates. The
occurrence estimation approach developed,for and used in this report reflects, to some degree, an
evolution of analytical approaches. Previously, EPA had developed an approach to estimate radon
occurrence, in drinking water, as well as another approach to estimate arsenic occurrence in drinking
water.
                                             ^-n
Multiple dataxsets, containing different proportions of non-detection data, were used in the radon ,
analysis. (These are described in detail in Methods, Occurrence, and Monitoring Document for Radon in
Drinking Water; CJSEPA, 200Qa.) "AJog-normal distribution assumption was primarily used to generate
system mean concentration valuegT When data sets contained less than 5% non-detection data, the log
mean (natural log of the geometric^mean) and log standard deviation (natural log of the geometric
standard deviation) were the primary statistics used. When the data contained a higher proportion of
non-detection data^thfr log mean and log variance parameters were estimated by a maximum likelihood
estimation (MLE) method, which involves the iterative calculation of log likelihood ratios while updating
the estimates of the non-defection Values of the data until the likelihood ratio is optimized within
specified limits. To calculate the proportion of systems above radon levels and the confidence limits on
the proportions, two different approaches were employed: a distributional approach and a non-
distributional approach. Tlie distributional approach simply applied the known properties of the
cumulative normal distribution to the estimated log mean and log standard deviation of radon occurrence
in a,given population ojlfo'urces/systems to estimate the proportion that would be expected to be above
the potential regulatp^level. A non-distributional approach was used when the fits of the radon
distributions tpjoj^ormal distributions were not very good.  This method calculated the upper and lower
confidence liimft?6n the estimated proportion of systems above a certain level. This method, which is
based on courits of actual systems/sources above specified levels, makes no assumptions about the
underlying shape of the distribution of radon levels.

The arsenic analysis used five steps for estimating national occurrence. First, system arithmetic means
were calculated using a method called "Regression on Ordered Statistics (ROS)", developed by Helsel
and Cohn (1988). This approach, which assumes that the underlying distribution of occurrence data are
reasonably well characterized by a log-normal distribution, "fills-in" values for non-detection data based
on the values of the detection data.  Although MLE (described above for radon) is an alternative method
Occurrence Estimation Methodology
                                               29
March 2002
-------
 for estimating the log-normal distribution parameters, its approach was somewhat more computationally
 involved than the ROS method.  In comparing methods for estimating distributional parameters, Helsel
 and Gilliom (1988) found that the MLE method was preferred for estimating percenfile values for non-
 detection water quality data, but that the regression methods (such as ROS) were preferred for estimating
 the distributional parameters (mean and standard deviation).  For this reason, and the relative ease of
 calculation compared with MLE approaches, the ROS method was used in estimating arsenic occurrence.
 Once the system means were generated, State exceedance probability distributions for ground water and
 surface water were calculated. Weighted sums of the exceedance probabilities generated for each state
 were then used to develop regional exceedance probability distributions for ground water anil surface
 water.  National exceedance probability distributions were developed as the weighted sum of the
 exceedance probability distributions derived for each Region. Finally, the estimated numbers of systems
 exceeding levels of interest were generated as the product of thenlffional proE£6ility distributions and the
 total number of ground water or surface water systems. For a detllled description of the protocol, refer
 to Arsenic Occurrence in Public Drinking Water Supplies (USEPA, 2000b).        >      »
                                                        1  "                    *~            *
                                                                             **<<               -j
 The arsenic "ROS approach" for estimating occurrence and exposure was used for preliminary    '
 estimations in this Six-Year Review of contaminant occurrence'estimation. However, since this
 occurrence modeling approach could not provide a complete quantitative estimation of statistical error,
 alternative modeling approaches were considered, and an approach using a Bayesian-based modeling
 approach was subsequently developed. As part of the Bayesianr-based model validation, a detailed
 comparison was made assessing the Bayesian-based model performance relative to the that of the ROS
 approach.                                           ^^

 VI.C.  General Description of Bayesian Statistics
                                                     **              / ^           r

 Bayesian statistics are named after an English mathematician^ Thomas Bayes, who first used probability
 inductively and established a mathematical basis for probability inference. The Bayesian approach is
 based on the concept that more may be known about:an actual situation than is contained in the data from
 a single experiment regarding that situation. Bayesian methods, for example, can be used to combine
 results and information from several different, but related situations or experiments. This type of
 approach considers not only what information is contained in the specific situation (or data) directly
 being assessed, but what outside expertise or information might also contribute to an understanding of
 the situation being assessed (such as an assessment of the likelihood of an event occurring). The
 Bayesian view of probability is related to a "degree of belief and measures the feasibility of an event
 occurring in the context of incomplete knowledge.

 Bayesian inference is best suited to problems/that involve making decisions under uncertainty. Bayes's
 Theorem begins with a statement of what is known prior to performing the experiment. (In the context of
 statistical modeling;' this prior knowledge's typically in the form of a probability density function, a
 mathematical expression that defines the likelihood of an event occurring.) The prior knowledge, or
 "prior," can be based on the results of other experiments, on expert opinion, or actual existing data. The
 Bayesian analytical approach is designed to start with a statement of initial (or "prior") knowledge, and
 then use that knowledge and related information to improve upon the initial state of knowledge.

 In the context of statistical estimations of contaminant occurrence, a "prior" is first specified and could
 be the analytical monitoring results of contaminant occurrence at a public water system. The prior is
 then supplemented with the inclusion of a likelihood function, which mathematically presents the
 distribution of similar, relate data. The modeling process then revises the prior distribution based on this
 additional (likelihood) information to generate an updated estimate (the "posterior" distribution). This
 "posterior" distribution represents what is now believed  about the original parameter (the "prior") in light
 of the supplemental data. This updating process is repeated again and again in an iterative process; the
 posterior from one distribution becomes the prior for the next, and so on. This updating proceeds until
the model "converges" (meaning that two successive estimates of the repeated updating process are
 equal, and no further updating is necessary).  Sections VLD.  - VI.G. summarize the Bayesian-based
Occurrence Estimation Methodology
30
                                                                                      MarcK2002
-------
estimation model. A more detailed, technical description of the Bayesian model, and its programming
code, are included in Appendix B.

VI.D.  Estimating System Mean Concentrations

The general Stage 2 approach is to use the available 16-State cross-section data to model contaminant
concentrations in drinking water as a function of system characteristics, such as source water type and
system size. As stated above, Bayesian methods allow various sources of variability and uncertainty in
occurrence to be explicitly quantified. For these analyses, a Bayesian-based hierarchical model is fit to
characterize uncertainty in the estimates.

The model is based on the assumption that each system is log-normally distributed with an unknown
mean and unknown variance. It is a common assumption that water data follow a log normal         ,-?f
distribution7.  The "priors" in this analysis are for the means and variance. For each system, a constant^'
variance, but non-constant mean, is assumed. Once the prior distribution has been established., a two*
level statistical model is built. The lower level features the observed concentrations (analytical   -,
detections and non-detections), which are treated as coming from a log-normal distribution, -The'upper
level features the unknown parameters of the log-normal probability distribution of each system, whose
values are estimated based on the detections and non-detections." Thus, the Bayesian-based approach
allows the model to produce a conditional distribution of the unknown features of interest (system mean
and standard deviation) as a function of the known data (both detections art
-------
  distribution, that can be regarded as a sample from the posterior distribution (Qian et al., 2001). Using
  these samples, it is then possible to calculate the statistics of interest (mean concentration and standard
  deviation). This technique also provides a means to generate a random sequence of model output that
  may be used to make inferences about the model uncertainties that derive from measurement
  uncertainties.

  VT.E.  Estimation of Probabilities of Threshold Exceedance

  Approximately 500 Monte Carlo simulations8, using the stratum-level mean and standard deviation as
  model input, then estimate the number of systems for each source water type and sys{em-'size category
  that are expected to exceed each specified concentration threshold. The estimated number of systems
  that exceed each threshold for a given stratum is then divided by|he total number, of systems in that
  stratum, resulting in the percent of systems estimated to exceed a specified thresKoid for a specific     f»
  stratum (the estimated mean "probability of threshold exceedarice").          '                      ^

  The estimates for population served exceedances are generated in a similar manner. In the process of the
  system exceedance estimation steps, the actual population served by each system in the data-set Is
  formally (mathematically) connected (or "attached") to each system. Therefore, when the Monte Carlo
  simulations are run to estimate the number of systems for each source water type and system-size
  category that are expected to exceed each specified concentration threshold,4here are corresponding
  population served values along with the system number estimates.  So; the estimated population served
  by systems that exceed each threshold for a given stratum is then divided by the total population served
  in that stratum, resulting in the percent of population estimated to be served by systems with a mean
  concentration that exceeds a specified concentration threshold for a specific stratum (the estimated mean
  "probability of threshold exceedance").       : t       !,

 VI.F.   Credible Intervals

 In Bayesian analysis, credible intervals are generated to quantify the uncertainty of each estimated mean
 probability of exceedance. A Bayesian credible interval defines the range of values within which the true
 value of the parameter is believed tp occur. The actual upper and lower numeric values of the credible
 interval are referred to as the Cupper credible tiojjfUJS zmdjtlie "lower credible bound," respecitvely
 Because the probability of exceedance is estimated ii|ing approximately 500 Monte Carlo simulations,
 there exists 500, instead of one, estimates of the probability. A credible interval is the central region
 within which a specified percentage of the posterior density lies equally within the distribution (e.g., the
 95% CI would be the region of the posterior density which lies between 2.5% and 97.5%). Thus, a 90%
 credible interval is an interval between the'5th'iand 95th percentiles of the 500 Monte Carlo values'of
 probability of exceedance.

 The Bayesian "credible interval" probability that the actual parameter lies within the interval is different
 from standard definition of "confidence interval", which is based on (hypothetical) repeated experiments.
 Because the credible interval directly relates to the distribution of the actual  data, this interval may or
 may not include the mean^ depending on the skewness of the estimated distribution.  In other words, the
 credible interval is not an interval around the mean (like the more traditional confidence interval). The
 traditional statistical ("frequentist") 90% confidence interval is an interval that will contain the true value
 of the mean 90% of the time. For a particular study, a confidence interval provides qualitative
 information since they are  really a measure of how precise an estimated effect is. If a confidence interval
 is wide, the estimated mean is less reliable.  In contrast, a Bayesian credible  interval, has the precise
 probabilistic meaning.  In our case, a 90% credible interval of the exceedance probability is interpreted as
 a 90% probability that the true value of the exceedance probability lies in the interval.
        8
         To test the number of Monte Carlo simulations necessary for this analysis, preliminary model runs were conducted using 500
simulations, 1,000 simulations, and 2,000 simulations. Expanding the amount of simulations did not alter the results. Thus, 500 simulations
proved adequate and were used for computational reasons.
Occurrence Estimation Methodology
32
                                                                                        March 2002
-------
For some extremely skewed estimated distributions, it is possible that the Monte Carlo estimated 5th and
95th percentiles are the same. For example, several estimates of the probability of a system mean
exceeding a given threshold have an upper 90% credible bound of zero and a lower 90% credible bound
also equal to zero, but a mean ("best estimate") probability of exceedance NOT equal to zero. This is
because the probability of a threshold exceedance is evaluated by several Monte Carlo samples and at
least 95% of the samples are equal to zero.  Under such a situation, one should conclude that the chance
is less than 5% to have an exceedance probability that is greater than zero.

Also note that the credible intervals for estimates of the totals (total ground water, total surface water,
and total combined ground plus surface water) are always narrower than the credible intervals for each
individual stratum. Because the estimates, and the associated standard errors, of the |Dtals are based on a
much larger sample size, the standard errors for totals are less and the credible inteVv,als are narrower
than for the individual stratum.                              ,£                   .               Ji
                                                       ^&,l*>?           •*.      f  /**              '••'%:"
VI.G.  Using the Occurrence Probability Estimates to Obtain National Occurrence Estimates

Once the probability of exceedance has been estimated through Stage 2 analysis, a straight-fcnrward
extrapolation can be used to estimate national occurrence9. The totajunational number of systems (or
population served by systems) estimated to exceed a specified threshokUs generated by multiplying the
representative cross-section probability of exceedance by the national numbers for systems (and
population served by systems) documented in the Water Industry Baseline Handbook, Second Edition -
2000 (USEPA, 2000c).  The total number of ground and surface water community water systems (CWSs)
plus non-transient, non-community water systems (NTNQWSs) in the Baseline Handbook is 65,030, and
the total population served by ground and surface water CWSs plus NTNCWSs is 213,008,182 persons.
(The handbook presents the system and population^served numbers stratified by source water type and
population served size categories as well.) Toderive thek|iational occurrence estimate for a specific
threshold/source water type/population servjld size category, the national number of PWSs (or population
served by PWSs) from the handbook is simply multiplied by the probability of exceedance (a percentage)
estimated by the statistical model.  (The process of generating the probabilities of exceedance are
described in Section VLB.).        -'          ^
                                           /'-        "'"';?"
Table VI.G.l. illustrates the calculation of national estimates of exceedance.  For example, to estimate
the number of systems natioh'ailyxexpected to have mean concentration values of fluoride exceeding 4
mg/L for ground water systems servjng 500 people or less, the best estimate probability of exceedance
(0.5895%) is1ii}ultjplied by the total number of ground water systems nationally that serve 500 people or
less (43,498 systems).. The resulting e^imate equals 256 systems (43,498*0.005895=256). The national
estimate of populatioirexposed to a'given contaminant is extrapolated in a similar fashion (i.e., the
probability of exceedance'is multiplied by the  total population served nationally).
Table VT.G.1. Calculating National Estimates of Exceedance
**
Population-
Served Size
- " Category
><50
-------
> 50,000
GW Total1
189
59,440
0.0160%
0.5496%
0.0000%
0.4685%
0.0000%
0.4685%
0
327
0
278
0
378
 1. System inventory data from the ttater Industry Baseline Handbook, Second Edition - 2000 (USEPA, 2000c).
 2. Estimates are generated separately for each level of aggregation. Therefore, estimates for the individual size stratum will not add to estimated
 totals at the source water level of aggregation, and estimates for the source water strata ("GW 'Etal" and "SW Total") will not add to the total
 estimated for all systems ("Total Ground & Surface Vfoter").


 The estimated number of systems and population served by systems in the 16 States were also
 extrapolated from the Stage 2 probabilities of exceedance.  To generate the 16-State estimates, the
 probabilities of exceedance were simply multiplied by the total number of systems (or population served
 by systems) with 16-State data for that particular contaminant/source water type/system size. (For the
 total number of systems and population served by systems for each contaminant, please'refer to Table
 VI.A.1.)

 VI.H.  Summary of Occurrence Estimations

 The Stage 2 analytical findings are summarized below.  The complete Stage 2 analytical findings,
 presented in Appendix C, include estimated contaminant mean concentrations, the statistical best
 estimates of exceeding contaminant concentration thresholds, and both the 90% and 95% credible
 intervals for the best estimates.  All findings presented in Appendix C arVstratified  by source water type
 and system size (based on population-served), presentedafor multiple contaminant concentration
 thresholds. These findings also include a single aggregate result for each contaminant/threshold (which
 provides a mean concentration, best estimate for exceeding that threshold, and the 90% and 95% credible
 intervals for the best estimate aggregated across'all system sizes for all water source types).
 Additionally, the best estimates (and credible,*intervals) liave been used to extrapolate to national values.
 These national extrapolations (including both stratified and aggregate values) present the modeled best
 estimates for the national number of systems, and the/populationiserved by those systems, that are
 expected to exceed the specified threshold concentrations for each of the  30 contaminants evaluated.

 The Stage 2 best estimate findings (based on this l&jState^national cross-section data) are presented in
 comparison to the Stage 1 (16-State) findings in TafalegfLH.!. The findings are presented as the percent
 of systems, and population-served by those systems, that exceed the current MCL for each contaminant.
 Note that this table compares the two different types of analytical findings of the Stage 1 (non-parametric
 "peak" concentration values) and the Stage 2 (parametric mean concentration values) analyses.  This
 comparison is included as a general, qualitative evaluation of the Stage 2  model, enabling assessments of,
 for example, the relative rankings of occurrence of contaminants in  Stage 1 compared to Stage 2. Also,
 for a given contaminant and concentration threshold, Stage 1  findings (e.g., the "percent of systems with
 at least a single sample analytical result greater than the MCL") should be greater than the corresponding
 Stage 2 estimates (e.g., the "percent of systems with an estimated mean concentration greater than the
 MCL"), 'Following these occurrence measurement differences, Stage 1 analyses can be described as
 conservative, roughly assessing "peak" concentrations in systems as compared to the mean
 concentrations, roughly assessing "long-term" contaminant concentrations, used in the Stage 2 analyses.

 Although Stage 1 findings are generally greater than Stage 2 findings, there can be exceptions to this
 general rule. JFor example, the Stage 1 findings for systems with l,2-dibromo-3-ch!oropropane greater
 than the MCL is less than the Stage 2 estimates.  Exceptions to the general rule can legitimately occur
 and result from technical aspects of the Bayesian-based modeling procedure itself. This is partly due to a
 phenomenon referred to as "Bayesian shrinkage," where the higher and lower values of the range of
 estimated values shift (or shrink) toward the mean, thereby increasing the lower values and decreasing
the higher values. Also, in the Bayesian-based hierarchical model developed for the Stage 2 analyses, a
Monte Carlo simulation step is used to estimate the number of systems with mean concentrations above a
specified threshold concentration.  The input for this Monte Carlo step is the estimated system mean
concentration and variance about the mean estimate. A high variance can affect the Monte Carlo
simulation results which, in turn, affects the final Stage 2 results.
Occurrence Estimation Methodology
34
                                                                                        March 2002
-------
Table VLH.1.  Comparison of Aggregate Stage 1 and Stage 2 Analytical Results Based on the 16-
State National Cross-Section - Percent of Systems and Population Served by Systems Greater than
the MCL
Contaminant
MCL
mg/L,)
% Systems > MCL
Stage 1
Stage 2
% Population-Served by Systems
>MCL
Stage 1
iocs A ,J?
Beryllium
Chromium
Fluoride
Mercury
Thallium

Alachlor
Bis(2-ethylhexyl)phthalate
Carbofuran
Chlordane
1 ,2-Dibromo-3-chloropropane
Diquat
Glyphosate
Heptachlor
Heptachlor Epoxide - -
Hexachlorobenzene
Hexachlorocyclopentadiene
Oxamyl ; ^"T
Picloram , „
Simazine —— /v
Toxaphene
0.004
0.1
4
0.002
0.002
0.217%
0.127%
1.28%
0.263%
0.679%
SOCs
0.002
0.006
0.04
0.002
0.0002
' 0.02 *
oy -
00004
_' 0.0002
B 0.001
'005, -
02 _^»
,x" 0.5 -'
,0,004
- X0.003
0.0419%
2.20%
0.000%
0,0152%
' 0.912%
0.0218>~
0.000%
OJOP7Q2%
^•f ^ *,~
CarbQB Tetrachlonde
1 ,4-DichloroBenzehe
1 ,2-Dichloroethane
0.005
0.005
0.075
0:005
0.189%
0.204%
0.000%
0.126%
0.0313%
0.0159%
0.000%
0.00479%
0.518%
7.35%
0.000%
8.40%
0.00947%
0.0316%
0.000%
0.000331%
Occurrence Estimation Methodology
                                             35
March 2002
-------
Contaminant
1 , 1 -Dichloroethylene
Dichloromethane
1 ,2-Dichloropropane
Telrachloroethylene
1,1,2-Trichloroethane
Trichloroethylene'
MCL
(mg/L)
0.007
0.005
0.005
0.005
0.005
0.005
% Systems > MCL
Stage 1
' 0.236%
0.669%
0.0682%
0.778%
0.0404%
0.647%
Stage 2
0.0911%
0.0131%
0.00358%
0.202%
0.000%
0.236%
% Population-Served by Systems
>MCL
Stage 1
8.69%
9.50%
1.18%
13.5% "
6.97%X
, 13.3%
Stage 2
0.331%
0.119%
0.0358%
0.685%
0.000%
8.19%
 Note that this table provides a qualitative comparison between the diferent estimation approaches of the Stage 1 (non-parametric "peaic"
 concentration values) and the Stage 2 (parametric mean concentration values) analyses  Therefore, two diferent types of statistical measures are
 being compared here.                                      .          ,                      „ —

 AH percentages are shown to three significant figures.                       >

 1. The low percentage of systems with trichloroethyiene MCL exceedances, as compared tq,the very higher percentage of population served by
 those systems with trichloroethyiene MCL exceedances, is the result of a few systems with MCL_exceedances that serve very Ige populations.


 Based on the generated Stage 2 probability of exceedance percentages, national extrapolations can be
 calculated. The Stage 2 probability of exceedance percentages are multiplied by the known national total
 number of systems, and population served by systems (based on national PWS inventory information
 from the Baseline Handbook). The result is an extrapolated national estimate of the number of systems
 (Table VI.H.2), and population served by systems (Table VI.H.3), that are expected to exceed the MCL.
 In general, J,2-dibromo-3-chloropropane has the laigest number of systems estimated to exceed the MCL
 (almost 200 systems in the 16 States, and over 90(Tsystems nationally). The second laigest number of
 systems estimated to exceed the MCL was for fluojide (justxjver 100 systems in the 16 States, and over
 300 systems nationally). Trichloroethyiene had, l>^far, the} largest estimated population served by
 systems exceeding the MCL, (over 9 million people intthe^i 6 States, and approximately 17 million people
 nationally). The next largest population potentially exposed to a contaminant greater than the MCL was
 l,2-dibromo-3-chIoropropane (approximately 2.3 million people in the 16 States  and about 5.5 million
 people nationally). For 14 of the  30 contaminants, zero systems were estimated to exceed the MCL in
 the 16 States and nationally. Range estimates (based on the 95% credible bounds around the best
 estimate) for the number of systems, and population served by those systems,  are also included in Tables
 VI.H.2 and VI.H.3.
Table VI.H.2. Best Estimate and Range of the Number of Systems Exceeding the MCL in the 16
Cross-Section States and Nationally
. Contaminant
MCL
(in mg/L)
Best Estimate of
Systems Estimated to
Exceed the MCL
16 States
National
Range Estimate of Systems Estimated to
Exceed the MCL
16 States
National
lOCs
Beryllium
Chromium
Fluoride
0.004
0.1
4
15
1
106
51
3
332
7-24
0-3
91 - 123
24-82
0-10
284 - 385
Occurrence Estimation Methodology
36
                                                                                          March 2002
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Contaminant
Mercury
Thallium
MCL
(in hig/L)

0.002
0.002
Best Estimate of
Systems Estimated to
Exceed the MCL
16 States
13
51
National
44
184
Range Estimate of Systems Estimated to
Exceed the MCL
16 States
8-18
35 - 66
National
27-62
./'127-239
SOCs
Alachlor
Bis(2-ethylhexyl)phthalate
Carbofiiran
Chlordane
1 ,2-Dibromo-3-chloropropane
Diquat
Glyphosate
Heptachlor
Heptachlor Epoxide
Hexachlorobenzene
Hexachlorocyclopentadiene
Oxamyl
Picloram
Simazine'
Toxaphene _,
/
Benzene ' s
Carbon TetrachlorideE
1 ,4-Dichlqrpbenzene
1 ,2-DicK16roethane
1,1-Dichloroethylene
Dichloromethane jf
Ij2-Dichloropropane ,/
Tetraehloroethylene '""'
1 , 1,2-TrichJoroethane
Trichloroethylene
0.002
0.006
0.04
0.002
0.0002
0.02
0.7
0.0004
0.0002
0.001
0.05
0.2
0.5
Q.004/
0.003
- i<
0.005 ' '
' 0,005
0.075
/ 0.005.
|; o.6l)7
0.005
0.005
0.005
• 0.005
0.005
0
24
0
. 0
199
0
0
0
0
0
0
0
0
0
0

7
4
0
1
17
3
1
45
0
54
0
166
0
0
920
0
0
0
,3- 0 "
o,;"
0
0
0
1
^0
VOCs
20
10
0
3
59
9
2
132
0
154
0-0 /
- 14 . 37 &
0-0^
, 0-0
1 T71-231
' O'-O
'"0-0 -
o-o'^s ,
0-0 '^
"' ' 0-0
6-0
0-0
0-0
0-0
0-0

4-12
2-5
0-0
0-3
13-23
1-6
0-2
37-53
0-0
47-63
0-0
97-256 J;
' 0-0
- 0-0 ^
'792'- 1,070
0-0
0-0
0-0
0-0
0-0
0-0
0-0
0-0
0-0
0-0

11 -34
6-14
0-0
0-8
44-78
3-18
0-6
108-154
0-0
133 - 178
The estimates for the number of systems in the 16 States and nationally are both based on the same modeled best estimate.  The 16-State values
are obtained by multiplying the probability of exceedance by the actual number of systems in the 16-State cross-section for each particular
contaminant. The national values are obtained by multiplying the same probability of exceedance by the total number of systems nationally
based on inventory numbers identified in the Wdter Industry Baseline Handbook (USEPA, 2000c). The range of values are based on the 95%
credible bounds around the best estimate.
Occurrence Estimation Methodology
37
March 2002
-------
  Note; All system values are rounded to the nearest whole system.

  1. Model output resulted in an estimate of less than half a system; howeverthe fraction was rounded up to 1.
  Table VI.H.3. Best Estimate and Range of the Population-Served by Systems Exceeding
  the MCL in the 16 Cross-Section States and Nationally
Contaminant

Beryllium
Chromium
Fluoride
Mercury
Thallium

Alachlor
Bis(2-ethylhexyl)phthalate
Carbofuran
Chlordane
l,2-Dibromo-3-chloropropane
Diquat
Glyphosate ,
Hcptachlor
Heptachlor Epoxide - -
Hexachlorpbenzene
Hexachlorocyclopentadiene
Oxamyl
Picloram
Simazine
Toxapbene

3enzene
Carbon Tetrachloride
1 ,4-Dichlorobenzene
,2-DichIorocthane
MCL
(in mg/L)
Best Estimate of
Population Served by
Systems Estimated to
Exceed the MCL
16 States
National
Range Estimate of Population Served by
Systems Estimated to Exceed the MCL
16 States'
National
IOCS „ < __ ,
0.004
0.1
4
0.002
0.002

0.002
0.006
0.04
0.002
0.0002
0.02
0-7
0.0004
0.0002
0.001
0.05
0.2
0.5
0.004
0.003
21,800
1,500
96,000
6,600
77,500
44,400
3,000
191,000 „
13,400
158.300
2,900 - 81,700
"'"6- 8,400
59,400-151,300
1,000-23,400
- 16,300-256,900"
5,900-166,300
0- 16,900
118,200-301,000
2,000-47,400
33,300 - 524,600
SOCs
0
93,400
0
0
2,278,300
0
0
• •;.••• Q>
7 o
0
0
0
0
100
0
-0
254,100
0
0
- 5.53I;800
0
0
0
0
0
0
0
0
200
0
o--o
14,600 - 284,500
0-0
0-0
1,853,700 - 3,307,300
0-0
0-0
0-0
0-0
0-0
0-0
0-0
0-0
0-0
0-0
VOCs
0.005
0.005
0.075
0.005
10,500
35,000
0
400
20,200
67,400
0
700
2,100 - 33,200
800 - 47,500
0-0
0-800
0-0 ,
39,700-774,100
0-0
0-0
4,500,900 - 8,030,400
0-0
0-0
0-0
0-0
0-0
0-0
0-0
0-0
0-0
0-0

4,000 - 63,800
1,500 - 91,400
0-0
0 - 1,500
Occurrence Estimation Methodology
38
                                                                                        March 2002
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Contaminant
1 , 1 -Dichloroethylene
Dichloromethane
1 ,2-Dichloropropane
Tetrachloroethylene
1 , 1 ,2-Trichloroethane
Trichloroethylene
MCL
(in mg/L)
0.007
0.005
0.005
0.005
0.005
0.005
Best Estimate of
Population Served by
Systems Estimated to
Exceed the MCL
16 States
352,700
131,200
39,500
757,200
0
9,062,500
National
704,600
253,700
76,200
1,458,900
0
17,451,800,
Range Estimate of Population Served by
Systems Estimated to Exceed the MCL
16 States
340,400-381,100
200-275,300 „
0 - 142,000 ,
519,700-965,100
0-0
8,828,000 - 9,302,500
National
678,900 - 760,000
300 - 532,300
/ 0 - 273,900
' 1,001,400-1,859,300
0-0
17,000,200-17,914,000
The estimates for the number of systems in the 16 States and nationally are both baseil on the same modeled best estimate.=3;he>i6-State values
are obtained by multiplying the probability of exceedance by the actual number of systems in file 16-State cross-section for each particular
contaminant The national values are obtained by multiplying the same probability of exceedance by the total number of systems nationally
based on inventory numbers identified in the Wter Industry Baseline Handbook (USEPA, 2000c); The range of values are based on the 95%
credible bounds around the best estimate.

Note: All population values are rounded to the nearest hundred.                         "
VI.I.   Stage 2 Model Verification           J      ^  '  '

Several approaches for model verification wejlTundertaKen. The first verification assessment (comparing
estimated mean concentrations) partially assesses both 1:he modeling process and a key component of the
cross-section construction. A simulation;(synthetic) data study was also conducted to compare the
Bayesian-based approach to the "ROS** method, and to test the assumption of constant variance and log-
normality at the system level for the national distribution of system means.
To partially assess the modeling process and a'Jcey component of the cross-section construction, the mean
concentration values for select contaminants were estimated for groups of top quartile and bottom
quartile States: (Eor a description of how quartiles are determined, please see Section II.B.) The cross-
section development approach presumes that the top quartile States have a higher pollution potential than
the bottom quartile States, and, therefore, the estimated mean concentrations for the top quartile States
should be greater 'than those for the bpttom quartile States. The estimated mean concentration values for
the top quartile States were always higher than the mean concentration for the bottom quartile States with
the lone exception of tieptachlbr (a very low occurrence SOC).
Table VLI.1.  Stage 2 Comparison of Top Quartile and Bottom Quartile States' Mean
Concentration Values
Contaminant Name
Mean Concentration (in mg/L) .
Top Quartile States
Bottom Quartile States
IOC1
Fluoride
0.70753270
0.33453498
SOC2
Alachlor
Carbofuran
0.00000693
0.00000170
0.00000099
0.00000113
Occurrence Estimation Methodology
39
                                                                                             March 2002
-------
Contaminant Name
Diquat
Glyphosate
Heptachlor
Heptachlor Epoxide
Hexachlorobenzene
Oxamyl
Picloram
Mean Concentration (in mg/L)
Top Quartile States
0.00001604
0.00002159
0.00000012
0.00000006
0.00000039
0.00000506 £
0.00000572
Bottom Quartile States
0.00000771 •
0.00001268
0.00000027
O.OOQ00004
0.00000022 , '
0.-, (V,    jV ^
 3. VOC - Ranking Based on Number of Manufacturing Establishments / Sq. Mile - Top Quartile States = CA, PL, IL NJ- Bottom Ouartile
 States = MT,NE,NM,SD.                               <,^'  '„'           V  >


 A rigorous, quantitative model verification was conducted through a simulation study, using six
 simulated (synthetic) data sets. This study was designed to explore the impact of the log-normal, as well
 as the constant variance, assumption made on the system level fqirthe national distribution of system
 means. In addition, the Bayesian-based hierarchical modeling approach was compared to the Regression
 on Ordered Statistics (ROS) plotting position method.        -

 The six simulated data sets were divided into three groups.; The first group was designed to emphasize
 the comparison of the Bayesian and ROS methods.  THie second group was generated to evaluate the
 constant variance assumption. Finally, the third^roup of simulated data sets tested the impact of a log-
 normal assumption at the system level on the national distribution of system means. Please refer to
 Appendix B for details regarding the simulated data study.

 Both the simulated study and the mixture model indicated that the Bayesian-based hierarchical model
 used for the study is appropriate.  The simulated study showed that the prior assumptions about the
 contaminant distribution do not have an undue influence on the posterior estimate of the national
 distribution of system means. The .mixture model study showed that using a log-normal  distribution at
 the system level is appropriate. When the log-normal assumption is not used, the estimated national
 distribution has a slightly larger variance, which may result in an overestimate of the exceedance
 probabilities.

 Another direct verification of the model consists of a traditional bounding analysis. A bounding analysis
 enables an assessment of how well the model estimates system mean concentrations, and by inference,
 how well the model estimates values for the non-detection values used in the mean concentration
 estimations. (Non-detections typically comprise a significant proportion of drinking water analytical
 records for any particular contaminant.) For the bounding analysis, EPA generated a data set based on the
 raw analytical results for each contaminant.  In this data set, a "lower bound" was generated by
 substituting the value of 0 (zero) for all non-detections, and an "upper bound" was generated by
 substituting a value equal to the non-zero modal MRL for all non-detections. For additional comparative
 detail, a value equal to Vz the MRL was also substituted for all non-detection records for each
 contaminant assessed.
Occurrence Estimation Methodology
40
                                                                                        March 2002
-------
Fifteen contaminants were assessed with this bounding analysis.  For all contaminants, the modeled
system mean concentration was 'bracketed' by the bounding values, with the lower bound below and the
upper bound above the modeled values. In all cases except for fluoride, the bounding value substituting
!/2 MRL for non-detections also was above the modeled system mean.  A complete graphical presentation
of the bounding analysis is included in Appendix D. (Also included in the graphs in Appendix D are the
90% Credible Bounds of model prediction.)

VI. J.   Stage 2 Model Validation

Another assessment of the model is based on the comparison of the modeled occurrence, estimations to
other known measures of contaminant occurrence in drinking water. In the next section, the Stage 2
occurrence estimates for fluoride conducted for the Six-Year Review were assessedhrelative to system
fluoridation findings reported in the US Department of Health and'Human Services Centers for Disease
Control and Prevention (CDC) Fluoridation Census 1992. Additional information was,'provided by the
CDC regarding the unpublished Fluoridation Census 2000. And in the following section, a general
assessment of the Stage 2 model findings relative to MCL violation records in SDWISTEED'was
conducted.
                                                         ***" -f // $ »**.
                                                             '"" *i* ""
VI.J.1.  Centers for Disease Control and Prevention Fluoridation Census
                                                         ^   . ^
This section provides a general comparative assessment between the Six-year Review's Stage 2 national
fluoride occurrence estimates (based on the 16-State national cross-section) primarily with public water
system fluoridation findings reported in the Centers for Disease Control and;Prevention (CDC)
Fluoridation Census 1992 as well as with findings'proVidedJjy'CDC staff from the unpublished
Fluoridation Census 2000 (CDC, 2002). A rigorous and direct comparison cannot be made between the
CDC Fluoridation Census 1992 (or 2000) findings and tlie EPA-OGWDW's Six-Year Review statistical
model estimations. The CDC census findings report the voluntary provision of qualitative/semi-
quantitative information from public drinking water systems that identify if a particular system is
operating as a fluoridating system (wjtjleither natural or "adjusted" concentrations of fluoride within the
optimum range of fluoride).  The OGWDW Six-"\fear Review|f tage 2 findings are quantitative,
parametric statistical estimations of fluoride occurrence bas^d on compliance monitoring analytical
results of fluoride concentrations in public drinking-walfjjiystems from the 16-State cross-section (with
the results from the 16-State cross-section then extrapolated to national occurrence estimates).
                            A   «•*• '             .                                   '
Despite the slgnificalrt differences in-ithe .underlying sources of fluoride occurrence information, the
comparison between trie CDC and OGWDW Stage 2 findings is  informative. The comparison suggests
that the Stage 2 modeled national estimates are valid, broadly reflecting and correlating with the general
fluoride concentratibns.implied by the fluoridation census findings when considering details of the
differences between'the census and statistical estimation approaches. Details of the comparative
assessment are included below,
                            ~, < /'
The CDC periodically conducts a'national fluoridation census which records the total national number of
public water systems, and gopulation served by those systems, that operate with natural or adjusted levels
offluoride in drinking wafer  at optimum levels. The "optimum range" of fluoride in drinking water
(regarding-prevention diSental cavities) is from 0.7 mg/L to 1.2  mg/L (although a system can be
considered to be operating as a fluoridating system if it operates  within the broader "control range" of
               ! operating
fluoride concentrations from 0.6 mg/L to 1.7 mg/L)10
                                                   To complete the fluoridation census, States
 10 The optimum amount offluoride in drinking water at PWSs is the range offluoride that assists in the prevention of dental cavities. The
 specific optimum level offluoride for a given PWS is generally inversely proportional to temperature. It is assumed that individuals drink more
 water in warmer climates and higher temperatures. The ingestion offluoride via drinking water is directly related to the volume of water
 consumed. Therefore, since high temperatures result in consumption of higher volumes of water, the amount offluoride considered optimal is
 at the low end of the optimal range (0.7 mg/L) in warmer regions (or warmer seasons) and at the high end of the optimum range (1.2 mg/L) in
 cooler regions (or cooler seasons). For example, the optimum level offluoride for PWSs in southern Florida is 0.7 mg/L and for PWSs in
 Maine is 1.2 mg/L. The "control range" recommended by CDC for the optimum concentration is 0.1 mg/L below to 0.5 mg/L above the
Occurrence Estimation Methodology
                                                41
                                                                                         March 2002
-------
  voluntarily report: the name, location, and public water system identification number of each fluoridated
  water system; the population served by each system; whether the system operates with adjusted, or
  natural, levels of fluoride; the chemical used for fiuoridation, if adjusted; and whether or not the system
  purchased water.  However, no quantitative analytical results are presented, no information is provided
  for systems with fluoride occurrence less than 0.7 mg/L (the low end of the optimum range), and the
  source water type is not specified.  Therefore, the implication is that all systems that reported as
  fluoridating (i.e., allsystemslisted in the CDC census) are considered for comparison purposes to have a
  minimum (average) fluoride concentration of 0.7 mg/L, the low end of the optimum fluoridation range.

  Table VI.J.I.a shows a comparison between the quantitative results based on the 16-State cross-section
  data and the qualitative reported findings of the CDC Fluoridation Census 1992 and the unpublished
  CDC Fluoridation Census 2000.  The table specifically presents the Stage 2 modeled estimates based on
  the Six-Year Review 16-State cross-section compared to the number of fluoridating systems (and       «;
  population served by those systems) as reported to the CDC.               .     *  "  *                ^
                                                                                                       •v

  Table VLJ.l.a. Comparison of the National Extrapolations of the Stage 2 Modeled Estimates with
  the CDC Fluoridation Census Findings
Stage 2 Modeled Estimates based on
Compliance Monitoring Results of the
16-State Cross-Section
Fluoride
Fhreshold
(mg/L)
4
2
0.7
Total Number of Systems Nationally
Estimated to Exceed Threshold
Best Estimate
332
1,885
13,390
Range
284-385, .:.-./
1,769-2,000
13,156-13,624.
Total Population Served by Systems !
Nationally Estimated fo s
Exceed Threshold
Best Estimate
191,000
1,978,600;.;:;
57,022;30p:2
Range
118200-301,000
; :1;50S, 100 -3,293, 100
51,803,600-61,346,400 2
• CDC Fluoridation Census
1992 and unpublished
* 2000 ' Findings
Total
Number of
Systems
Fluoridating
145 '
746'
14,496 3
Total Population
Served by
Systems
Fluoridating
152,527 '
849,591 '
141, 107,164 3
 Fora detailed description of how the Stage 2 modeled estimations are derived, please refer to Section VI.A. through VI.H. of this report.

 1. The number of systems and population-served by systems With reported fluoride concentrations greater than 2 mg/L and 4 mg/L were
 provided by the CDC from the unpublished Fluorfdaiion Census 2000.  (These measures of fluoride occurrence relative to these specific
 fluoride thresholds are not included in the 1992 or earlier census publications.)
 2. There were no .compliance monitoring records for fluoride for the Chicago Water System in the State of Illinois' compliance monitoring
 data set.  Therefore, since Illinois is one of the states in the 16-state cross-section and the Chicago Water System is known to fluoridate  the
 Stage 2 modeled estimates presented here do not reflect the population served by the fluoridated water provided by  the Chicago Water System
 (and its Consecutive systems). (The Chicago Water System fluoride were requested, but were received after the Stage 2 modeled estimates were
 generated for this draft report.)
 3. This estimate includes public water systems that operate within the "control range" of optimum fluoride concentrations  Therefore this
 estimate includes systems that maintain fluoride concentrations as  low as 0.6 mg/L while the Stage 2 model estimates are based on the 0 7
 mg/L fluoride concentration values which is the low end of the optimum (rather than control) range.  •



 The CDC Fluoridation Census 1992 indicates that a total of 14,496 public water systems, serving
 141,107,164 people, report that they operate as a fluoridated system11. In comparison, the Stage 2
 national occurrence estimates based on the 16-State cross-section indicate a total of 13,390 systems,
 serving 57,022,300 people, with estimated mean  concentrations of fluoride greater than 0,7 mg/L. (For a
optimum.

   The system and population totals listed here are equal to the exact system and population summations of the 50 States. These total sums do
not equal the sums presented in the CDC Fluoridation Census 1992, in part due to the inclusion of the District of Columbia.
Occurrence Estimation Methodology
42
                                                                                                March 2002
-------
detailed presentation of Stage 2 modeled estimations of fluoride occurrence, please refer to Appendix C,
Tables C.16.f and C.16.n).  A system with a mean concentration of fluoride greater than 0.7 mg/L is
approximately equivalent to a "fluoridated" system (in the CDC census) that reports operation at
optimum fluoride levels, though systems are included in the CDC census as fluoridating if systems
operate within the broader control range and above 0.6 mg/L fluoride.

The differences between the national estimates for fluoridating systems (CDC-14,496 PWSs and
national cross-section-13,390 PWSs) and population served by fluoridating systems (CDG-141,107,164
people and national cross-section-57,022,3 00 people) appear to relate to several factors.  First, the lack
of fluoride occurrence data from the Chicago Water System certainly results iii an underestimate for the
model estimated number of systems, and population served by those systems, (Fluoride data for Chicago
were not included in the original compliance monitoring data sets'Bbtained'directly'from the state of
Illinois. Fluoride compliance monitoring data are reported to the state's public health agency. These  ~"
fluoride data were subsequently requested, but were received after the Stage"2 estimations prepared for
this draft report.)                       .                 '1                       '""'-.
                                                       •>           ^             Si
                                                                 s*v                  •*
The size distribution of fluoridating systems (based on population^ served size categories) is a second
factor influencing the difference in  population served between the Staie.data and the CDC census data.
Table VLJ.l.b illustrates the distribution of fluoridating systems based on six population served size
categories. Although the number of systems serving 1,000 people or less \i similar in the State data and
CDC data (2,824 and 2,540 respectively), this equals a much larger percentage of the smallest systems in
the cross-section data set (66%) than are represented in the CDC census {only 42%).  Therefore, the
cross-section data set (comprised of compliance monitoring data records acquired directly from the
States) has a proportionately larger amount of the smallest systems than does the CDC census (based on
voluntary reporting of which systems fluoridate)/This differing system size profile can result in a
smaller population served by a similar number of systems (as is the case for the national extrapolations
based on the cross-section data).


Table VLJ.l.b. Distribution of Fluoridating Systems in the 16 Cross-Section States and the CDC
Fluoridation Census 1992        ; *            >•    ^ '
Population
„ Served
* 1,000- •;.
1,001- 5,000'
-" 5,001 - 10,000
• 10,001 - 50,000
50,001 - 100,000
> 100,000
Total x -"•
Nu mber of Systems
thaf Fluoridate -
State Date ' ,
, <* f^f *
„, 2,824-
/f 750
, - '244>
»347
54
42
4,261
Percent of State
Totaf Number of
Fluoridating
Systems
66%
18%
6%
8%
1%
1%
100%
Number of Systems
that Fluoridate -
CDC Data 2
2,540
1,983
578
716
103
79
5,999
Percent of CDC
Total Number of
Fluoridating
Systems
42%
33%
10%
12%
2%
1%
100%
 1. The State data results of "number of systems that fluoridate" are derived by using the cross-section data, calculating a simple arithmetic
 mean fiii6fide: concentration for each system in a particular population served system size category, and then counting all systems with a mean
 concentration greater than 0.7 mg/L (which represents the low end of the range of optimum fluoride concentration for fluoridation).
 2. CDC "number of systems that fluoridate" are derived from qualitative reported findings of the CDC 1992 Fluoridation Census.


 A third factor influencing the system number and population differences between the CDC and national
 cross-section estimates relates to systems that report as "fluoridated systems." In the CDC Fluoridation
 Occurrence Estimation Methodology
                                                43
March 2002
-------
 Census 1992, systems that operate within the control range (of optimum fluoride concentration) of 0.6
 mg/L and 1.7 mg/L are considered to fluoridate. The Stage 2 statistical estimations and related national
 extrapolations were based on a fluoride concentration threshold of 0.7 mg/L (the low end of the
 optimum, not the control, range of fluoride levels).  Therefore, the Six-Year Review Stage 2 estimates of
 systems with estimated mean concentrations of fluoride greater than 0.7 mg/L will likely be lower the
 CDC census number of systems reporting to operate within the control range (between 0.6 mg/L and 1.7
 mg/L fluoride).

 Other factors relate to the type of systems included in EPA's Six-Year Review and the CFJG fluoridation
 census. The Six-Year Review, based on compliance monitoring, does not include analytical results for
 consecutive systems. Because consecutive systems compliance monitoring requirements are at the
 discretion of the individual States, the consecutive system compliance monitoring record is not uniform
 from state to state. Therefore, systems identified as consecutive (or, synonymously, as "purchased")
 were removed in the raw data sets prior to Stage 2 estimations. The CDC fluoridaf ion census does
 include consecutive systems. (CDC estimates that there may be approximately 1,696 consecutive
 systems serving a population of 12,850,000 in the 16 states that comprise the 16-State cross-section used
 in this Six-Year Review analysis.) Also, while the Six-Year Review 16-State cross-section (compliance
 monitoring) data does include monitoring results from non-transient non-community water systems
 (NTNCWSs), the CDC does not include NTNCWs in the fluoridation" census.

 In summary, given the differences between the CDC census numbers and the«EPA model estimates,
 rigorous and systematic comparisons cannot be directly made between the two assessments of fluoride
 occurrence in public water systems. However, general  comparisons suggest that the EPA Six-Year Stage
 2 modeling approach is valid in that it tracks relatiyely closely to CDC voluntarily reported qualitative
 census findings. These comparisons are closer still when the underlying differences between the CDC
 census findings and the Six-Year Review model estimates are considered.

 The comparison of the number of systems estimated by the SixjVear model to have an estimated mean
 fluoride concentration greater than 0.7 mg/L compared to the number of systems reporting to the CDC
 census as fluoridating exhibits the largest difference between the two fluoride occurrence assessments.
 However, the two differing estimates are likely much closer when considering that:  the CDC fluoridating
 systems include systems operating with the "control range" (as low as 0.6 mg/L); the Six-Year Review
 estimates did note have data for the Chicago Water; System, and; the Six-Year Review estimates
 generally do not include consecutive systems.

 The comparison between the Six-Year Review model estimates and the unpublished 2000 Census
 numbers for systems with fluoride concentrations above 2 mg/L and 4 mg/L are generally good. For
 example, relative,to.4.mg/L, the Six-Year Review model estimates are not dramatically higher than the
 CDC estimates, especially when comparing the total population served. The EPA system numbers are
 modeled estimates, and therefore, it is appropriate to consider the estimated range of results rather than
 the single "best estimate."  The modeled estimates indicate that from 118,200 people to 301,000 people
 could be served by systems with a mean fluoride concentration greater than 4 mg/L. The CDC estimate
 (of approximately 153,000 people) falls into this range. The other comparisons with the unpublished
 2000 CDC census findings, while not within the statistical model estimate ranges, are relatively similar
 (hot orders of magnitude'apart) given the differences between the two (CDC and EPA) sources of
 information/data; The differences in hundreds of systems or hundreds of thousands of population served
 by systems can be interpreted as somewhat close when considered  relative to the total US population or
 the total US population served by fluoridated water.

 VI.J.2.  SDWIS Comparison

A preliminary comparison of Stage 2 model findings to MCL violation records in the Safe Drinking
Water Information System (SDWIS) was conducted.  Due to many qualifying factors, this must be
regarded as a very general, indirect comparison. A primary reason inhibiting a direct comparison is the
somewhat incomplete State reporting to the SDWIS  database over the time frame of interest (roughly
Occurrence Estimation Methodology
44
                                       March 2002
-------
1993-1999). Also, the method for calculating a contaminant's concentration in a system is somewhat
different for the Stage 2 analysis as compared to MCL violation determinations. A brief description of
some key topics related to MCL compliance information is presented below to provide background on
SDWIS MCL violation data.

For systems that monitor more frequently than annually, compliance with the MCL is determined by a
running annual average of results from all samples taken at each sampling point. If this contaminant
mean concentration exceeds the MCL, then the system is out of compliance. For systems that monitor
annually or less frequently,  if the level of a contaminant at any sampling point exceeds the MCL, the
system is out of compliance with the MCL.                              ^,
                                                                   £?   **'*/'
More systems have MCL exceedances than actual MCL violations. A systejn with anJMCL violation
always has an MCL exceedance. However, a system with an MCL-exceedance may not always incur anic
MCL violation. For example, if a system on quarterly monitoring has one quarter m'whjch the      ,*.,
concentration is above the MCL, but the running annual average of this high sample result and the three
preceding quarters are below the MCL, the system would have an MCL exceedance But not an, MCL
violation.  Also, if the State requires a confirmation sample, compliance with the MCL is calculated
using the average of the routine arid confirmation sample. If the average is below the MCLTthe system
would have an exeeedance  but not an MCL violation.         H-
                                                      ,s           <-                   -
Many States experienced delays in implementation of the Phase II/V rule. In some cases, approval of
State primacy took many years. Laboratory capacity, resource and staffing Jevels, and waivers were
recurring issues. States are required to  report MCL vi|||tlons to SDWIS: However, delays in
determining MCL violations and reporting them to^§l|lS werf commonplace. States had to create new
databases or modify existing databases  for Phasf ff/V compliance trackingjuid reporting. As a result,
many States had delays in reporting chemicaljf iolation data to SDWIS.  Underreporting of violations for
chemicals may still be an issue for some States. SDWIS has the capability of storing data on MCL
exceedances; however, reporting of these is optional.
                                  •~^ir           -,
When comparing the modeled national  occurrence estimates tothe SDWIS MCL violation data, one must
also consider the different time frames at hand. The SDWJ|,MCL violation data are roughly from 1993-
 1999.  The Stage 2 estimate is based'on compliance monfjinng analytical results predominantly between
 1992 and  1997.  (Potentially more than five years'of monitoring results are used to estimate a single
system mean concentration).' TheJStage 2 estimated number of systems with a mean concentration
greater than the MCL (based on data for many years) is an approximation of, though not directly
comparable to, the number of SDWIS ,MCL violations for a single year.
                  j              *fj *,{'
                      ••   „        '-'"'/
Table VI.J.2.a compares the reported SDWIS MCL violations (between January 1, 1993 and December
31, 1999) to the Stage 2,estimates of mean concentration MCL exceedances for beryllium, chromium,
fluoride,,and tetrachloroethylene. tBased on the qualifying factors described above, it is not surprising
that the Stage 2 estimates are higher than the reported SDWIS MCL violations (with the exception of
chromium). Even given the inherent differences between the SDWIS MCL violation records and the
 Stage 2 analytical findings, measured relative to the MCL, the comparison between the two assessments
of occurrence are reasonably comparable, providing additional measures that suggest a validation of the
 Stage 2 modeling approach.
 Occurrence Estimation Methodology
                                              45
March 2002
-------
 Table VLJ.2.a. Preliminary Comparison of Stage 2 Analytical Findings and SDWIS MCL
 Violation Information
Contaminant
(MCL in mg/L)
Beiyllium (0.004)
Chromium (0.1)
Fluoride (4)
Tetrachloroethylene (0.005)
Number of Systems '
SDWIS
MCL Violations
17
9
247
128
Stage 2 Estimates of
Mean Concentration
Greater than the MCL
51 '
3' '*" * '
332'^ .:, , .
132
 vn. CONCLUSION                                     --  ,  '-

 A broad evaluation of regulated contaminant occurrence in public drinking water systems has been
 conducted in support of the Six-Year Review of National Primary Drinking Water Regulations. Safe
 Drinking Water Act compliance monitoring analytical results reported to the States provided the
 occurrence data used in the occurrence estimates.  Statffwere evaluated through a methodology that
 included a ranking of States' based on measures pfpcjllutibn potential, dividing States into quartiles
 based on these rankings, and then selecting Statet-that equally -represent the four pollution potential
 quartiles. By also considering geographic distribution of the selected States, a "cross-section" of States
 was selected to reflect a national representation of pollution potentialsand climatic/hydrologic
 differences.                           f:       . ir        I"""-1

 The analyses presented in this report are based on compliance monitoring data from the 16 selected
 cross-section States, which include:  Alabama, California, FJprida, Illinois, Indiana, Kentucky, Michigan,
 Montana, Nebraska, New Jersey, New Mexico; Oregon; fSbuth Carolina, South Dakota, Texas, and
 Vermont. These data have undergone extensivf quality review and editing, including discussions with
 State data management staff This Instate national Cross-section represents the largest compliance
 monitoring .data set compiled to date by the USEPA.

 The 16-State cross-section contains compliance monitoring data for the following: 5 inoiganic
 contaminants with occurrence data from approximately 18,000 to 21,000 public water systems
 (depending oh the particular contaminant) that serve an approximate total  of 105,000,000 people; 15
 synthetic organic contaminants with occurrence data from approximately 8,000 to 14,000 public water
 systems .(depending on the particular contaminant) that serve an approximate total of 90,000,000 people,
 and; 10 volatile organic contaminants with occurrence data from approximately 19,000 to 23,000 public
 water systems (depending on the  particular contaminant) that serve an approximate total of 106,000,000
 people. For comparison, the total number of (non-purchased) public water systems nationally is
 approximately 65,000 and the total population served by these public water systems is approximatelv
 213,000,000.                                                                        '      J

 A two stage occurrence assessment approach was developed to evaluation the assembled 16-State cross-
 section occurrence data.  The first stage of analysis (Stage 1) provides a straight-forward, non-parametric,
 and preliminary assessment of occurrence.  The primary Stage 1 measure is a simple statistical count
 (and calculation of the percentage) of PWSs with at least one analytical result that exceeds a specified
 contaminant concentration threshold. These initial statistics were developed for each contaminant
 according to water system source water type.
Occurrence Estimation Methodology
46
                                                                                      March 2002
-------
For the second stage of analysis (Stage 2), a Bayesian-based hierarchical model was developed for use to
generate detailed, stratified national occurrence estimates from the 16-State cross-section data. This
statistical estimation method has been peer-reviewed, has been assessed relative to another drinking
water contaminant occurrence estimation method (the Regression on Ordered Statistics, ROS), and has
been evaluated with simulated data sets designed to assess the impact of the log-normal, as well as the
constant variance, assumption made on the system level regarding the national distribution of system
means.

All model assessments suggest the Bayesian-based hierarchical model used for the occiurence
estimations in this report is appropriate. The peer-review generally supported the use and application of
the model. Compared to the Regression on Ordered Statistics/ROS (part of ttie simulated data study), the
Bayesian-based model estimates system means that are closer to the true system Jt|eans of the simulated
data sets.  The simulated study also showed that the assumption^o£ log-normal contaminant distribution
does not have an undue influence on the estimate of the national 'distribution of system means. When the
log-normal assumption is not used, the estimated national distribution has^a slightly laiger variance,""
which may result in an overestimate of the exceedance probabilities. The detailed evaluations of the
Bayesian-based model suggest that the occurrence estimations, based*on the 16-State cross-section of
public water system compliance monitoring, are valid.
Occurrence Estimation Methodology
                                               47
March 2002
-------
                                         References
 Cadmus. 2000. First Stage Occurrence and Exposure Report for Six-Year Review. Draft report
               submitted to EPA for review May 12, 2000.

 Center for Disease Control and Prevention (CDC). 1992. Fluoridation Census 1992.  Atlanta, GA:
               Centers for Disease Control and Prevention, Public Health Service, U.S>.' Department of
               Health and Human Services.
                                                           /;          f .-~   ,
 Center for Disease Control and Prevention (CDC). 2002. WrittenScomments {including information
               from the unpublished Fluoridation Census 20(0ji&om CDC staff to OGWDW staff,   :
               January 8,2002.
                                                                  /                       '
 Hall, B.3 and M.L. Kerr.  1993. 1991-1992 Green Index: A State-By-State Guide to the Nation's -
               Environmental Health. Washington, DC: Island Press,.

 Helsel, D.R., and Cohn, T.A. 1988. "Estimation of Descriptive Statistics for Multiply Censored Water
               Quality Data." Water Resources Research, 24,' 199T-2004.

 Helsel, D.R., and Gilliom, R.J. 1988. "Estimation of Distributional Parameters for Censored Trace
               Level Water Quality Data. 2. Verification andNApplications." Water Resources
               Research, 24,  147-155.          *-."_,

 Lockwood, J.R.  HI, MJ.  Schervish, P. Gurian, and M,, J.  Small. 2001. "Characterization of Arsenic
               Occurrence in US Drinking Water Treatment Facility Source Waters (Revised Version).
               accepted by Journal of the-American StatisticaljAssociation (March 2001).

 Porter, P., R.C. Ward and H.F.  Bell. 1988.  Environ. Sci. Technol. v.22, pp. 856-61.

 Qian, S.S., C.A.  Stow, and M.E. Borsuk. 2001. 0n Monte Carlo Methods for Bayesian Inference.

 Squillace, P.J., MJ. Moran,W.W  Lapham, C.V: Price, R.M. Clawges, and J.S. Zogorski. 1999.
               "Volatile Organic Compounds in Untreated Groundwater of the United States, 1985-
           '   1995."'Environ. Sci. Technol,  v.33, no.  23, pp. 4176-4187.

 Travis, CC. andMJL Land.  1990.  Estimating the mean of data sets with nondetectable values.
              Environ, Sci. .Technol. v.24, no. 7, pp.  961.

 U.S. Department of Commerce (USDOC), Bureau of the Census. 1994. 1992 Census of Agriculture.
              Washington, D.C.:  U.S. Government Printing Office.

 USDOC, Bureau of the Census. 1997. 1995 Annual Survey of Manufactures. Washington, D.C.: U.S.
              Government Printing Office.

 USDOC, Bureau of the Census. 1996. 1992 Census of Manufactures. Washington, D.C.:
              U.S.Government Printing Office.

U.S. Environmental Protection Agency (USEPA). 1999. A Review of Contaminant Occurrence in
              Public Water Systems. EPA Report # 816-R-99-006, Office of Water, 78 pp.

USEPA. 2000a. Methods, Occurrence, and Monitoring Document for Radon in Drinking Water.  EPA
              Office of Ground Water and Drinking Water.
Occurrence Estimation Methodology
48
                                                                                    March 2002
-------
USEPA. 2000b.  Arsenic Occurrence in Public Drinking Water Supplies. EPA Office of Ground Water
              and Drinking Water.

USEPA. 2000c.  Water Industry Baseline Handbook, Second Edition (Draft). March 17.

USEPA. 2001. TRI Explorer (Data from 1988-1995). Available on the Internet at:
              http://www.epa.gov/triexplorer/chemical.htm (Last modified October 4,2001).
Occurrence Estimation Methodology
49
March 2002
-------
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-------
 Occurrence Estimation Methodology and Findings - DRAFT
 Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
Six-Year Review
     Detailed Description of the Stage 2 Bayesian-Based Hierarchical Model

      The Hierarchical Modeling Approach for Estimating National Distributions of
                  Contaminant Concentrations in Public Water Systems
 I.  INTRODUCTION

 The goal of this analysis is to estimate contaminant occurrence in public water systems (PWSs)        a
 nationally by estimating system mean contaminant concentrations, as well as the probability that those
 estimated system means will exceed specified health thresholds. However, it is difficult to measure  r "
 contaminant occurrence in drinking water because concentrations are generally quite low. As a result,
 concentration values below the Minimum Reporting Level (MRL) are common.  (The Minirniirh
 Reporting Level is the lowest level that can be reliably achieved, within specified limits of precision and
 accuracy under routine laboratory operating conditions.) When a concentration is below the MRL (a
 "non-detection"), the exact concentration value is only known to be less than that specified MRL. When
 the underlying probability distribution of the contaminant concentration is of interest, a non-detection
 contributes less information than an exactly measured value (a "detection") does. Nevertheless, it has
 information that cannot be disregarded when estimating the probabilistic distribution parameters.

 Historically,  many different methods have been used for estimating distribution parameters when non-
 detection data are present. The simplest method is to replace  all non-detection values by a specific
 number (e.g., zero, Vz the MRL, or the MRL). However, this substitution method is unreliable, since it
 likely underestimates occurrence (when zero is used) and likely overestimates occurrence (when !/2 the
 MRL or the MRL is used).

 Alternatively, Gilliom and Helsel (1986) and Helsel arid Gilliom (1986) proposed a regression on
 ordered statistics (ROS) method for estimating the mean and variance of a log-normal distribution. The
 ROS method  is based on the fact that a straight line is formed  when plotting the quantiles of a normally
 distributed random variable (with mean m and variance s2) against the same quantiles of a standard
 normal random variate. The intercept of the line is m and the  slope of the line is s.  ROS  was the method
 used by the Environmental Protection Agency (EPA) to estimate PWS mean concentrations of arsenic in
 drinking water (USEPA, 2(JOOa).

 Another frequently used method for estimating distribution parameters of data containing non-detection
 values is the maximum likelihood estimator (MLE).  As in the conventional MLE, the likelihood of a
 detection (a value above the MRL) is the corresponding density value. For a non-detection, the
 likelihood is evaluated as the probability of observing a value  that is less than the MRL, or the
 cumulative density of the MRL.  For a given family of probability distributions, both the probability
 density and the cumulative density can be (in principle) explicitly expressed as a function of the
 probability distribution parameters. By assuming observations are independent random samples from the
 same distribution (or Independently, Identically Distributed, i.i.d.), the likelihood function is the product
 of the likelihoods of all observations. The MLE is the estimator that maximizes the likelihood function.
However, the  presence of non-detections makes computation of the MLE more difficult.  A commonly
used computational method is the Expectation-Maximization (EM) algorithm (Tanner, 1991). The MLE
-------
Occurrence Estimation Methodology and Findings - DRAFT
Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
                                                                                    Six-Year Review
method was used in EPA's radon analysis to generate system mean concentration values (USEPA,
2000b).

Because both the ROS and MLE methods assume observations are i.i.d., when used for estimating the
national distribution, it is necessary to apply both methods separately for each PWS, since it is a
reasonable assumption that the contaminant concentration distribution varies from systemic system.
Those separately estimated system means are then pooled to form the national distribution of system
means.  Separately estimating distribution parameters for each PWS may lead to a biased estimate of the
national distribution of system means, because (1) uncertainty of the estimated system means varies from
system to system due to differences in sample size and other factors; systems with a large sample size  |*
will have much less uncertainty than systems with a small sample size and (2) systems yitith a large   jr
number of non-detection values may be excluded since their distribution parameters may not be.  ;.  '
adequately estimated, which will result in over-estimate of the contaminant mean concentration.' In
addition, because the national distribution of system means is the primary target, it is less'firiportant
whether the distribution parameters for each system can be estimated or not.
                                                                   ?
                                                                   i
Drinking water contaminant occurrence data exhibit a hierarchical structure. In other words, it is
possible to imagine that there is a "super" probability distribution that governs the mean concentrations,
as well as the variance, of PWSs in the United States. These  means and variances determine the
magnitude and spread of contaminant concentrations observed from each system.  This national
distribution is on the top, which generates a series of system distributionsj^af concentration values. Thus,
the data can be seen as having a two level structure: the top level is the national distribution, and the
bottom  level is the collection of system distributions.  When analyzing hierarchically structured data, a
hierarchical modeling approach is preferred (Gelman  et al., 1995). This appendix presents a hierarchical
model for estimating the national distribution of system mean contaminant concentrations.  The model is
inherently Bayesian because (1) the^rnean concentration of an unknown system is treated as a random
variable and (2) (non-informative) prior distributions  for all parameters are used in the numerical
procedure.
II. METHOD

Bayesian methods are currently experiericing an increasing popularity in the sciences as a means of
probabilistic inference (Malakoffj 1999). Among their advantages are the ability to incorporate prior
information, the ease of incorporation into a formal decision analytic context, the explicit handling of
uncertainty, and the straightforward ability to assimilate new information in contexts such as adaptive
management.  In some problems, a Bayesian approach has been shown to lead to very different
conclusions than a classical approach (Ludwig, 1996; Al-Khatib et al., 2001). Introduction to Bayesian
statistics and decisiotftheory can be found in Box and Tiao (1973) and Bernardo and Smith (1994).

Under the Bayesian paradigm, random variables are inferred by using probability distributions. Since
distributions have unknown parameters, it is necessary to infer the distributions of parameters at many
levels. If linkages among the data at various levels in the hierarchical structure can be assumed, than
information at the various levels can be used to support the parameter estimation at higher levels, or
within the same level. Such hierarchical thinking helps  in understanding multiple parameter problems,
and also plays an important role in developing computational strategies.
-------
 Occurrence Estimation Methodology and Findings - DRAFT
 Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
Six-Year Review
 Perhaps even more important in practice is that non-hierarchical models are usually inappropriate for
 hierarchical data: with few parameters, they usually cannot fit large data sets accurately, whereas with
 many parameters, they tend to "overfit" such data in the sense of producing models that fit the existing
 data well but lead to inferior predictions for new data. In contrast, hierarchical models can have enough
 parameters to fit the data well, while using a population distribution to structure some dependence into
 parameters, thereby avoiding problems of overfitting. Details of the Bayesian-based hierarchical
 modeling approach can be found in Gelman, et al. (1995) and Congdon (2001)^

 The model is based on the assumption that each contaminant concentration distribution at the system
 level can be approximated by a log-normal distribution. The national distribution is then estimated as a
 mixture of system distributions. The model is summarized in Equation 1:
                                                                                  (i)
                                     Gamma(Q.Q 1,0.01)
 where jfyt is the £* observed concentration value (in Iogarithm0rom system i, in strata/, ju/j is the mean
 and T, is the precision (or the inverse of variance, l/o2). The4otation I(,S) indicates the corresponding
 concentration value is less than S or nbn-detectionii;I?or Detection, S is set to be infinity. The mean n,
 is modeled as the sum of three normal random variables, representing the grand mean (//), the strata
 adjustment (c0, and the system adjustment (by). The prior distributions p, ap and b,j are normal
 distributions with mean 0 and unknown variances.  By selecting a widely dispersed prior distribution for
 the precision parameters (Gamma (0.01, 0.01), the prior distributions used here are essentially flat and
 non-informative.

 The objective of the model is to estimate the posterior distributions of/*, ap bip and TJ. It should be noted
 an dpriori constant precision TJ is used. This constant variance assumption is necessary because many
 systems in the data have only one observation. However, this prior constant variance assumption will
 not result in a constant posterior variance for all systems.  This is because the mean fia is modeled as a
 random variable. In another words, the posterior distribution of yijk is estimated by:
where nfjt&Y) and ^(T,|?) are the posterior distributions of the system mean and precision, respectively.
Unless two systems have exactly the same posterior distribution of the mean, two systems will have
different posterior variance.  This setting will also result in the separation of .between and within system
variances. In addition, by modeling the mean as another normal random variable, the resulting log-
concentration distribution is more robust against unusually large concentration values.
-------
Occurrence Estimation Methodology and Findings - DRAFT
Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
                                                                                    Six-Year Review
Intuitively, a two-level statistical model is built, reflecting all the sources of variability and uncertainty.
The lower level features the observed concentration values (both detections and non-detections). Those
observed log concentrations are treated as though they come from a normal distribution. When the
concentration value is below the MRL, its value is uncertain and is imputed based on the fact that the
value is known to be below a given value (i.e., below the MRL). The upper level features those (for the
most part, completely uncertain) features of the model that govern groups of or perhaps alljbf the
observations, about which information may be learned by pooling the evidence from many observations
at thousands of PWSs. The upper level of the model uses widely-dispersed normal distributions to
model fj, a/, and bip and widely-dispersed gamma distribution to model t, to reflect broad uncertainty
about them.
                                                                                              '. :f
A Markov chain Monte Carlo simulation (MCMC) method (Gilks, et al.,,1996) is used for  -
simultaneously estimating the distribution parameters by sampling the parameters from their joint
posterior distribution. The MCMC is implemented using a freely  available software WinBUGS
(Spiegelhalter, et al., 1996). The national distribution, as well as the probabilities of exceeding certain
thresholds, are estimated in the same Monte Carlo simulation.  The MCMC method allows the sampling
of fly and TI from their joint posterior distribution.

Since the PWSs included in the 16-State cross-section data set are a representative sample of PWSs
nationally, the system means estimated for these systems are considered to be a sample from the national
system mean distribution.  (Since it is assumed that the concentration values follow a log-normal
distribution at the system level, the arithmetic system mean, m,j, is calculated from the generated log-
normal mean/4, an^ variance T,, i.e., /w,y |= fecpC^//+ OjS/T,].)  For each set of system mean concentrations,
an empirical cumulative distribution fujfetibn (CDF) of the national distribution, as well as probabilities
of system mean concentrations exceeljprtg certain thresholds, can be estimated.  By repeated sampling of
the system means, there exists many empirical cumulative distribution functions (CDFs) of the national
distribution and many estimates of the exceedance probabilities. These empirical CDFs are used to
summarize the national distribution, as well as the uncertainty about the distribution. Note that the
estimated means and variances are based on log-transformed concentration values. Thus, it is necessary
to obtain the'system means in the original metric.

Comparing the samples of system means to a threshold value, many samples of the proportion  of systems
with a mean concentration value exceeding the threshold are obtained. (These proportions  are  samples
of the probability of a system niean exceeding the threshold.) If the MCMC process produces 500 pairs
of random samples of /^and T£'there exists 500 empirical  CDFs of the national distribution, 500 random
samples of the arithmetic system mean, and hence, 500 exceedence probabilities for each threshold.
From these 500 probabilities, the mean, median, and the 2.5th and 97.5th percentiles (or the 95% credible
interval) can be calculated to summarize the uncertainty on the quantity.

It is worthwhile to discuss the method of presenting uncertainty used by a Bayesian. The Bayesian
method treats an unknown parameter as a random variable. The uncertainty of the parameter is reflected
in the estinfated posterior distribution.  This posterior distribution  is a combination of uncertainty about
the data, the prior knowledge, and maybe the model. A 95% credible interval is interval between the
2.5th and 97.5th percentiles of the posterior distribution. This interval may or may not include the mean,
depending on the skewness of the posterior distribution.  In other words, the credible interval is not an
interval of the mean (such as the frequentist confidence interval).  For some extremely skewed  posterior
distributions, it is quite possible that the Monte Carlo estimated 2.5th and 97.5th percentiles are the same.
-------
 Occurrence Estimation Methodology and Findings - DRAFT
 Appendix B.  Detailed Description of the Stage 2 Bayesian Hierarchical Model
Six-Year Review
 For example, the several estimates of the probability of system mean exceeding a given threshold have a
 lower 90% credible bound of zero, as well as an upper 90% credible bound of zero.  This is because the
 posterior distribution of the probability is evaluated by Monte Carlo samples and at least 95% of the
 samples are equal to zero. Under such a situation, one should conclude that the chance is less than or
 equal to 5% to have an exceedence probability that is larger than zero.
 III. EVALUATION OF THE MODEL

 Various tests were performed to evaluate the proposed model.  A simulation study, conducted with six /
 simulated data sets, was designed to explore the impact of the log-normal, asvwell as the constant
 variance, assumption made on the system level. In addition, the Bayesian hierarchical modeling
 approach was compared to the ROS plotting position method.

 The six synthetic (or simulated) data sets were divided into three groups. The first group emphasized the
 comparison of the Bayesian and ROS methods.  The second group of the simulated data sets were
 generated to evaluate the constant variance assumption.  Finally, the third group of simulated data sets
 tested the impact of a log-normal  assumption at the system level on the national distribution of system
 means.                                               J" ^          -

 The ROS method was compared to the Bayesian-based model by applying both methods to a series of
 synthetic data sets. The two synthetic data sets in the first group were constructed to represent both a
 high and low information case. The high information case was modeled after the fluoride data set, where
 approximately 80% of the total observations were detections. The low information case was modeled
 after the thallium data set, where only about 2%,of the total observations were detections.

 The fluoride-like and thallium-like data sets were generated,  each containing the same number of PWSs
 and the same number of observations per PWS, as contained  in the actual 16-State cross-section data set
 for fluoride and thallium, respectively. A number of system means were generated from a log-normal
 distribution.  These means, along with a constant variance, were used to generate a number of log-
 concentration values for each system. These generated log-concentration values were censored (i.e.,
 considered non-detections) at a fixed value: log(0.11) for the fluoride-like data and log(0.001) for the
 thallium-like data. This operation resulted in about 25% of the values below MRL of 0.11 for fluoride,
 and almost 90% of the values below the MRL of 0.001 for thallium.  The system means of the simulated
 high information data sets were generated to approximately followed a log-normal distribution, A^-1.15,
 1.33), while the system means of the simulated low information data sets were generated to  •
 approximately followed a log-normal distribution, N(-10, 2.4).

 The second group of the simulated data sets were generated to evaluate the constant variance assumption.
 It is worth mentioning that although a constant variance was used to specify the model, the constant
 variance 5s the Bayesian prior model specification.  However, the posterior variance of each system is not
 necessarily the same for all systems. However, two simulated data sets were produced to evaluate the
 constant variance assumption. Again, one data set was modeled after the 16-State fluoride data and the
 other modeled after the 16-State thallium data. The system means were generated in the same way as in
the first group and the system variance were generated from an inverse gamma distribution.
-------
Occurrence Estimation Methodology and Findings - DRAFT
Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
                                                                                    Six-Year Review
The third group of simulated data sets tested the impact of a log-normal assumption at the system level
on the national distribution of system means. Instead of using a normal distribution to generate log-
concentration values for each system, two other distributions were used: (1) a Weibull distribution and
(2) a 50-50 mixture of log-normal and Weibull distributions. The Weibull distribution was chosen
because it is a feasible probability distribution for water quality data and it has the largest tail area
difference from the log-normal distribution (Ott, 1995). Both data sets were modeled after the 16-state
fluoride data. Again, a log-normal distribution was used  to generate the mean and an inverse gamma
distribution was used to generate the variance for each system.  The mean and variance were used to
calculate the scale parameter of the Weibull distribution.  The shape parameter was^fixed at 2, which
resulted in a skewed distribution.                             ,            *                      /;

Tables  1-3 summarize the six synthetic data sets.  Table 1 presents general summary statistics describing
each of the six synthetic data sets. The simulated system  means and variances for each data set are
described Tables 2 and 3, respectively.
Table 1.  Summary Statistics of the Six Synthetic Data Sets
High/Low
Information
High
Low
High
Low
High
High
Distribution
Assumption
Constant
Variance
Constant
Variance
Variable
„ Variance
Variable
Variance
Weibtill
Mixed
Distribution
Minimum
0.11
0.001 .
,;o.n
n
?
0.00 1
0.11
OJ 1
25th
Percentile;
~v
0.2389
;0.00163
0.2317
,0.001618
0.2422
0.2502
Median
0.4668
0.002975
0.4339
0.002989
0.4659
0.4892
Mean
i
0.9881
0.01554
0.8627
0.02073
0.9 i49
0.9744
75*
Percentile
1.019
0.007449
0.9282
. 0.007388
0.9735
1.041
Maximum
66.98
6.179
88.45
35.92
47.79
69.87
%
Non-
Detections
20.3%
86.4%
20.0%
87.6%
19.2%
19.0%
 Table 2.  Summary Statistics of Simulated System Means
High/Low
Information
High
Low
Distribution
Assumption
Constant
Variance
Constant
Variance
Minimum
-5.698
-20.12
1st Quarter
-1.94
-11.6
Median
-1.156
-9.981
Mean
-1.159
-9.993
3rd Quarter
-0.3816
-8.375
Maximum
2.959
0.2593
-------
 Occurrence Estimation Methodology and Findings - DRAFT
 Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
Six-Year Review
High/Low
Information
High
Low
High
High
Distribution
Assumption
Variable
Variance
Variable
Variance
Weibull
Mixed
Distribution
Minimum
-5.323
-19.26
0.00158
0.003666
1st Quarter
-1.941
-11.59
0.184
0.185
Median
-1.17
-9.984
0.4022
0.4026
Mean
-1.152
-9.994
;;;>. 0.7867
0.7896
3rd Quarter
-0.3642
-8.378
0.8839
0.8829
Maximum
3.356
-1.279
31.72
; 34,3,8!-"
 Table 3. Summary Statistics of Simulated System Variances
High/Low
Information
High1
Low1
High
Low
High
High
Distribution
Assumption
Constant
Variance
Constant
Variance
Variable •
Variance
Variable
Variance
Weibull
Mixed
Distribution
Minimum


0.04
0.32
0.001
0.002
1st Quarter


0.16
1.33 X
0.10
0.10
Median
'0-49
: 2.25
0.21
> 1.86
0.21
0.21
Mean;^*:;-
'--!,-_..,•

0.24
2.20
0.41
0.41
3r?l Quarter


0.28
2.66
0.46
0.46
Maximum


1.91
20.81
16.58
17.97
 1. These two data sets have a constant variance. Therefore, summary statistics, other than the median, could not be generated.
Simulation results are presented in Figures 1 - 6. The national distribution estimated by the Bayesian-
based hierarchical model was almost identical to the true distribution (Figure 1), while the ROS plotting
position method yielded a distribution with slightly larger variance and smaller median. Although the
ROS plotting method yielded an estimate that was very close to the true CDF, the ROS method is unable
to quantify the uncertainty in the estimated CDF. When the log-normal distribution was used at the
system level, results similar to Figure 1 were obtained.  (These results, however, are not shown.) A
numerical summary of the  simulated results is riot presented since the graphical presentation clearly
indicates that the Bayesian-based model tracks most closely to the true distribution. In addition, the
assumptions of log-normality and constant variance made in the model do not appear to influence the
results.
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Occurrence Estimation Methodology and Findings - DRAFT
Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
                                                                                    Six-Year Review
Figure 1. High Information-Constant Variance Synthetic Data Set
                                      Run 2.9: Fluoride,
                    Bayes Mean
                    Bayes Cl
                    Empirical CDF
                    Empirical Bounds
                    True CDF
                    ROS
                                                                                10
                                         Concentration (mg/L)
-------
Occurrence Estimation Methodology and Findings - DRAFT
Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
Six-Year Review
Figure 2. Low Information-Constant Variance Synthetic Data Set
                                       Run 9.9: Thallium,
                        Bayes Mean
                        Bay'es Cl
                        Empirical CDF
                        Empirical Bounds
                        True CDF
                        ROS
            1e-009
                    16-008
                             1e-007
                                     1e-006
                                             le-005
                                                     0.0001
                                                              0.001
                                                                      0.01
                                          Concentration (mg/L)
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Occurrence Estimation Methodology and Findings - DRAFT
Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
                                                                                         Six-Year Review
Figure 3.  High Information-Variable Variance Synthetic Data Set
                                         Run 2.95: Fluoride,
0.999


0.990
   •§  0.900

   CL
   0)  0.75-0


   -§  0.500

   E
   Q  0.250
   «*—
   2  0.100
   •g  O.OSfl

   ol
       0.01«
       o.oot
           0001
                          Bayes Mean
                          Bayes Cl
                          Empirical CDF
                          Empirical Bounds
                          True CDF
                          ROS
                              001
                                                                   T
                                          0.1                 1


                                      Concentration (mg/L)
                                                                                      10
                                                   10
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Occurrence Estimation Methodology and Findings - DRAFT
Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
                                                                 Six-Year Review
Figure 4. Low Information-Variable Variance Synthetic Data Set
       0.999
       0.990
   •8  0.950

   •§  0.900
                                       Run 9.95: Thallium,
	 Bayes Mean
	 Bayes Cl
	 Empirical CDF
	Empirical Bounds
	 True CDF
	ROS
               16-009    1e-008    1e»007    1e-006
                                               1e-005
                                   T	:—T
                                  0.0001    0.001
                                                                        0.01
                                           Concentration (mg/L)
                                                11
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Occurrence Estimation Methodology and Findings - DRAFT
Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
                                                                                      Six-Year Review
Figure 5. High Information-Weibull Distribution Synthetic Data Set
                                      Run 2.96: Fluoride,
                        Bayes Mean
                        Bayes Cl
                        Empirical CDF
                        Empirical Bound
                        True CDF
                        ROS
          0001
                                          Concentration (mg/L)
                                                 12
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Occurrence Estimation Methodology and Findings - DRAFT
Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
                                                         Six-Year Review
Figure 6. High Information-Mixed Distribution Synthetic Data Set
      0.999
      0.990
  ro   °-9SO
  •g   0.900
                                      Run 2.99: Fluoride,
Bayes Mean
Bayes Cl
Empirical CDF
Empirical Bounds
True CDF
ROS
               0,001
                                0.01
                                                 0.1
                                         Concentration (mg/L)
                                               13
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Occurrence Estimation Methodology and Findings - DRAFT
Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
                                                                                    Six-Year Review
The second evaluation of the proposed model involved a test of the assumption of log-normality.  This
assumption was tested using the 16-State fluoride data set.  While the log-normal distribution is
commonly used in analyzing environmental data and one can argue its adequacy on both empirical and
physical basis (Ott, 1995). It is, however, an assumption that is rarely tested. A mixture of two normal
distributions was used at the system level to determine whether a better model can be found without
using log-normal distribution at the system level. In other words, the first line of equation.(l) was
replaced by:
where 0 
-------
 Occurrence Estimation Methodology and Findings - DRAFT
 Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
                                             Six-Year Review
 Figure 7. Mixture of Normal Distributions Model

     E
    QL
    3
    o
                        <- 18033 (of 93062)censored
                        0.001
0.01            0.1

   Concentration (mg/L)
This graphical comparison is favorable since the four CDFs converge at higher concentration values
where non-detection values are less likely to occur. Since the substitutions occur at the lower end of the
distribution, the differences among the four CDFs, therefore, appear at the left tail of the distribution.
When examining the MRLs, it is important to note that the majority of the MRL values are equal to 0.1
mg/L. This is reflected in the figure as the widest gap between the model estimated CDF and the 1-line.
The second most occurring MRL value is 0.2 mg/L, where the 1-line diverted from the model estimated
CDF slightly. As expected, the estimated CDF is bounded by the 0- and 1- lines, and is close to the 0.5-
line.

Table 4 presents a comparison of selected percentiles of the estimated national distribution, based on
model prediction, to three empirical CDFs, based on the substitutions.  As expected, the difference
between the model predicted and the empirical percentiles are mainly in the lower half of the
distribution.
                                               15
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Occurrence Estimation Methodology and Findings - DRAFT
Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
                                                                                       Six-Year Review
Table 4.  Comparison of Selected Percentiles (mg/L) of Five Estimated National Distributions of
System Mean Fluoride Concentrations
Estimated
National
Distribution
Low1
Middle 2
. High3
Mixed 4
Model Prediction
5th
Percentile
0
0.05
0.10
0.03
0.05
10th
Percentile
0
0.05
0.10
0.05
0.07
25lh
Percentile
0.08
0.10
0.13
0.13
0.13
50lh
Percentile
0.21
0.23 ,/vj;
0.2|?'
0.30
0.27
75th
Percentile
0.59
0.607 f -
0.60 '
o:?4
0.60
90th
Percentile
LID
1.10
'/' 1.10
LSI
1.11
95th
Percentile
1.68
1.68
1.68 $?
2.34
1.57
 1.  The "low" estimated national distribution was calculated from system means where all non-detection values were substituted with zero.
 2.  The "middle" estimated national distribution was calculated from system means where all non-detection values were substituted with 1/2 the
 modal MRL.
 3.  The "high" estimated national distribution was calculated from system means where all non-detection values were substituted with the
 modal MRL.
 4.  The "mixed" estimated national distribution was calculated using a mixture of t*o normal distributions at the system level.
                                                        *                                           '

 In conclusion, both the simulated study and the mixtureimodel indicated that the Bayesian-based
 hierarchical model used for the study is appropriate. The simulated study showed that the prior
 assumptions about the contaminant distribution do not have an undue influence on the posterior estimate
 of the national distribution of system means.  The mixture model study showed that using a log-normal
 distribution at the system level is appropriate. When the log-:normal assumption is  not used, the
 estimated national distribution has a slightly larger Variance, which may result in an overestimate of the
 exceedance probabilities.

                     /
 IV. NATIONAL DISTRIBUTIONS OF 15 CONTAMINANT CONCENTRATIONS
                      •*.»
                      3     -
 The estimated.national distributions of system means are presented in Appendix D  for 15 select
 contaminants. Similar to Figure^, each figure includes the estimated CDF (the median and the 90%
 credible interval), the detected observations, and the various health thresholds for which the probabilities
 of exceedance are estimate!!; AJso presented for each contaminant are the estimated probabilities of
 system mean concentratiort^exceeding each threshold (along with their corresponding 90% and 95%
 credible intervals).  The,se?probabilities are estimated for 10 different types of systems classified based
 on source water type and population served size category.

 Most of the contaminant occurrence data have a very high rate of non-detections. Therefore, no
 statistical, method can result in unbiased estimate of the national distribution.  However, the objective of
 the project is to estimate the percent of PWSs with a mean concentrations above specified health
 thresholds. It is, therefore, important to evaluate the accuracy of these probabilities.  As demonstrated in
 the evaluation presented  in Section III, the estimated distribution percentiles are very close to the same
 percentiles of the actual observations when the concentration values are above the MRL.  In other words,
                                                  16
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 Occurrence Estimation Methodology and Findings - DRAFT
 Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
Six-Year Review
 one should have confidence in the portion of the estimated cumulative distribution containing detections.

 A large number of non-detections can certainly make the estimated probability distribution unreliable.
 However, a large number of non-detections can also indicate a strong confidence on the low probability
 of a system mean exceeding the MRL.  In this regard, when evaluating the uncertainly of the estimated
 probabilities of threshold exceedance, the specified thresholds and the relevant MRLs shpuld be
 compared. If the MRLs are well below the threshold of concern, the uncertainty on the probability will
 be small. The CDF plots presented in Appendix D show that thresholds for all contaminants are well
 above their respective MRLs.  As a result, estimates of the exceedance probabilities can be regarded as
 reliable. With the exception of fluoride, which has a non-detection rate of 21%, the remaining 14
 contaminants have non-detection rates above 90%, including 2 contaminants with non-detection rates
 between 90% and 92%, 2 contaminants with rates between 97% and 98%, and 10 contaminants with
 rates close to 99.9%.
 V. DISCUSSION

 There are three advantages of using the hierarchical modeling approach in this study. First, the log-
 normal assumption has much less of an impact on the final estimate of the national distribution. This can
 be explained in two levels: (1) The national distribution is expressed as a mixture of many log-normal
 distributions, and the resulting national distribution is not subject to the log-normality assumption.  This
 flexibility makes the model prediction more realistic; (2) At the system level, the log-normality is
 conditional on the system mean, and the system mean is modeled as a sum of two random variables. As
 a consequence, the log-normal assumption at the system level is also relaxed.

 The second advantage of the hierarchical approach is the relatively light computational burden. This is
 because the hierarchical model produces the national distribution in one model run, while for the ROS
 plotting position method to be used properly, mean concentration distribution for each water supply
 system has to be estimated separately.

 The third advantage of using the hierarchical modeling  approach is its Bayesian feature that allows
 combining information from all systems. This is a desired feature because not all the water supply
 systems have the same amount of data and some systems have all measurements below the MRL. As a
result, if the national distribution were estimated based  on individual system distributions as in the ROS
plotting position method, uncertainty in estimated individual system distributions would vary
significantly.            ,
                                              17
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Occurrence Estimation Methodology and Findings - DRAFT
Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
                                                                                  Six-Year Review
                                        REFERENCES

Al-Khatib, S., R.M. Califf, V. Hasselblad, J.H. Alexander, D.C. McCrory, and J. Sugarman. 2001.
       Placebo-Controls in short-term clinical trials of hypertension. Science, 292:2013-2015.

Bernardo, J.M.  and A.F.M. Smith.  1994. Bayesian Theory. Wiley, West Sussex, England.

Box, G.E.P. andG.C. Tiao.  1973. Bayesian Inference in Statistical Analysis, Afddisori-Wesley,
       Reading, MA.                                     „_,,.         ^4 ~  -  ;
                                                        ^v             '   " ~t
Congdon, P., 2001.  Bayesian Statistical Modelling. Wiley, West Sussex, Erigland. -

Ferguson, T.S., 1983. Bayesian density estimation by mixtures'of normal distributions, In. Recent
       Advances in Statistics: Papers in Honor of Herman Cherndffon His Sixtieth Birthday.
       Academic,  New York, pp:287-302.
                                                       *" /
Gelman, A., J.B. Carlin, H.S. Stern, and D.B. Rubin. 1995. Bayesian Data Analysis.  Chapman & Hall,
       London.
                                                       •"            » •?                  "
Gilks, W.R., S. Richardson, and D.J. Spiegelhalter, 1996. Markov Chain Monte Carlo in Practice.
       Chapman & Hall, London.          _> -'         *   / ~  ,
                                        j&?<:-        ' -£   ''""-'~  ^   5«
Gilliom, R.J. and D.R. Helsel.  1986. Estimation of distribution |afameters for censored trace level water
       quality data 1: estimation techniques. Water ResourcesJResearch. 22:135-146.
                                                       ,f
Helsel, D.R. and R.J. Gilliom.  1986.  Estimation of distribution parameters for censored trace level
       water quality data 2: verification and applications. Water Resources Research. 22:147-155.
                            ^               "~
                            * &''%'                ^
Ludwig,  D. 1996. Uncertainty and the assessment of extinction probabilities. Ecological Applications, 6:
        1067-1076.

Malakoff, D.M. 1999. Bayes/offers "new" way to make sense of numbers. Science, 286: 1460-1464.

Ott, W.R. 1995. Environmental Statistics and Data Analysis. Lewis Publishers, Boca  Raton.

Spiegelhalter, D.J., A. Thomas;-N. Best, and W.R. Gilks. 1996. BUGS 0.5: Bayesian  inference Using
       Gibbs Sampling Manual. Medical Research Council Biostatistics Unit, Institute of Public
       Health, Cambridge, UK.

Tanner, M.A., 1991 /Tools for Statistical Inference: Observed Data and Data Augmentation Methods.
       Springer-Verlag, New York.

USEPA.  2000a. Arsenic Occurrence in Public Drinking Water Supplies. EPA Office of Ground Water
       and Drinking Water.

USEPA.  2000b. Methods, Occurrence, and Monitoring Document for Radon in Drinking Water.  EPA
       Office of Ground Water and Drinking Water.

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Occurrence Estimation Methodology and Findings - DRAFT
Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
Six-Year Review
                                           ADDENDUM

This addendum includes the WinBUGS program of the hierarchical model, as well as the S-Plus
programs used for creating input files and processing output from the hierarchical model.  These,
programs are included for review purpose only. They are not to be distributed without written consent
from the developer.
A. The WinBUGS Program of the Hierarchical Model

# Song S. Qian, 30 March 2001, revised 17 April 2001,25 May 2001
# National distribution of regulated contaminants concentrations.
# A hierarchical modeling for normally distributed data containing detections and non-detections

# Data:
#      y - contaminant concentrations (sorted by system id)
#      n - length of y
#      cj-minimum reporting levels (if detection cj = exp( 1000))
#      pwsid - public water system id
#      strata - M (10) level strata indicating source water type and population served
#      mstrata-strata id of each system
#           npwsid - incremental # of observations in water systems       *  ",
#           cr - water quality criteria
H      K-length of cr
*                                      '•'•"
# Output to be monitored:
#      beta-slope of strata
if      prob - prob. of system mean exceeding cr (for each strataj
#      cdf - cdf of the system mean distribution      :  ..";-!
#      cbar - system means
#           cbarsys- mean of cbar
H      cbarstrata - mean concentrations in each strata
model{
        for (i in l:n){
                y[i] ~ dnorm(mu[i], tau)I(, cj[i]);
                mu[i] <- mul(pwsid[i]] + beta[strata[i]];

        for(iinl:M){
                beta[i] ~ dnorm(0, prec[2]);
                cbarstrata[i] <-sum(cbarst[l:L, i])/nstrata[i];

        for(linl:L){,
                n>u I [1] ~ dnorm(0, prec[3]);
                cbar[l] <- exp(mul[l] + beta[mstrata[l]] + 0.5/tau);
                for(kinl:K){
                        excedfk, 1] <- step(cbar[l] -  cr[k]);
                for(kinl:(CUTS[3]
                        cdfsys[l,k] <- step(cut[k] - cbar[l]);
                                                   19
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Occurrence Estimation. MetKodology and Findings - DRAFT
Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
                                                                                            Six-Year Review
                for(jinl:M){
                         cbarstfl, j] <- cbar[l] * equals(mstrata[l], j);
       .for(kinl:K){
                for(iinl:L){
                         forQin 1:M){
                                 ex[k, i, j] <- excedfk, i] * equals(mstrata[i], j);
                 for(jinl:M){                                   *              ,^~
                         probjj, k] <-sum(ex[k,l:L,j])/nstrata[j];  t,                         ,

                 probAllfk] <- sum(ex[k,,])/L;                 ,   I >     ,                 *      .
                 probG[k] <- (sum(ex[k,, 1 ])+sum(exDc,,2])+sum(expk,,3"])+sum(ex[k,,4])+sum(ex[k,,5]))/nG;
                 probS[k] <- (sum(ex[k,,6])+sum(ex[k,,7])+sum(ex[k,>8J)^sun>(ex[k,,9])+sum(ex[k,, 10]))/nS;

        for(iinl:3){
     prec[i] ~dgamma(0.01, 0.01);

        for (k in 0:CUTS[3]){                      , '  l~   ~~'
                 cut[k+l] <- pow(10, CUTS[1] + k*CUTS[2]); -
                 cdf[k+l] <- mean(cdfsys[l :L, k-t-1]); # mean of system means

        tau ~ dgamma(0.01, 0.01);
        sigma <- sqrt(lTtau);            !??  ;
   cbarsys <- mean(cbar[ 1 :L]);
B. S-Plus Program for Creating the BUGS Input Data Files

# creating input data files for BUGS run  ,
# Necessary inputs for function bugs.in:
#               y[i]: concentration data iog-fransformed.
#          _     sourcep]: typ& of source water 1 or 2
#       ,,!;"     pops[i]: population served 1,..., 5
#     ;f  '       cj[i]: minirnum reporting levels (log-transformed).
# Initial values:
#               y[i]: non-detection y values, use 0.5*cj
#  ,             e[i]: residuals: rep(0, n)
#     '          prec^l;;4;]: precision of ei, betaI,beta2,mul
#               betalQ], beta2[k], rep(0,1), rep(0, K); I: # of source type, K: number of population category
#•       „,  ,  ,mirl[l]:rep(0,L);L:# of systems
#    ,           tau: 0.1
to2 <-function(n)  {if(n<10)paste("0",as.character(n),sep="")else
                        as.character(n)}                            ,
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 Occurrence Estimation Methodology and Findings - DRAFT
 Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
Six-Year Review
 # Input Data
 pops.fun <- function(x){
         ifelse(x<=500,        l,
         ifelse(x>500  &x<=3300, 2,x)->x                                                »
         ifelse(x>3300 &x<=10000, 3, x)->x
         ife]se(x> 1 0000 & x<=50000, 4, x)->x
         5felse(x>50000,       5, x)->x
         return(x)
 >
 bugs.in <- fiinction(run = 0, base = "c:\\users\\song\\cadmus\\occurrence",                                ',
         infile = Flu, contaminant = "Fluoride", cuts=c(-4, 2), ncuts=40,
         cr=c(4,2,0.5,0.1)>{
                 # This version sorts the data by system id (pwsid)
                 # for calculating both strata means and systems means.
                 # cuts: concentration range where CDF will be estimated
                 # cr: critical values in original scale
         rundir <- paste(base, "runs", to2(run)., sep="\\")
 # input data
         oo <- order(infile$PWSID)
         infile <- infile[oo,]
         y <- log(infile$ VALUE)
         n <- length(y)
         m <- sum(infile$DETECT=l)
         y[infile$DETECT=0] <- NA
         source <- as.numeric(ordered(infile$SOURCE)) # 1=G^ 2=S
         I<- Iength(unique(source))
         pops <- pops.fun(infile$POPSERV)
         strata <- paste(source, pops, sep- '.")
         M <- length(unique(strata))
         strata <- as.numeric(ordered(strata))
         pwsid <- as.numeric(ordered(infileSPWSID))
         L <- length(unique(p\vsid))
         npwsid <- as.vector(table(ordered(infile$PWSID)))
         mstrata <- strata[cumsum(npwsid)]
         nstrata <- as.vector(table(mstrata))
         if(sum(nstrata)!=L)stop("nurnber of systems not equal")
        J <- length(nstrata)
        nG <- length(unique(pwsid[source=l]))
        nS <- length(unique(pwsid[source=2]))
        if(L!=(nG+nS))stop("S+G!=AH")
        cj <- log(infile$VALUE)
        cj[iiifile$DETECT=l] <- 1000
        bugs.dat <- Iist(n=n, M=M, K=length(cr), L=L, y=y, cj=cj, srrata=strata, nstrata = nstrata, mstrata=mstrata,
                pwsid=pwsid, npwsid=c(0,cumsum(npwsid)), CUTS=c(cuts[l], (cuts[2]-cuts[]])/ncuts, ncuts),
                cr=cr, nS=nS, nG=nG)
# initial values
        yi <- 0.5 *cj
        yipnfile$DETECT=l] <-NA
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Occurrence Estimation Methodology and Findings - DRAFT
Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
Six-Year Review
        mul <-rep(0, L)
        beta <- rep(0, M)
        tau <- 0.01
        bugs.ini <- list(y=yi, mul=mul, beta=beta, tau==tau, prec=rep(0.01, 3), tt = rep(0, n))
# log file
        bugs.log <- list(run=run, contaminant=contaminant, rundir=rundir,
                                 CUTS=c(cuts[l], (cutst2]-cuts[l])/ncuts, ncuts), cr=cr, K=lengtli(cr),
nstrata=nstrata)
# BUGS files                                                                  -  -„ *
 dput(bugs.dat, paste(rundir,"occdat.txt",sep="\\"));                 ,             /. v,
 dput(bugs.ini, paste(randir,"occini.txt",sep="\\"));                                       '
 dput(bugs.log, paste(rundir,"occlog.txt",sep="\\"));
invisible()
C. S-Plus Program for Processing the BUGS Output Data Files

# Routines for plotting CDF's and saving summary statistics.
#
# Gamma priors on s.d. scale                              -  -
fsig <- functions, a, t) { return(fs <- 2 * exp(-t/sA2) / sA(2*a+l)};}
pfsig <- function(a, t, lab=NA, hi=0) {
        md <- sqrt(t/(a + 0.5));
     if(a>.5) {mu <- sqrt(t)*exp(lgamma(a - 0,5)-lgamma(a)); }
     else { mu <- Inf;}
        if(a>l) { sd <- sqrt(t/(a-l)-muA2);}
     else {sd<-Inf;}                 d,:           ^  -
     hi <- max(hi,3*md);
        x<-seq(,0,hi,,101);
        y<-Ysig(x,a,t);         ,   ' ,
     if(is.na(lab)) (lab <- paste("sd= J/sqrt(t) if t~Ga(",
       signif(a,2),».», signif(tJ2))")")sep-"«) }
        plot(x, y, type = "1", axes=F, ylab=;'ProB Density", xlab=lab);
     axis(side=l);
     abline(v=0);
     if(a>,5) { abline(v=mu); }„
     list(mode=md, mean=mu/sdev=sd);

>    ^
if(!exists("ps.colors.hsb"))source("c:/users/song/cadmus/water/bugs/hsb.q");
# Finds (approximate) quantiles from cdf vector
p2q <-'function(x, cdf»|»pii1?=c(-6,^5,40), con) {
       ' if(missing(con)j|is.null(con)) con <- c(-5:2)
 '   iftmjssingCx))   x <- log(10)*seq(cut[l],,cut[2],H-cut[3]);
     if(missing(cdf)) cdf <-pnorm(x);
     if(missing(p))   p<-.01 *c(5,10,25,50,75,80,90,95);
     xj <- seq(nx <- length(x));
     np <-length(p<-c(p));
     q  <-rep(NA,np);
     for(iin l:np) {
     j <- sum(cdf<=p[i]);
                                                    22
-------
 Occurrence Estimation Methodology and Findings - DRAFT
 Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
                                                                                            Six-Year Review
      if(G=l)l!G=™0)
      else
         i] <- xQ] + (xD-*-l]-xD])*(p[i]-cdfO])/(cdfO+l]-cdfO]);

                 nc <- length(con)
                 pc <- rep(NA, nc)
                 for (i in l:nc){
                        j<-sum(x<=log(10)*con[ij)
                                pc[i] <- cdfjj]
                        else
                                pc[i] <- cdfD] + (cdfn+l]-cdfO)*(con[i]-xp])/(xD+l]-xtJ])
     myj <-round(l+(con-cut[l])/cut[2]);                                                      V-
     myj[myjcut[3]] <- l+cut[3];
     invisible(list(p 1 =p,    q 1 =signif(exp(q),3),
             p2=cdf[myj], q2=exp(x[myj]),
             p3=pc,    q3=signif(10A(co.n),3),
             y=cdf, x=exp(x)));                           ~  '*                     1

# Plot posterior cdf from BUGS run of EPA data:
my.cdf <-                                                -*-
function(run = 0, base = "c:/users/song/cadmus/occurrence", ps = T, wmf=F, infile=Flu, ifoame="Flu",
Con=NULL, unit="mg/L")

        rundir <- paste(base, "runs", to2(run)j sep = "/")
        print(paste("Using directory ", rundir, ".", sep = ""))
        psw <- dget(paste(rundir, "occlbg.txt", sep = "/"))
        run<-psw$run                .
        cr<-pswScr
        mycon <-pswScontaminant
        mytitle <- paste("Run ", run, ": ", tnycoh, ", ", sep = "")
        new .wmf <- function(n, name = ")Vdir=.mndir){
                if (wmf) {
                        fiiame <- paste(dir, "/", name, to2(n), ".wmf, sep = "")
                        win.printer(file=fhame, height=6, width=8, format="metafile")
                        print(paste("Writing Windows Meta file ", feame, sep = ""))
       new.ps <- function(n, name = "", dir = rundir)
"red 1", "purple",
                       fhame <- paste(dir, "/", name, to2(n), ".ps", sep = "")
                       postscript(rhame, hori = T, colors = ps.colors.hsb[c("black", "white", "RoyalBluel"

                                "green4", "yellow2"), ])
                       print(paste("Writing postscript file ", fname, sep = ""))
                                                  23
-------
         Occurrence Estimation Methodology and Findings - DRAFT
         Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
                                                                                                   Six-Year Review
                  mswcol <- 1;
                  rawcol <-. 6      # Green for empirical stuff
                  ps.off <- functionO
                          if(ps){
                                  dev.offO
                  wmf.off <- funclionO
                          if(wmf){
                                  dev.offQ
}
                  cdf <- read.table(paste(rundir, "cdf.txt", sep = "/"), head =-T) sep = "\t")

                  prob <- read.table(paste(rundir, "prob.txt", sep = "/"), head =' T, sep - "\t?)
                  probG <- read.table(paste(rundir, "probG.txt", sep = "/"), head = T, sep = "\t")
                  probS <- read.table(paste(rundir, "probS.txt", sep = "/"), head = T, sep - "\t")
                  probAll <- read.table(paste(rundir, "probAH.txt", sep = "/'% head = T, sep = "\t"j
                  cbarstrata <- read.table(paste(rundir, "cbarstrata.txt", sep = ?/'"), head = T, sep = "\t")
                  cbarsys <- read.table(paste(rundir, "cbarsys.txt", sep = "/"), head = T, sep = "\t")
                  cbarG <- sum(cbarstrata$mean[l: 5]*psw$nstrata[l: 5j)/sum(psw$nstrata[l: 5])
                  cbarS <- sum(cbarstrata$mean[6: 1 0]*psw$nstrata[6: l'0])/sum(ps\v$nstrata[6: 1 0])
                  cbarG.sd <- sum(cbarstrata$sd[l: 5]*pSw$nstrata[I: 5])/sum(piw$hstrata[l: 5])
                  cbarS.sd<-sum(cbarstrata$sd[6:10]*psw$nstrata[6:10])/sum-------
Occurrence Estimation Methodology and Findings - DRAFT
Appendix B. Detailed Description of the Stage 2 Bayesian Hierarchical Model
Six-Year Review
        new.ps(run, "cdf', rundir)
        new.wmf(run, "cdf, rundir)
        X <- log(10) * seq(psw$CUTS[l], , psw$CUTS[2], psw$CUTS[3] + 1)
        xx <- Iog(10) * psw$CUTS[2] + x # Trailing edge of step
        xat <- log(10) * seq(psw$CUTS[l], psw$CUTS[l] + psw$CUTS[2] * psw$CUTS[3])
        xlab <- as.character(signif(10Aseq(psw$CUTS[l], psw$CUTS[l] + psw$CUTS[2] * psw$CUTS[3]), 1))
        plot(x, cdfSmean, type = "n", axes = F, xlab = paste("Concentration (", unit, ")",sep=""), ylab =
"Cumulative Probability", ylim=c(-0.04, 1))
        disclaimer <- paste("Draft for Discussion:", substring(date(), 4, 10), ",", substring~(date(), 20), sep = "")
        stamp(disclaimer)
        axis(side = 1, at = xat, labels = xlab)
        axis(side = 2, at = seq(0, !,,!!))
        lines(x, cdfSmean, col = mswcol, Iwd = 2)  # Mean
        lines(x, cdfSXS.O, col = mswcol, Ity = 2)    # 5%              _'  '
        lines(x, cdfSX95.0, col = mswcol, Ity = 2)  # 95%
        old.ht<-1000000000
        xraw <-log(infile$VALUE)                                    ' •
        nraw <- length(xraw)
        xraw.clean <-xraw[infile$DETECT=l]

        segments(log(cr), rep(0, length(cr)), log
-------
-------
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 Appendix D. Stage 2 Bounding Analysis
                 Figure D.I. Alachlor — Bounding Analysis of the
                 Distribution of Model Estimated System Means
                                Run 10:  Alachlor,
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le-008 1e-006 0.0001 0.01 0.1 1 10
                                  Concentration (mg/L)
This diagram presents a plot of the cumulative density function (CDF) of the modeled, best
estimate system means for alachlor (and its 90% Credible Interval) compared to three calculated
"bounding" CDFs.  The model-predicted CDF of system means, based on compliance monitoring
analytical data from the 16-state cross-section, is represented by the solid line labeled "Bayes
Mean." The two dotted lines most closely straddling and nearly parallel to the "Bayes Mean"
represent the 90% Credible Interval around the model prediction (labeled "Bayes CI").  The
lower bound (labeled "low") represents a CDF of calculated system means where all non-
detection data were set equal to zero. The middle bound (labeled "median") represents the
distribution of data where all non-detection data were set equal to one-half of the modal MRL
(0.0001 mg/L). The upper bound (labeled "high") represents the distribution of data where
system means were calculated with all non-detection data were set equal to the modal MRL
(0.0002 mg/L). The two vertical lines represent the contaminant concentration thresholds of
interest for alachlor: 0.002 mg/L,  and 0.0002 mg/L.
Occurrence Estimation Methodology
March 2002
-------
      . P.  Stage 2. Bounding Analysis
               Figure D.2. Beryllium — Bounding Analysis of the
                Distribution of Model Estimated System Means
                              Run  4:  Beryllium,
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                                 Concentration (mg/L)
This diagram presents a plot of the cumulative density function (CDF) of the modeled, best
estimate system means for beryllium (and its 90% Credible Interval) compared to three
calculated "bounding" CDFs.  The model-predicted CDF of system means, based on compliance
monitoring analytical data from the 16-state cross-section, is represented by the solid line labeled
"Bayes Mean." The two dotted lines most closely straddling and nearly parallel to the "Bayes
Mean" represent the 90% Credible Interval around the model prediction (labeled "Bayes CI").
The lower bound (labeled "low") represents a CDF of calculated system means where all non-
detection data were set equal to zero. The middle bound (labeled "median") represents the
distribution of data where all non-detection data were set equal to one-half of the modal MRL
(0.0005 mg/L). The upper bound (labeled "high") represents the distribution of data where
system means were calculated with all non-detection data were set equal to the modal MRL
(0.001 mg/L). The three vertical lines represent the contaminant concentration thresholds  of
interest for beryllium: 0.01  mg/L, 0.004 mg/L, and 0.001 mg/L.
Occurrence Estimation Methodology
                                                                             March 2002
-------
 Appendix D. Stage 2 Bounding Analysis
               Figure D.3. Carbofuran — Bounding Analysis of the
                  Distribution of Model Estimated System Means
                             Run  16: Carbofuran,
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                                  Concentration (mg/L)
This diagram presents a plot of the cumulative density function (CDF) of the modeled, best
estimate system means for carbofuran (and its 90% Credible Interval) compared to three
calculated "bounding" CDFs.  The model-predicted CDF of system means, based on compliance
monitoring analytical data from the 16-state cross-section, is represented by the solid line labeled
"Bayes Mean."  The two dotted lines most closely straddling and nearly parallel to the "Bayes
Mean" represent the 90% Credible Interval around the model prediction (labeled "Bayes CI").
The lower bound (labeled "low") represents a CDF of calculated system means where all non-
detection data were set equal to zero. The middle bound (labeled "median") represents the
distribution of data where all non-detection data were set equal to one-half of the modal MRL
(0.00045 mg/L).  The upper bound (labeled "high") represents the distribution of data where
system means were calculated with all non-detection data were set equal to the modal MRL
(0.0009 mg/L). The three vertical lines represent the contaminant concentration thresholds of
interest for carbofuran:  0.04 mg/L,  0.007 mg/L, and 0.004 mg/L.
Occurrence Estimation Methodology
                                                                            March 2002
-------
Appendix P. Stage 2 Bounding Analysis
               Figure D.4.  Chromium — Bounding Analysis of the
                 Distribution of Model Estimated System Means
                              Run 3: Chromium,
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                                  Concentration (mg/L)
 This diagram presents a plot of the cumulative density function (CDF) of the modeled, best
 estimate system means for chromium (and its 90% Credible Interval) compared to three
 calculated "bounding" CDFs. The model-predicted CDF of system means, based on compliance
 monitoring analytical data from the 16-state cross-section, is represented by the solid line labeled
 "Bayes Mean." The two dotted lines most closely straddling and nearly parallel to the "Bayes
 Mean" represent the 90% Credible Interval around the model prediction (labeled "Bayes CI").
 The lower bound (labeled "low") represents a CDF of calculated system means where all non-
 detection data were set equal to zero. The middle bound (labeled "median") represents the
 distribution of data where all non-detection data were set equal to one-half of the modal MRL
 (0.005 mg/L). The upper bound (labeled "high") represents the distribution of data where system
 means were calculated with all non-detection data were set equal to the modal MRL (0.01 mg/L).
 The five vertical lines represent the contaminant concentration thresholds of interest for
 chromium: 0.1 mg/L, 0.07 mg/L, 0.05 mg/L, 0.02 mg/L, and 0.01 mg/L.
 Occurrence Estimation Methodology
                                                                             March 2002
-------
 Appendix D. Stage 2 Bounding Analysis
          Figure D.5. 1,4-DichIorobenzene — Bounding Analysis of the
                 Distribution of Model Estimated System Means
                     Run  11: 1,4-dichlorobenzene,
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	 Thresholds
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1e-005 0.001 0.01 0.1 1 10
                                 Concentration (mg/L)
This diagram presents a plot of the cumulative density function (CDF) of the modeled, best
estimate system means for'l,4-dichlorobenzene (and its 90% Credible Interval) compared to
three calculated "bounding" CDFs. The model-predicted CDF of system means, based on
compliance monitoring analytical data from the 16-state cross-section, is represented by the solid
line labeled "Bayes Mean." The two dotted lines most closely straddling and nearly parallel to
the "Bayes Mean" represent the 90% Credible Interval around the model prediction (labeled
"Bayes CI"). The lower bound (labeled "low") represents a CDF of calculated system means
where all non-detection data were set equal to zero. The middle bound (labeled "median")
represents the distribution of data where all non-detection data were set equal to one-half of the
modal MRL (0.00025 mg/L). The upper bound (labeled "high") represents the distribution of
data where system means were calculated with all non-detection data were set equal to the modal
MRL (0.0005 mg/L). The three vertical lines represent the contaminant concentration thresholds
of interest for 1,4-dichlorobenzene: 0.075 mg/L, 0.005 mg/L, and 0.0005 mg/L.
Occurrence Estimation Methodology
March 2002
-------
   idix D. Stage 2 Bounding Analysis
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                Figure D.6.  Diquat - Bounding Analysis of the
                Distribution of Model Estimated System Means
                                Run  15: Diquat,


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                                                  10
                                  Concentration (mg/L)
This diagram presents a plot of the cumulative density function (CDF) of the modeled, best
estimate system means for diquat (and its 90% Credible Interval) compared to three calculated
"bounding" CDFs. The model-predicted CDF of system means, based on compliance monitoring
analytical data from the 16-state cross-section, is represented by the solid line labeled "Bayes
Mean."  The two dotted lines most closely straddling and nearly parallel to the "Bayes Mean"
represent the 90% Credible Interval around the model prediction (labeled "Bayes CI").  The
lower bound (labeled "low") represents a CDF of calculated system means where all non-
detection data were set equal to zero.  The middle bound (labeled "median") represents the
distribution of data where all non-detection data were set equal to one-half of the modal MRL
(0.0002 mg/L). The upper bound (labeled "high") represents the distribution of data where
system means were calculated with all non-detection data were set equal to the modal MRL
(0.0004 mg/L). The three vertical lines represent the contaminant concentration thresholds of
interest for diquat: 0.02 mg/L, 0.004 mg/L, and 0.002 mg/L.
Occurrence Estimation Methodology
                                                                             March 2002
-------
 Appendix D. Stage 2 Bounding Analysis
                 Figure D.7. Fluoride -- Bounding Analysis of the
                  Distribution of Model Estimated System Means
                                 Run  2:  Fluoride,
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                                                                         '»Kv£sy;i;-ii;if 5;ii
                      0.001
0.01
                                        0.1
                                                                           10
                                   Concentration (mg/L)
 This diagram presents a plot of the cumulative density function (CDF) of the modeled, best
 estimate system means for fluoride (and its 90% Credible Interval) compared to three calculated
 "bounding" CDFs. The model-predicted CDF of system means, based on compliance monitoring
 analytical data from the 16-state cross-section, is represented by the solid line labeled "Bayes
 Mean." The two dotted lines most closely straddling and nearly parallel to the "Bayes Mean"
 represent the 90% Credible Interval around the model prediction (labeled "Bayes CI"). The
 lower bound (labeled "low") represents a CDF of calculated system means where all non-
 detection data were set equal to zero. The middle bound (labeled "median") represents the
 distribution of data where all non-detection data were set equal to one-half of the modal MRL
 (0.05 mg/L).  The upper bound (labeled "high") represents the distribution of data where  system
 means were calculated with all non-detection data were set equal to the modal MRL (0.1  mg/L).
 The seven vertical lines represent the contaminant concentration thresholds of interest for
 fluoride: 4 mg/L, 2 mg/L, 1.5 mg/L, 1.2 mg/L, 0.7 mg/L, 0.5 mg/L, and 0.1 mg/L.  Note:
 Fluoride occurrence was also assessed relative to 3 mg/L. However, this  threshold is not
presented in the above figure.
Occurrence Estimation Methodology
                                                                             March 2002
-------
         Stage 2. Bounding Analysis
              Figure D.8.  Glyphosate — Bounding Analysis of the
                 Distribution of Model Estimated System Means
                            Run 12: Glyphosate,

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                                  Concentration (mg/L)
 This diagram presents a plot of the cumulative density function (CDF) of the modeled, best
 estimate system means for glyphosate (and its 90% Credible Interval) compared to three
 calculated "bounding" CDFs. The model-predicted CDF of system means, based on compliance
 monitoring analytical data from the 16-state cross-section, is represented by the solid line labeled
 "Bayes Mean." The two dotted lines most closely straddling and nearly parallel to the "Bayes
 Mean" represent the 90% Credible Interval around the model prediction (labeled "Bayes CI").
 The lower bound (labeled "low") represents a CDF of calculated system means where all non-
. detection data were set equal to zero. The middle bound (labeled "median") represents the
 distribution of data where all non-detection data were set equal to one-half of the modal MRL
 (0.003 mg/L). The upper bound (labeled "high") represents the distribution of data where system
 means were calculated with all non-detection data were set equal to the modal MRL (0.006
 mg/L). The three vertical lines represent the contaminant concentration thresholds of interest for
 glyphosate: 0.7 mg/L, 0.06 mg/L, and 0.006 mg/L.
 Occurrence Estimation Methodology
                                                                             March 2002
-------
  Appendix D. Stage 2 Bounding Analysis
                Figure D.9. Heptachlor - Bounding Analysis of the
                  Distribution of Model Estimated System Means
                               Run 8: Heptachlor,

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f :
1 1 ' 	 1 	 : 	 1 	 '
1e-010
                        1e-008
                         1e-006
                                                 0-0001
                                                  0.01    0.1
                                  Concentration (mg/L)
 This diagram presents a plot of the cumulative density function (CDF) of the modeled, best
 estimate system means for heptachlor (and its 90% Credible Interval) compared to three
 calculated "bounding" CDFs. The model-predicted CDF of system means, based on compliance
 monitoring analytical data from the 16-state cross-section, is represented by the solid line labeled
 "Bayes Mean." The two dotted lines most closely straddling and nearly parallel to the "Bayes
 Mean" represent the 90% Credible Interval around the model prediction (labeled "Bayes CI").
 The lower bound (labeled "low") represents a CDF of calculated system means where all non-
 detection data were set equal to zero. The middle bound (labeled "median") represents the
 distribution of data where all non-detection data were set equal to one-half of the modal MRL
 (0.00002 mg/L).  The upper bound (labeled "high") represents the distribution of data where
 system means were calculated with all non-detection data were set equal to the modal MRL
 (0.00004 mg/L).  The three vertical lines represent the contaminant concentration thresholds of
interest for heptachlor: 0.0004 mg/L, 0,0001 mg/L, and 0.00004 mg/L.
Occurrence Estimation Methodology
                                                                            March 2002
-------
        Stage 1 Bounding Analysis
        Figure D.10.  Heptachlor Epoxide ~ Bounding Analysis of the
                Distribution of Model Estimated System Means
                      Run 7:  Heptachlor  Epoxide,

.999-
-^ QQ-
5
E 0.9-
o
e 0.75-1
0) 0.5-
"«j °-25
3
E .05-
O -01 ~
.001-

I \ i \
	 Bayes Mean f •/•'
	 Bayes Cl "•. •/_•'
	 High ;- /:
	 Low « /• )
	 Median i f .;
i , • / }
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T 	
,,.;.^_;™5x^....-..-...:-,»™»,4,™,^
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if;.'
:,
} i •. : :
? •! ; i
s . ; ' -

n' ! ; : . ,.
_ 	 . 	 . 	 j 1
                                                            0.01    0.1
                                 Concentration (mg/L)
This diagram presents a plot of the cumulative density function (CDF) of the modeled, best
estimate system means for heptachlor epoxide (and its 90% Credible Interval) compared to three
calculated "bounding" CDFs. The model-predicted CDF of system means, based on compliance
monitoring analytical data from the 16-state cross-section, is represented by the solid line labeled
"Bayes Mean." The two dotted lines most closely straddling and nearly parallel to the "Bayes
Mean" represent the 90% Credible Interval around the model prediction (labeled "Bayes CI").
The lower bound (labeled "low") represents a CDF of calculated system means where all non-
detection data were set equal to zero. The middle bound (labeled "median") represents the
distribution of data where all non-detection data were set equal to one-half of the modal MRL
(0.00001-mg/L). The upper bound (labeled "high") represents the distribution of data where
system means were calculated with all non-detection data were set equal to the modal MRL
(0.00002 mg/L). The three vertical lines represent the contaminant concentration thresholds of
interest for heptachlor epoxide: 0.0002 mg/L, 0.0001 mg/L, and 0.00002 mg/L.
Occurrence Estimation Methodology
                                                                           March 2002
-------
 Appendix D. Stage 2 Bounding Analysis
          Figure D.ll.  Hexachlorobenzene — Bounding Analysis of the
                 Distribution of Model Estimated System Means
   .a
    05
   .0
    s.
   Qu
    0)
   t£5
    as
    zi
    E
    =j
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                      Run 13: Hexachlorobenzene,

.999"
.99-


0.9-
0"7C-
,/b
0.5-
Ooc-
.05-
.01-
.001-

	 ,„















""" • 	 " 	 • 	 :. .; -7.:*
	 Bayes Mean
	 Bayes Cl
	 Thresholds
	 High
* - Low
	 Median




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	 ..?/ 	 _
y
i i
1e-009 1e-007
•/•'
*
,-f
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1 :
r:

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i
i i i.i i — i — i — •
1e-005 0.001 0.01 0.1 1 10
                                 Concentration (mg/L)
This diagram presents a plot of the cumulative density function (CDF) of the modeled, best
estimate system means for hexachlorobenzene (and its 90% Credible Interval) compared to three
calculated "bounding" CDFs. The model-predicted CDF of system means, based on compliance
monitoring analytical data from the 16-state cross-section, is represented by the solid line labeled
"Bayes Mean." The two dotted lines most closely straddling and nearly parallel to the "Bayes
Mean" represent the 90% Credible Interval around the model prediction (labeled "Bayes CI").
The lower bound (labeled "low") represents a CDF of calculated system means where all non-
detection data were set equal to zero. The middle bound (labeled "median") represents the
distribution of data where all non-detection data were set equal to one-half of the modal MRL
(0.00005 mg/L). The upper bound (labeled "high") represents the distribution of data where
system means were calculated with all non-detection data were set equal to the modal MRL
(0.0001 mg/L). The three vertical lines represent the contaminant concentration thresholds of
interest for hexachlorobenzene:  0.001 mg/L, 0.0005 mg/L, and 0.0001 mg/L.
Occurrence Estimation Methodology
                                                                           March 2002
-------
           i 2 Bounding Analysis
               Figure D.12. Oxamyl — Bounding Analysis of the
                Distribution of Model Estimated System Means
                               Run  5: Oxamyl,
   CO
   2
  Q.
   (U
  i
   1
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.999-
.99-

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-
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	 Bayes Mean
	 Bayes Cl
	 Thresholds
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Low
	 Median

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           1e-010
1e-008
                                 1e-006
                      0.0001
                                                        0.01   0.1
                                                    10
                                 Concentration (mg/L)
This diagram presents a plot of the cumulative density function (CDF) of the modeled, best
estimate system means for oxamyl (and its 90% Credible Interval) compared to three calculated
"bounding" CDFs. The model-predicted CDF of system means, based on compliance monitoring
analytical data from the 16-state cross-section, is represented by the solid line labeled "Bayes
Mean."  The two dotted lines most closely straddling and nearly parallel to the "Bayes Mean"
represent the 90% Credible Interval around the model prediction (labeled "Bayes CI").  The
lower bound (labeled "low") represents a CDF of calculated system means where all non-
detection data were set equal to zero. The middle bound (labeled "median") represents the
distribution of data where all non-detection data were set equal to one-half of the modal MRL
(0.001 mg/L). The upper bound (labeled "high") represents the distribution of data where system
means were calculated with all non-detection data were set equal to the modal MRL (0.002
mg/L). The five vertical lines represent the contaminant concentration thresholds of interest for
oxamyl: 0.2 mg/L, 0.04 mg/L, 0.03 mg/L, 0.02 mg/L, and 0.007 mg/L.
Occurrence Estimation Methodology
                                                                            March 2002
-------
  Appendix D. Stage 2 Bounding Analysis
                 Figure D.13.  Picloram - Bounding Analysis of the
                  Distribution of Model Estimated System Means
                                 Run 6: Picloram,
    OS
    2
    Q_
    0)

    I
    1
    O


.yytr
.99-
0.9-
0*7 C-i
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0.5-
025"
.05-
.01-
.001-



• 7.^.:-— 	 	 	 — 'i
	 Bayes Mean „ ;•• -' '.•/•' f;
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, 	 ,. 	 Thresholds 	 '. ./•' /•'.
•••• High ~ " ~; '"' ™>- ' 	 	 —J.~
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—


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                       1e-009
                                                         0.001
0.1    1
                                  Concentration (mg/L)
 This diagram presents a plot of the cumulative density function (CDF) of the modeled, best
 estimate system means for picloram (and its 90% Credible Interval) compared to three calculated
 "bounding" CDFs. The model-predicted CDF of system means, based on compliance monitoring
 analytical data from the 16-state cross-section, is represented by the solid line labeled "Bayes
 Mean." The two dotted lines most closely straddling and nearly parallel to the "Bayes Mean"
 represent the 90% Credible Interval around the model prediction (labeled "Bayes CI"). The
 lower bound (labeled "low") represents a CDF of calculated system means where all non-
 detection data were set equal to zero. The middle bound (labeled "median") represents the
 distribution of data where all non-detection data were set equal to one-half of the modal MRL
 (0.00005 mg/L).  The upper bound (labeled "high") represents the distribution of data where
 system means were calculated with all non-detection data were set equal to the modal MRL
 (0.0001 mg/L). The three vertical lines represent the contaminant concentration thresholds of
 interest for picloram:  1 mg/L, 0.5 mg/L, and 0.05 mg/L.
Occurrence Estimation Methodology
                                                                             March 2002
-------
      P. Stage 2 Bounding Analysis
  .Q
   05

   2
  CL.
   
-------
 Appendix D. Stage 2 Bounding Analysis
                Figure D.15. Thallium — Bounding Analysis of the
                  Distribution of Model Estimated System Means
                                Run 9: Thallium,
   CO

   2
   Q_
   (D
   E
   O


.999^
.99-

0.9-

0.75-
0.5-
.4&O
.05-
.01-
.001-

*


	 Bayes Mean '.
	 Bayes Cl
	 	 Thresholds ,
	 High .- jf
	 Low " " ./
	 Median / .
• / 1
1 / 1
: ./ /
•• /: /^
•/ P
'•?•' -• 	 -•','— —iJ
1 1 1 1 1 1 1
e-010 1e-008 1e-006 0.0001


f
/





ms

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V'' , !

•




»»«»>» i, »••»..' ,
1 1 II -- "I 	 '
0.01 0.1 1 10 100
                                  Concentration (mg/L)
This diagram presents a plot of the cumulative density function (CDF) of the modeled, best
estimate system means for thallium (and its 90% Credible Interval) compared to three calculated
"bounding" CDFs. The model-predicted CDF of system means, based on compliance monitoring
analytical data from the 16-state cross-section, is represented by the solid line labeled "Bayes
Mean." The two dotted lines most closely straddling and nearly parallel to the "Bayes Mean"
represent the 90% Credible Interval around the model prediction (labeled "Bayes CI"). The
lower bound (labeled "low") represents a CDF of calculated system means where all non-
detection data were set equal to zero. The middle bound (labeled "median") represents the
distribution of data where all non-detection data were set equal to one-half of the modal MRL
(0.0005 mg/L). The upper bound (labeled "high") represents the distribution of data where
system means were calculated with all non-detection data were set equal to the modal MRL
(0.001 mg/L). The two vertical lines represent the contaminant concentration thresholds of
interest for thallium: 0.002 mg/L, and 0.001 mg/L.
Occurrence Estimation Methodology
March 2002
-------