Draft 

ADVISORY BOARD ON 

RADIATION AND WORKER HEALTH 

National Institute for Occupational Safety and Health

DRAFT REVIEW OF ORAUT-RPRT-0053: 

ANALYSIS OF STRATIFIED COWORKER DATASETS, REV. 1 

Contract No. 200-2009-28555 

SCA-TR-PR2013-0053, Revision 0 

Prepared by 

H. Chmelynski 

J. Lipsztein 

S. Marschke 

J. Stiver 

S. Cohen & Associates 

1608 Spring Hill Road, Suite 400 

Vienna, VA 22182 

April 2013 

Disclaimer 

This document is made available in accordance with the unanimous desire of the Advisory Board on 

Radiation and Worker Health (ABRWH) to maintain all possible openness in its deliberations. However, 

the ABRWH and its contractor, SC&A, caution the reader that at the time of its release, this report is predecisional and has not been reviewed by the Board for factual accuracy or applicability within the 

requirements of 42 CFR 82. This implies that once reviewed by the ABRWH, the Board’s position may 

differ from the report’s conclusions. Thus, the reader should be cautioned that this report is for 

information only and that premature interpretations regarding its conclusions are unwarranted.

 
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Document No. 

SCA-TR-PR2013-0053 

S. COHEN & ASSOCIATES: 

Technical Support for the Advisory Board on

Radiation & Worker Health Review of 

NIOSH Dose Reconstruction Program 

Effective Date: 

Draft – April 23, 2013 

DRAFT REVIEW OF ORAUT-RPRT-0053: 

ANALYSIS OF STRATIFIED COWORKER 

DATASETS, REV. 1 

Page 2 of 55 

Task Manager: 

________________________ Date: ___________ 

Stephen F. Marschke 

Supersedes: 

N/A 

Project Manager: 

________________________ Date: ___________ 

John Stiver, MS, CHP 

Reviewers: 

 A. Makhijani, PhD 

 

 

Record of Revisions 

Revision 

Number 

Effective 

Date Description of Revision 

0 (Draft) 04/23/2013 Initial issue 
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TABLE OF CONTENTS 

Abbreviations and Acronyms ..........................................................................................................5 

Executive Summary.........................................................................................................................6 

1.0 Introduction........................................................................................................................11 

1.1 Related ORAUT Publications................................................................................12 

1.1.1 Source Documents.....................................................................................12 

1.1.2 Dependencies.............................................................................................12 

2.0 Statistical Methods for Analyzing Coworker Urinalysis Datasets ....................................13 

2.1 Regression on Order Statistics (ROS)....................................................................15 

2.2 Effective Fit ...........................................................................................................17 

2.3 Binomial Fit ...........................................................................................................18 

3.0 One Statistic per Worker per Time Period.........................................................................19 

3.1 Outline of OPOS Procedure...................................................................................19 

3.2 Simulation to Compare OPOS and Full Coworker Models...................................22 

3.3 OPOS and Full Model Coworker Models Comparison with Individual 

Worker Exposures..................................................................................................23 

4.0 Stratification of the Coworker Population .........................................................................27 

4.1 Hypothesis Testing.................................................................................................27 

4.1.1 The Gray Region for a Statistical Test.......................................................30 

4.1.2 Test Performance Plots..............................................................................31 

4.1.3 Simulated Test Performance Plots.............................................................33 

4.2 Description of the Monte Carlo Permutation Test.................................................38 

4.3 Other Nonparametric Methods ..............................................................................44 

4.3.1 Peto-Prentice Test......................................................................................45 

5.0 Review Checklist ...............................................................................................................48 

6.0 Conclusions........................................................................................................................51 

References......................................................................................................................................53 
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NOTICE:

LIST OF TABLES 

Table 1. Proposed Stages of the Dose Reconstruction Process................................................11 

Table 2. Bias of OPOS Parameter Estimates versus Individual Samples.................................23 

Table 3. Comparison of OPOS and Full Coworker Models for SRS Tritium, 

1962 to 1964 ...............................................................................................................25 

Table 4. Sample Sizes, Ratio of Geometric Means, and Upper Bound of the Gray 

Region (UBGR) for Tests of the No Difference Hypothesis......................................36 

Table 5. Retention of Np-237 in the Body after a Single Intake ..............................................38 

Table 6. Comparison of Lognormal Distributions for Group A and Group B .........................38 

Table 7. Procedure Review Outline/Checklist..........................................................................48 

LIST OF FIGURES 

Figure 1. Bias of Simulated OPOS Estimates for Geometric Mean, Geometric Standard 

Deviation, and 95 Percentile vs. Individual Samples ...............................................23 th

Figure 2. ROS Plot for Worker 2, 1962 .....................................................................................24 

Figure 3. Scatter Plot of GSD vs. GM by Worker with OPOS and Full Models, 1962.............25 

Figure 4. Scatter Plot of GSD vs. GM by Worker with OPOS and Full Models, 1963.............26 

Figure 5. Scatter Plot of GSD vs. GM by Worker with OPOS and Full Models, 1964.............26 

Figure 6. Simulated Test Performance Plot and Gray Region for 2-Sample t-Test for 

Difference between Coworker Model Lognormal Distributions for CTW and 

non-CTW Neptunium Whole-Body Counts in 1975..................................................30 

Figure 7. Scatter Plot of ROS Estimates of GM and GSD for Samples of Size n and n

from the Lognormal Distributions for Group A and Group B....................................40 

A B

Figure 8. Distribution of ROS Estimates of GM for Samples of Size n and n from the 

Lognormal Distributions for Group A and Group B ..................................................41 

A B

Figure 9. Distribution of ROS Estimates of GSD for Samples of Size n and n from the 

Lognormal Distributions for Group A and Group B ..................................................41 

A B

Figure 10. Distribution of ROS Estimates for Differences in GM and GSD for Samples of 

Size nA and nB from the Lognormal Distributions for Group A and Group B ..........42 

Figure 11. Permutation Test for a Significant Difference in ROS Estimates of GM and 

GSD with No Nondetects ...........................................................................................43 

Figure 12. Permutation Test for a Significant Difference in ROS Estimates of GM and 

GSD with Approximately 40% Nondetects................................................................44 
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ABBREVIATIONS AND ACRONYMS 

AMW All Monitored Workers 

CERCLA Comprehensive Environmental Response Compensation and Liability Act 

CTW Construction Trades Worker 

DQO Data Quality Objectives 

EPA U.S Environmental Protection Agency 

GM Geometric Mean 

GSD Geometric Standard Deviation 

LBGR Lower Bound of the Gray Region 

MARSSIM Multi-Agency Radiation Survey and Site Investigation Manual 

MCPT Monte Carlo Permutation Test 

MDA Minimum Detectable Amount 

MDD Minimum Detectable Difference 

MPM Maximum Possible Mean 

nCi nanocurie 

NIOSH National Institute for Occupational Safety and Health 

non-CTW Non-Construction Trades Worker 

NRC U.S. Nuclear Regulatory Commission 

OPOS One-Person, One Sample 

ORAUT Oak Ridge Associated Universities Team 

OTIB ORAUT Technical Information Bulletin 

PROC Procedure 

ROS Regression on Order Statistics 

RPRT Report 

SC&A S. Cohen and Associates 

SEC Special Exposure Cohort 

SRS Savannah River Site 

UBGR Upper Bound of the Gray Region 

WBC Whole Body Count 

WRS Wilcoxon Rank Sum test 
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EXECUTIVE SUMMARY 

This report presents SC&A’s initial review of ORAUT-RPRT-0053, Analysis of Stratified 

Coworker Datasets (ORAUT 2012d), which describes the National Institute for Occupational 

Safety and Health’s (NIOSH’s) proposed methods for reconstructing exposures to unmonitored 

workers using coworker data. RPRT-0053 addresses three major topics: 

(1) Methods for analyzing coworker urinalysis datasets with varying proportions of samples 

below the detection limit (nondetects), with and without the assumption of lognormality 

(2) Reduction of coworker datasets containing individual urinalysis samples to one statistic 

per worker per time period 

(3) Methods for evaluating the stratification of the worker population into two distinct 

subgroups of workers (strata) using distributions based on the reduced data 

The three topics are discussed separately in this report. 

RPRT-0053 reviews several statistical methods that are available for analyzing the coworker 

datasets. A range of methods is included for analysis of datasets with a varying proportion of 

nondetects, ranging from none to essentially all or most of the available data from monitored 

workers. The proposed methods for analyzing datasets summarize, and in some cases improve 

on, methods previously reported in ORAUT-OTIB-0019, Analysis of Coworker Bioassay Data 

for Internal Dose Assessment (ORAUT 2005); ORAUT-PROC-0095, Generating Summary 

Statistics for Coworker Bioassay Data (ORAUT 2006a); ORAUT-OTIB-0075, Use of Claimant 

Datasets for Coworker Modeling (ORAUT 2009a); and ORAUT-RPRT-0044, Analysis of 

Bioassay Data with a Significant Fraction of Less-Than Results (ORAUT 2009b). 

The methods presented in RPRT-0053 serve as the theoretical basis for several subsequent 

reports related to the coworker models at the Savannah River Site (SRS), including ORAUTRPRT-0055, A Comparison of Exotic Trivalent Radionuclide Coworker Models at the Savannah 

River Site (ORAUT 2012a); ORAUT-RPRT-0056, A Comparison of Neptunium Coworker 

Models at the Savannah River Site (ORAUT 2012b); and ORAUT-RPRT-0058,A Comparison of 

Mixed Fission and Activation Product Coworker Models at the Savannah River Site (ORAUT 

2012c). Hence this review also addresses potential issues related to the application of the 

proposed methods to the SRS coworker models, especially those issues that might be considered 

Special Exposure Cohort (SEC)-related, in order to review their suitability in practice. We note 

that the detailed review of the SRS SEC issues is being done separately by SC&A; it is 

anticipated that that material will be reviewed by the SRS Work Group. 

NIOSH proposes a one person-one sample (OPOS) statistic be applied by averaging all 

urinalysis samples collected from a worker in a given time period. This would reduce the 

urinalysis dataset to a single mean value for each worker in each time period. The set of mean 

values is then used to fit an exposure distribution in each period. The exposure distribution is 

used to provide estimates of the geometric mean (GM) and geometric standard deviation (GSD) 

in that period for use in the coworker model. As the mean value cannot be calculated when there 

are samples below the detection limit (nondetects) present in the data, NIOSH proposes to use 
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the maximum possible mean (MPM) as an upper bound on the true mean value. The MPM is the 

mean obtained after first replacing the nondetect samples with the values of their detection 

limits. 

The use of average values does not account for variability of the samples within the time period 

and the procedure will result in lower values of the GSD used in the coworker model. The 

OPOS approach represents a significant departure from the previous coworker model 

methodologies. This change may require re-evaluation of all previous cases with determinations 

that were based on coworker model estimates. Two analyses were conducted to examine the 

changes introduced by using the OPOS approach in the development of coworker models. 

SC&A conducted a simulation analysis to determine the difference between the lognormal 

models developed under the OPOS approach versus the use of the full set of individual samples 

from all workers. In a second analysis by SC&A, the SRS tritium database from 1962 through 

1964 was examined to compare the parameters of lognormal distributions generated under the 

OPOS and full coworker models to lognormal distributions estimated for individual workers in 

each year. 

A hypothesis testing procedure is proposed for determining when there are “significantly 

different strata.” The hypothesis test procedure compares two worker groups using the Monte 

Carlo permutation test (MCPT) based on a parametric lognormal model and the nonparametric 

Peto-Prentice test. The MCPT compares parameters of lognormal distributions fitted to the 

OPOS data using the regression on order statistics (ROS) method (Helsel 2005). The ROS 

method permits estimation of lognormal parameters from data containing nondetects. 

Two examples are provided in RPRT-0053 to demonstrate the application of these tests. One of 

these examples with a borderline decision was re-examined using a simulation approach to 

validate the permutation test results. 

The recommended hypothesis tests apply to only two groups, although several methods for 

multiple comparisons are discussed. Stratified models generally contain more than two strata 

with the objective of developing estimates for each strata. There is usually no a priori

requirement that the strata be significantly different, although the resulting estimates may have 

sufficient precision to determine significant differences if the sample sizes are sufficiently large. 

SC&A has shown in prior work that more than two strata are necessary in at least some cases, so 

as to ensure that coworker dose estimates are claimant favorable. In one example, we found that 

SRS construction workers need to be subdivided by job type and area of work (SC&A 2010a, 

SC&A 2010b). This issue and the possibility of addressing it by multiple comparisons is 

addressed briefly in the main body of this report. 

SC&A has identified the following findings. 

Finding No. 1: Due to the dependencies that exist in the ranked data, the R2

 for ROS does not 

have the usual interpretation. The recommendations in RPRT-0053 for using ROS do not 

address this concern. 
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Finding No. 2: In the application of the procedures recommended in RPRT-0053, the issue of 

completeness of the available coworker data has not been addressed. If the unmonitored workers 

are from a different population, the applicability of a coworker model derived from monitored 

coworkers would be in question. The matter of the relative exposure potential of the monitored 

workers needs to be demonstrated rather than assumed. The methods proposed in RPRT-0053 

for analyzing the coworker datasets require verification that (1) the available coworker data are 

representative of all groups of workers, and (2) the manner of use of the data is claimant 

favorable for the specific datasets to which the method is applied. A sound statistical 

methodology is subject to these two important caveats. 

Finding No. 3: The OPOS statistic methodology summarizes a worker’s exposure by averaging 

overall urine samples collected during the specified time period. The use of average values does 

not account for variability of the samples within the time period, and the procedure will result in 

lower values of the GSD used in the coworker model. 

Finding No. 4: The OPOS method must strictly be applied to comparisons where the sampling 

protocol was the same. Specifically, when there is evidence that the sampling protocol for one 

group of workers was different than the protocol used for the other group, the tests do not 

provide a valid comparison. For example, if the monitoring of one group of workers is incidentdriven and the other is not, then the OPOS approach is not appropriate for comparing the two 

distributions. 

Finding No. 5: The methods in RPRT-0053 require a high level of confidence before deciding 

that the two worker groups are significantly different. The requirement for a high level of 

confidence in this decision is not claimant favorable when using a null hypothesis of “No 

Difference.” The power of the tests to detect differences given the limited quantity of available 

data has not been established. The Data Quality Objectives (DQO) process should be used to 

balance Type 1 and Type 2 decision errors. 

Finding No. 6: Given the small number of trades worker (CTW) data points, in many years the 

tests cannot reliably detect differences smaller than a factor of 4 to 10 in the CTW/nonconstruction trades worker (non-CTW) ratio of GMs. Larger differences have a 95% or better 

chance of detection. Smaller differences would be in the “gray region” for the test, sometimes 

detected, sometimes not. Overall, SC&A concludes that the NIOSH method of concluding that 

there are no significant differences based on the available data would often lead to very claimantunfavorable results. 

Finding No. 7: The statistical tests for comparing two strata require that the samples in each 

group be independent. If a worker in one group is exposed to radionuclides with long retention 

in the body and then changes jobs and becomes part of the other group in the same year, the 

OPOS values are correlated for this worker. This correlation not only violates the assumptions 

of the tests, but also creates a bias toward a decision of “No Difference” between the two groups.

Finding No. 8: Although one example where a significant difference is found is presented in the 

report, NIOSH has not provided any measure of the power of the hypothesis test procedure to 

detect differences within the worker population. This deficiency should be corrected before the 
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test is adopted as an appropriate procedure for coworker models. Conducting the tests at a 90% 

level of confidence would be claimant favorable. 

RECOMMENDATIONS: 

(1) NIOSH might consider reversing the null hypothesis for the Peto-Prentice test. NIOSH’s 

implementation of the hypothesis tests to test for differences between CTWs and nonCTWs at SRS uses a null hypothesis that is not claimant favorable, as it places the burden 

of proof on the CTW claimants to prove a significant difference. The Peto-Prentice test 

is more generally applicable and may be applied using a claimant-favorable null 

hypothesis. The groups of workers with suspected high exposures should be considered 

different in the absence of strong evidence that they are not. This is more likely to result 

in a claimant-favorable model. 

(2) More than two strata would be required to properly characterize the varied worker 

populations at many sites. Multiple comparisons when there are more than two strata 

may be possible, but could be complex and suffer from limits imposed by small sample 

sizes. The analysis may spiral into large numbers of comparisons with inconclusive 

results. 

(3) There is persuasive evidence provided by the analysis of SRS CTWs by job type and by 

area of work (SC&A 2010a, 2010b) that subgroups of CTWs are not drawn from the 

same distribution as non-CTWs. When the distributions of CTW subgroups are different 

from non-CTW, CTW data by job type and area can be used to construct coworker 

models for their CTW peers. Of course, this requires sufficient data in each job/area 

category for which a coworker model is to be constructed. 

(4) NIOSH has stated that each of the two groups must have a sufficient number of samples; 

at least 30 samples in each group would be required. If the total number of samples is 

less than 30, the method is not suitable. Boiling down the number of samples by using 

OPOS reduces the number of samples and produces greater uncertainty and a larger gray 

region, making the test less claimant favorable. As an example, the number of samples 

used in the coworker study for neptunium at SRS was so small in approximately one-half 

of the years analyzed in RPRT-0056 that the difference between groups would have to 

exceed a factor of 3 to 4 for a significant difference with these sample sizes. In all 

remaining years except for 1985, the difference between groups would have to be as large 

as a factor of 4 to a factor of over 10 before the tests would indicate a significant 

difference. Due to the low power of these tests, NIOSH findings of no significant 

differences are due mainly to an inadequate sample size and the use of OPOS values that 

has further reduced the sample sizes. 

(5) In principle, multiple comparisons can be done for more refined groupings, like CTWs by 

job type with all non-CTWs. But this will run into difficulties in many cases, as we 

found in prior analyses even for a 10-sample threshold. It will be much more difficult to 

meet the 30-sample threshold needed for the tests recommended in RPRT-0053, but this 

is essential for a valid comparison. Moreover, a valid comparison requires that the 
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NOTICE:

30-sample threshold be met for each of the two groups, not just one. RPRT-0053 is not 

explicit on this point, though it is implied in footnote 6 on page 9. The 30-sample 

threshold for each group should be made explicit.
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1.0 INTRODUCTION 

This report presents SC&A’s initial review of ORAUT-RPRT-0053, Analysis of Stratified 

Coworker Datasets (ORAUT 2012d), which describes the National Institute for Occupational 

Safety and Health’s (NIOSH’s) proposed methods for reconstructing exposures to unmonitored 

workers using coworker data. RPRT-0053 summarizes and extends the statistical methods for 

analysis of coworker data that were previously published. The proposed analyses follow the 

general framework shown in Table 1. The shaded areas in Stage 2 and Stage 3 indicate the main 

subject areas of the report. 

Table 1. Proposed Stages of the Dose Reconstruction Process 

Stage 1: Urinalysis Data 

Stage 2: OPOS Urinalysis Data 

Stage 3: 50th and 84th Percentile Urinalysis Estimates from OPOS Data 

Stage 4: 50th and 84th Percentile Intake Rates 

Stage 5: Person-specific Intakes and Doses 

Stage 6: Probability of Causation 

The report addresses three major topics: 

(1) Methods for analyzing coworker urinalysis data in Stages 2 and 3 with varying 

proportions of nondetects, with and without the assumption of lognormality. RPRT-0053 

reviews a toolbox of statistical methods appropriate for analyzing the available data in 

each stratum. 

(2) Reduction of the Stage 1 coworker urinalysis dataset containing individual urinalysis 

samples to a single statistic per worker per time period (Stage 2). NIOSH proposes that a 

one person-one sample (OPOS) statistical approach be applied by averaging all urinalysis 

samples collected from a worker in a given time period. This would reduce the urinalysis 

dataset in Stage 1 to a single mean value for each worker in each time period (Stage 2). 

(3) Methods for evaluating the stratification of the worker population into subgroups of 

workers (strata) using distributions based on the reduced data. Several hypothesis testing 

procedures are proposed for determining when there are “significantly different strata.” 

The Peto-Prentice form of the Wilcoxon Rank Sum (WRS) test is recommended for 

comparing the strata in each time period based on the OPOS statistics (Stage 2). The 

Monte Carlo permutation test (MCPT) described in ORAUT-RPRT-0049 (ORAUT 

2010a) is also recommended for comparing the strata in each time period based on the 

parameters obtained by fitting lognormal distributions to the OPOS statistics (Stage 3). 

The three topics are addressed separately in the following sections of the report. 
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NOTICE:

1.1 RELATED ORAUT PUBLICATIONS 

1.1.1 Source Documents 

RPRT-0053 includes a toolbox of statistical methods that are available for analyzing the data in 

each strata. A range of methods is included for analysis of datasets, with the proportion of 

nondetects ranging from none to essentially all or most of the available data from monitored 

workers. The range of proposed methods for analyzing datasets summarizes methods previously 

reported in: 

 ORAUT-OTIB-0019, Analysis of Coworker Bioassay Data for Internal Dose Assessment

(ORAUT 2005) 

 ORAUT-PROC-0095, Generating Summary Statistics for Coworker Bioassay Data 

(ORAUT 2006a)

 ORAUT-OTIB-0075, Use of Claimant Datasets for Coworker Modeling (ORAUT 

2009a) 

 ORAUT-RPRT-0044, Analysis of Bioassay Data with a Significant Fraction of LessThan Results (ORAUT 2009b) 

 ORAUT-RPRT-0049, Discussion of Tritium Coworker Models at the Savannah River 

Site – Part 1 (ORAUT 2010a) 

1.1.2 Dependencies 

Several recent Oak Ridge Associated Universities Team (ORAUT) documents are based on the 

analytical methods proposed in RPRT-0053. These documents include: 

 ORAUT-RPRT-0055, A Comparison of Exotic Trivalent Radionuclide Coworker Models 

at the Savannah River Site, (ORAUT 2012a) 

 ORAUT-RPRT-0056, A Comparison of Neptunium Coworker Models at the Savannah 

River Site (ORAUT 2012b) 

 ORAUT-RPRT-0058, A Comparison of Mixed Fission and Activation Product Coworker 

Models at the Savannah River Site (ORAUT 2012c) 

As the titles indicate, these applications address comparisons of coworker models for the CTWs 

and non-CTWs at the Savannah River Site (SRS). The reports use the Monte Carlo permutation 

test methodology recommended in ORAUT-RPRT-0053 and/or the Peto-Prentice test for these 

comparisons. In RPRT-0055, trivalent radionuclides bioassay data are first reduced using the 

OPOS method. Similar applications of the RPRT-0053 methodology at SRS are made in 

ORAUT-RPRT-0056 and ORAUT-RPRT-0058. All of these applications discussed the 

comparison of coworker models at SRS. Our review includes several examples of the RPRT0053 methodology drawn from these derivative publications.
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2.0 STATISTICAL METHODS FOR ANALYZING COWORKER 

URINALYSIS DATASETS 

Several statistical procedures are recommended in RPRT-0053 to estimate parameters for use in 

the coworker model. The coworker model is used in the dose reconstruction process to estimate 

dose to an individual in periods with unmonitored or undocumented exposure. RPRT-0053 

provides a toolbox of statistical methods for analyzing the available coworker data and 

estimating the 50th and 84th percentiles of exposure. Three approaches for fitting probability 

distributions to bioassay data are discussed. The three approaches cover a range of methods 

appropriate for analysis of datasets with a number of nondetects ranging from none or few to 

essentially all or most of the available data from monitored workers. RPRT-0053 summarizes 

and extends the statistical methods for analysis of coworker data previously published in 

ORAUT-OTIB-0019, Analysis of Coworker Bioassay Data for Internal Dose Assessment

(ORAUT 2005); ORAUT-PROC-0095, Generating Summary Statistics for Coworker Bioassay 

Data (ORAUT 2006a); ORAUT-OTIB-0075, Use of Claimant Datasets for Coworker Modeling 

(ORAUT 2009a); ORAUT-RPRT-0044, Analysis of Bioassay Data with a Significant Fraction 

of Less-Than Results (ORAUT 2009b); and ORAUT-RPRT-0049, Discussion of Tritium 

Coworker Models at the Savannah River Site – Part 1 (ORAUT 2010a). 

RPRT-0053 recommends the OPOS statistic approach to derive a single value that represents the 

exposure to each worker in each time period. The OPOS methodology summarizes a worker’s 

exposure by averaging the concentration in all urine samples collected during the specified time 

period. The following guidelines are provided in the text and footnotes on page 9 of RPRT-0053 

for the application of the OPOS methodology: 

As a general guideline, the minimum sample size used for coworker modeling is 30 

individuals (i.e., 30 OPOS results) in a given period.5 This minimum6

 can be 

relaxed if, in the judgment of the statistician performing the analysis, the uncertainty 

in the resulting parameter estimates is not excessive. 

5

 Data from multiple years (usually no more than 3) can be combined to achieve this 

minimum if the conditions in the workplace are reasonably constant over the period in 

question. 

6 The U.S. Environmental Protection Agency ([EPA 2010], p. 27) discusses minimum 

sample size required for performing statistical tests on censored datasets and 

recommends ~15 results per sample (stratum) as a minimum. Here we are estimating 

parameters from the data, so the default minimum has been increased to 30.

Time periods may be as long as 3 years, but more often as short as 1 year. Yearly OPOS 

estimates are calculated for workers at SRS for exotic trivalent radionuclides in RPRT-0055, for 

neptunium in RPRT-0056, and for mixed fission and activation products in RPRT-0058, with 

few exceptions. Problems associated with the use of the OPOS statistic to represent annual 

worker exposure are discussed in more detail in Section 3. The questions of minimum sample 

size and EPA’s advice on the sample size issue noted in footnote 6 in the passage above are 

addressed further in Section 4. 
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The regression on order statistics (ROS) method for estimating the geometric mean (GM) and the 

geometric standard deviation (GSD) of a lognormal distribution was described in ORAUTPROC-0095, Generating Summary Statistics for Coworker Bioassay Data (ORAUT 2006a). 

The deficiencies of ORAUT-PROC-0095 when there is a large proportion of nondetects were 

noted by SC&A in Findings from 3rd set of Procedures (SC&A 2007). In NIOSH Responses to 

Selected Findings from 3rd set of Procedures (ORAUT 2010b), NIOSH explained that a new 

report (i.e., ORAUT-RPRT-0044) has been developed to better address the issue of censored 

data. RPRT-0044 describes in more detail the methods recommended in RPRT-0053 applicable 

to datasets with a large proportion of nondetects. SC&A identified the following relevant 

findings during the review of RPRT-0044 (SC&A 2010c). 

Finding No. 1: The statistical methods proposed in ORAUT-RPRT-0044 are 

based on sound statistical methodologies, and the material is well presented. The 

proposed methods are an improvement over the regression methods proposed in 

ORAUT-PROC-0095 when essentially all or most of the data are less-than 

results, the limit of detection was the same for all samples in the dataset, and the 

samples above the limit of detection are randomly spread across workers, job 

types, and work areas. 

The work location and work assignments of the workers with positive results are 

not considered in the NIOSH approach. Before these methods are used in a 

coworker model, further analysis of the positive results is required. In particular, 

identification of the workers, work areas, and processes accounting for the 

positive results in the datasets is required to reveal possible patterns that may 

explain the occurrence of positive results. 

NIOSH does not offer any consideration relating to the pattern or time 

distribution of the positive results. For example, the positive results could be 

present x times per year, during defined periods of time, or during a specific 

campaign. It is possible that the same subgroup of workers accounted for most of 

the positive readings year after year. 

Finding No. 2: ORAUT-RPRT-0044 does not address the representativeness of 

the dataset for workers in all work areas and job types. No individual worker 

analysis was performed, as the report concentrates only on analysis of a 

collection of analytical results. (...) 

Finding No. 4: The methods proposed in RPRT-0044 for datasets with 

essentially all or most of the less-than results are based on samples obtained from 

all workers, regardless of job type or location. No attempt was made to 

determine the work areas, processes, or job types of workers with positive results. 

This approach is not claimant favorable for construction workers for three 

reasons: 

(1) In many cases, construction workers were not monitored as 

frequently as non-construction workers, hence the dataset may not 
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be representative of the distribution of construction worker 

exposures. 

(2) Because constructions workers were sampled less frequently, a 

higher percentage of these workers will require use of the 

coworker model. 

(3) The positive samples may come from very few workers or 

restricted time periods, which may not be representative of the 

worker population. 

The work assignments of the workers with samples in the upper tail of the mixture 

distribution may have an unexpectedly high number of construction workers when 

compared with their degree of monitoring. The work assignments of workers with 

samples in the two populations should be inspected and categorized by job type to 

look for such disparities. 

A part of the present report reviews whether NIOSH has addressed these concerns in RPRT0053. 

2.1 REGRESSION ON ORDER STATISTICS (ROS) 

The ROS method has been used routinely by NIOSH as a convenient way to estimate parameters 

of a lognormal distribution when there are nondetects in the dataset. The ROS method is 

incorporated in RPRT-0053 by reference to prior publications. On page 9 of RPRT-0053, 

NIOSH explains that the recommended ROS procedure is the same as that recommended in 

PROC-0095, with the following exception: 

ORAUT-PROC-0095 uses Hazen plotting points (...), which are referred to as 

"percentile midpoints" in the procedure. Hazen plotting points are valid only for 

datasets with a single left-censoring level (i.e., where a single decision level is 

applied to all the data in the dataset). Here, Helsel-Cohn plotting points are used 

(...), which are suitable for single and multiple left-censoring... With the 

exception of the plotting points, the ROS used here is the same as the ROS used in 

ORAUT-PROC-0095. 

The ROS method is based on least squares regression. The regression model for a dataset of size 

n is written as: 

 

bmxyi)ln(  i 

where the values yi, i = 1, ... , r denote the r ≤ n values above the limit of detection (i.e., not 

including the “less than” values). The symbols b and m denote the y-intercept and slope of the 

regression line, respectively, and ln denotes the natural logarithm. 
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

Each observation is assigned a corresponding normal score depending on its plotting position: 

i   i /5.0 nRx for i = 1, ... , r. Here, Φ 1   -1[∙] denotes the inverse of the cumulative normal 

distribution function. The argument used for this function is a function of the rank Ri, which is 

the rank of yi when all n data values are included in the ranking and the (n-r) values below the 

minimum detectable amount (MDA) are assigned the lowest (n-r) ranks. In this example, Hazen 

plotting position is the percentile midpoint; ROS with other plotting positions has the same form 

of model with slightly different values for the xi. The regression estimates are based on the 

entire set of data above the detection limit. If the data fit a lognormal distribution where the 

logarithms have mean μ and standard deviation σ, then a scatter plot of the r points [xi , ln(yi)] 

will lie on a straight line with slope m = σ and a y-intercept b = μ. The regression method may 

be used not only to verify that the data follow a lognormal distribution, but also to provide 

estimates for the parameters of the lognormal distribution when there are values in the dataset 

below the detection limit. 

A determination of the goodness-of-fit of the lognormal distribution is based on regression R2

although, due to the dependencies that exist in the regression estimates derived from ranked data, 

the R2 does not have the usual interpretation. RPRT-0053 states on page 8: 

Operational bioassay programs can generate multiple results for an individual in 

a given period (e.g., a year), which creates a related problem if an individual is 

involved in an incident and has more (...) bioassay results than other workers. If 

these are not accounted for, the problems of correlated data and unequal number 

of samples per person can violate the assumptions on which the linear regression 

used to model the data and the statistical tests used to compare strata in the 

population are based (...). 

 

Although NIOSH has an apparent concern that the assumptions of linear regression apply, the 

data values in the ROS scatter plot are not independent observations. If xi ≤ xj, then it is known 

with certainty that yi ≤ yj. This dependence among the observations violates the usual 

assumption of conditional independence of the y values in the regression, given the set of x

values. In addition, the yj are autocorrelated and heteroscedastic, as noted long ago in Looney 

and Gulledge (1985): 

(...) we propose the use of the correlation coefficient in constructing a goodnessof-fit test statistic from a plot based on any particular plotting position. Since the 

Y(i) are highly correlated and heteroscedastic, the usual distributional results 

for the correlation coefficient do not apply. Instead, empirical sampling methods 

must be used to determine the null distribution of the test statistic. 

The heteroscedasticity of the order statistics derived from a set of samples is well known (David 

and Nagaraja 2003). Clearly, the sample minimum and maximum have the greatest sampling 

variance. Moreover, when the order statistics are used in ROS, these extreme values on the far 

left and far right of the distribution have the greatest influence on the lognormal parameter 

estimates. The GSD derived from the ROS slope estimate is particularly sensitive to the 

influence of heteroscedasticity in the order statistics. The recommendations in RPRT-0053 for 

using ROS do not address these serious deviations from the standard linear regression model 
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assumptions when interpreting the R2 values as a measure of goodness of fit of the ROS 

probability plot. 

Finding No. 1: Due to the dependencies that exist in the ranked data, the R2

 for ROS does not 

have the usual interpretation. The recommendations in RPRT-0053 for using ROS do not 

address this concern. 

When there is a large proportion of nondetects and/or the ROS method generates a GSD estimate 

over 6, NIOSH suggests the use of the maximum likelihood methods discussed in ORAUTRPRT-0044, Analysis of Bioassay Data with a Significant Fraction of Less-Than Results 

(ORAUT 2009b). A second method recommended in RPRT-0053 for datasets with a large 

proportion of nondetects (>85%) is the binomial fit method, also discussed in RPRT-0044. The 

binomial fit method is not recommended by NIOSH in RPRT-0053 for use in stratifying 

datasets, as detailed in Section 2.3 of this report. 

2.2 EFFECTIVE FIT 

The maximum likelihood method, which is also called “effective fit,” attempts to fit a mixture of 

two distributions. The effective fit method assumes the distribution of results is not a single 

lognormal distribution, but a mixture of two distinct distributions, one normal and the other 

lognormal. In this model, there are two populations of samples; most samples have no 

measureable level of analyte in the urine, but a small fraction of the samples do. In this mixed 

model, the former group of samples with less-than results is assigned a normal distribution 

representing “background” exposures, and the latter group of samples is assigned a lognormal 

distribution of exposures. 

Maximum likelihood techniques are used to estimate the parameters of the mixed model. If a 

dataset contains urine results for which most of the workers do not have analyte in their urine but 

a small fraction of the workers do, then the methods presented in RPRT-0053 are an 

improvement over the PROC-0095. However, NIOSH does not offer any consideration relating 

to the pattern or time distribution of the positive results. It is necessary to know if the positive 

results occur every year, and if those results are related to a particular procedure. For example, 

the positive results could be present x times per year, during defined periods of time, or during a 

specific campaign. 

In the application of the procedure recommended in RPRT-0053, the issue of completeness of 

the available coworker data has not been addressed. Some workers were not monitored; 

otherwise there would be no need for a coworker model. The underlying assumption appears to 

be that the workers with the most exposure potential were monitored, but we have seen in a 

number of cases that this was not necessarily true. If the unmonitored workers are from a 

different population, the applicability of a coworker model derived from monitored workers 

would be in question. 

Finding No. 2: In the application of the procedures recommended in RPRT-0053, the issue of 

completeness of the available coworker data has not been addressed. If the unmonitored workers 

are not from a population that had the highest exposure potential, the applicability of a coworker 
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model derived from monitored coworkers would be in question. The matter of the relative 

exposure potential of the monitored workers needs to be demonstrated rather than assumed. The 

methods proposed in RPRT-0053 for analyzing the coworker datasets require verification that 

(i) the available coworker data are representative of all groups of workers, and (ii) the manner of 

use of the data is claimant favorable for the specific datasets to which the method is applied. A 

sound statistical methodology is subject to these two important caveats.

2.3 BINOMIAL FIT 

The binomial fit method is recommended in RPRT-0053 if the coworker dataset has a very large 

proportion of nondetects, up to and including 100%. This method for estimating the GM and 

GSD was presented previously in ORAUT-RPRT-0044 (ORAUT 2009b). In this situation, there 

are insufficient data to permit a comparison of distributions. This method will not be used in 

comparing worker groups, as NIOSH recommends the following: 

Datasets that are modeled using the binomial fit are considered to not contain 

enough information to decide if strata are different, and it is recommended that 

such datasets not be stratified.
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3.0 ONE STATISTIC PER WORKER PER TIME PERIOD 

Prior to RPRT-0053, coworker models were constructed from the full set of samples for the 

workers of interest, as indicated by NIOSH in the Introduction: 

Coworker models are typically constructed using data from all monitored workers 

by fitting a lognormal probability distribution to the data (...) to estimate the 

geometric mean (GM) and geometric standard deviation (GSD) of the doses. This 

procedure was extended to use a simple random sample of the monitored workers 

when a complete dataset was not available (...) 

RPRT-0053 recommends a new approach to estimating coworker models. NIOSH proposes that 

an OPOS approach be applied by averaging all urinalysis samples collected from a worker in a 

given time period. NIOSH also proposes that the sample statistic selected for the OPOS statistic 

is the mean of the individual sample values (average value). As the mean value cannot be 

calculated when there are samples below the detection limit (nondetects) present in the data, 

NIOSH proposes to use the maximum possible mean (MPM) as an upper bound on the true mean 

value. The MPM is the mean obtained after first replacing the nondetect samples with the values 

of their detection limits. 

3.1 OUTLINE OF OPOS PROCEDURE 

The basic steps of the OPOS approach are as follows. 

 For each individual and for each bioassay sample determine the group classification 

(Group A, Group B, or unknown). 

 Determine the OPOS statistic (usually the MPM) for each individual and time period. 

 Determine the GM and GSD urinary excretion rates using the ROS, effective fit, or 

binomial methods as appropriate for each strata for each time period. 

 Compare the strata using the MCPT at Stage 3 and/or Peto-Prentice test at Stage 2 to 

determine if there is a statistically significant difference between the two strata. 

This procedure would reduce the original urinalysis sample dataset to a single mean value for 

each worker in each time period. The set of mean values is then used to fit an exposure 

distribution for the coworker model in each period. The exposure distribution is used to provide 

estimates of the GM and GSD in that period for the coworker model. The following discussion 

of the OPOS approach is recorded in the notes from the Subcommittee on Procedures Review 

meeting on November 1, 2012 (Meeting Transcript 2012, pp. 118 to 120): 

MEMBER ZIEMER: It would change the distribution. 

MR. HINNEFELD: Nominally probably. 

CHAIR MUNN: Yes. 
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MR. HINNEFELD: Yes, it would change the distribution of doses because you 

drop out some of the high-end stuff. So no one has yet jumped in to correct me, so 

maybe I got it right. 

In this section of the report, we examine how the distribution will change if the recommended 

OPOS procedure is adopted. The OPOS exposure distributions are compared with the exposure 

distributions derived from the full set of samples. The OPOS methodology summarizes a 

worker’s exposure by averaging overall urine samples collected during the specified time period. 

In the case of nondetect samples, the detection limit is used for the nondetects in the calculation 

of the average to yield the MPM. The use of average values does not account for variability of 

the samples within the time period, and the procedure will result in lower values of the GSD used 

in the coworker model compared with previous procedures. A GSD must be assigned for the 

missing dose to a worker in each year, and that GSD should reflect the variability in that 

worker’s exposure during the year. The OPOS GSD measures the variability of average annual 

dose across workers, and ignores variability for an individual worker within the year. 

Finding No. 3: The OPOS statistic methodology summarizes a worker’s exposure by averaging 

overall urine samples collected during the specified time period. The use of average values does 

not account for variability of the samples within the time period and the procedure will result in 

lower values of the GSD used in the coworker model.

The OPOS methodology does not examine the temporal pattern of individual exposures for 

longer than one time period. NIOSH’s strategy for bounding internal dose based on bioassay has 

been to assume a claimant-favorable chronic intake throughout the year. That is, the bounding 

assumptions presumably account for the variability in intake regimens. It remains to be 

determined whether those assumptions sufficiently bound intakes based on the OPOS 

methodology. It will be necessary to develop a list of radionuclides for which the procedure 

reflects the temporal patterns of exposure and subsequent organ doses. 

When comparing two populations using a statistical test for differences, it is important that the 

data are collected following the same protocol for both groups of workers. In the specific case of 

CTW versus non-CTW comparisons in RPRT-0056, NIOSH has said that sampling was 

incident-related for CTWs and routine for non-CTWs, so the OPOS method does not appear 

appropriate for comparing the two distributions. 

The valid use of OPOS values in two-group comparisons requires that the sampling protocols 

used for each group be similar. There are many ways that the sampling protocols may differ, and 

NIOSH has not addressed the extent of this problem. For example: 

(1) Do some workers have OPOS results for a short period of time and not for the whole 

year? 

(2) Do some workers have OPOS results derived from a large number of samples during the 

period of time and other workers from the same population have one or only a few 

samples? Should a lognormal distribution be formed by combining OPOS and individual 

samples into a single distribution? 
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(3) Does the lognormal distribution from one population consist of OPOS results for all 

workers and the other lognormal distribution from the second population have a mixture 

of OPOS results and individual samples, or consist almost entirely of individual samples? 

Should the two lognormal distributions be compared? 

The answers to these questions are important because the use of OPOS values introduces 

complications in the subsequent coworker model analyses that rely on these values. OPOS 

values are not measurements, but are statistics derived from a set of measurements. The OPOS 

values are averages of a varying number of samples, with a different number for each worker. 

Since it is an average, each OPOS value has an uncertainty associated with the calculated value. 

Mathematically, the sampling variance of an average of n independent samples nXX n

i i / 1  is 

 /)()( nXVarXVar . The sampling variance of the average increases with the variance in the 

individual worker’s samples during the time period covered by the OPOS value, and the 

sampling variance of the OPOS average is smaller for workers with a larger number of samples 

during the period. Use of the MPM in place of a simple average for the OPOS value when there 

are nondetects introduces an additional level of uncertainty in the OPOS values that is not 

addressed in the equation above. 

A difference in the number of samples available for the workers in each group implies a 

difference in the uncertainty for the OPOS values for each group. In general, more samples are 

available for the onsite workers who are part of an ongoing monitoring program. Due to the 

larger number of samples, the OPOS values for the onsite workers may be measured with greater 

precision than is available for other groups of workers. 

Since there is uncertainty in the OPOS statistics, and this uncertainty varies from worker to 

worker and from one group of workers to another, all subsequent analyses based on OPOS 

values are conducted using heteroscedastic data. Finding 1 in Section 2.1 indicates that the ROS 

method conducted on individual samples ignores the heteroscedastic nature of the order statistics 

derived from the sample values. If the order statistics are derived from OPOS values, this 

introduces a second problem unique to the use of OPOS values in ROS: values that are being 

ranked may not come from the same distribution unless the monitoring protocol is the same for 

all members of the group. 

The uncertainty in the OPOS averages affects the hypothesis tests used for comparing two 

groups of workers. Since the MCPT is conducted using ROS on OPOS values to estimate the 

lognormal parameters for the test, this test does not address the issue of heteroscedasticity in the 

OPOS values. The uncertainty in the OPOS averages also affects the nonparametric two-sample 

tests used for comparing two groups of workers. The assumptions underlying the tests are 

violated if the nonparametric tests are applied using data with different variances in each group. 

The WRS test and the generalized WRS tests, including the Peto-Prentice test, are based on an 

assumption that the only difference between the two groups is a difference in the location of the 

distributions (Conover 1980, p. 217). This means that the shapes and variances of the two 

distributions should be approximately the same. If the OPOS values for one group of workers 

are derived from a relatively small number of samples per worker while the OPOS values from 

the other group are derived from a larger number of samples per worker, the assumption of equal 

variance for both groups is suspect. Attachment B to RPRT-0053 reviews the discussion of the 
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generalized WRS tests found in Helsel (2005). The literature search does not include reference 

to the Brunner-Munzel test (Brunner and Munzel 2000). This nonparametric test is another 

generalization of the WRS test designed for comparisons of populations with different variances. 

Given the problems introduced by the use of OPOS when there are different sampling protocols 

for each group, SC&A recommends that: 

(1) OPOS values should not be combined into a single lognormal distribution when the 

sampling protocols for subsets of workers in the group differ 

(2) Distributions of OPOS values can be compared only when the sampling protocols are the 

same for both groups. 

Finding No. 4: The OPOS method must strictly be applied to comparisons where the sampling 

protocol was the same. Specifically, when there is evidence that the sampling protocol for one 

group of workers was different than the protocol used for the other group, the tests do not 

provide a valid comparison. For example, if the monitoring of one group of workers is incidentdriven and the other is not, then the OPOS approach is not appropriate for comparing the two 

distributions. 

The OPOS approach proposed in RPRT-0053 represents a significant departure from the 

previous coworker model methodologies. This report contains results of two analyses of the 

effects of the OPOS approach in the development of a coworker model. First, a simulation is 

conducted to determine the difference between the lognormal models developed under the OPOS 

approach versus the use of the full set of individual samples from all workers. In the second 

analysis, the SRS tritium database from 1962 through 1964 is examined to compare the 

parameters of lognormal distributions generated under the OPOS and full models to lognormal 

distributions estimated for SRS individual workers in each year. 

3.2 SIMULATION TO COMPARE OPOS AND FULL COWORKER MODELS 

The simulation analysis indicates that the OPOS approach results in underestimation of the range 

of variability across workers reflected in estimates of the GSD and 95th percentile, which are 

biased low relative to the original samples. As shown in Table 2, the magnitude of this bias 

increases as the number of samples per worker used in the MPM increases. A positive bias in 

the GM estimate is also noted. This complementary bias acts to keep expected values at 

approximately the same level. In Figure 1, the combined effect of the downward bias in the 

GSD and upward bias in the GM generates a downward bias in the estimates of the 95th

percentile. For a 5-sample MPM, the bias may be as large as minus 30%. When a larger number 

of samples is averaged, the bias would be larger in magnitude. 
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Table 2. Bias of OPOS Parameter Estimates versus Individual Samples 

Bias (%)

Number of 

Samples in MPM 

GSD 

(Slope) 

GM 

(Intercept) 95th Percentile 

1 0 0 0 

2 -23 32 -13 

3 -30 38 -24 

4 -33 46 -24 

5 -35 45 -29 

‐50

‐25

0

25

50

123456

Number of Samples in MPM

Bias (%)

GSD GM 95th Percentile

Figure 1. Bias of Simulated OPOS Estimates for Geometric Mean, Geometric 

Standard Deviation, and 95th Percentile vs. Individual Samples 

The large differences between the OPOS GSD and 95th percentile and the full data model GSD 

and 95th percentile observed in this initial simulation provided the impetus for a second analysis 

of the OPOS method using actual data. In this analysis, the tritium bioassay data at SRS are used 

to compare OPOS and full models with individual worker distributions. 

3.3 OPOS AND FULL MODEL COWORKER MODELS COMPARISON WITH 

INDIVIDUAL WORKER EXPOSURES 

To evaluate the impacts of changing to an OPOS methodology, tritium bioassay data from 

workers at SRS from 1962 to 1964 are used to construct annual lognormal exposure distributions 

for the OPOS and Full models. The tritium dataset used for this analysis is robust in the sense 

that it contains many bioassays per worker in each year, enabling the construction of individual 

lognormal exposure distributions for each worker. The dataset contains a reasonably large 

number of detects per worker, and no very extreme values. However, the data may include 

workers with many closely spaced, high sample values collected after incidents. 
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In this analysis, the OPOS and Full model coworker distributions are compared with the 

exposure distributions estimated for individual workers. The unscreened 1962–1964 SRS tritium 

dataset contains approximately 50 workers, many with a relatively large number of samples per 

worker in each year. Many samples are nondetects, so the ROS method was used to estimate a 

lognormal distribution for each worker. An example of a worker distribution for a worker with 

46 bioassays in 1962 is shown in Figure 2. The ROS lognormal estimates were developed in 

each year for all workers with more than 3 detects in their samples. 

y = 0.8283x + 0.9964

R2

 = 0.8965

-1

0

1

2

3

4

-2 -1 0 1 2 3

Normal Score

ln(Data)

Figure 2. ROS Plot for Worker 2, 1962 

Table 3 shows a comparison of the lognormal distributions generated by the two models for the 

1962 through 1964 time period. The table shows the GM and GSD estimated using each model, 

and the mean, standard deviation, and 95th percentile of each model. The highlighted region of 

each table shows the ratio of the GSD, standard deviation, and 95th percentile for each model. 

The ratio is obtained by dividing the OPOS model estimate by the Full model estimate. 

The GM and GSD of the worker lognormal distributions are plotted in Figures 3, 4, and 5. The 

plots also show points for the lognormal distributions for the OPOS and Full models. As 

expected based on the previous analysis, the OPOS model has a GSD that is substantially lower 

than the GSD of the Full model, and a higher GM. The OPOS estimates shown in Table 4 for 

the standard deviation and the 95th percentile are also substantially lower than the Full model 

estimates. The OPOS estimates for these three measures of the spread of the coworker 

distribution are from 20% to 44% lower than the estimate generated by the Full model. 
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Table 3. Comparison of OPOS and Full Coworker Models for SRS Tritium, 

1962 to 1964 

1962 1963 1964 

OPOS Full Ratio OPOS Full Ratio OPOS Full Ratio 

GM 1.59 0.95 1.67 1.71 0.84 2.04 2.56 2.15 1.19 

GSD 2.03 3.31 0.61 1.99 3.52 0.56 1.80 2.62 0.69 

Mean 2.03 1.95 1.04 2.16 1.85 1.17 3.04 3.43 0.89 

Standard Deviation 1.58 2.42 0.66 1.66 2.47 0.67 2.19 3.31 0.66 

95th Percentile 5.06 6.81 0.74 5.28 6.64 0.80 6.73 10.53 0.64 

The Full model tends to have a GSD near (or below) the upper 10% of workers with the highest 

GSDs. The OPOS model tends to have a GSD near (or below) the median worker. In all three 

figures, the OPOS GSD is exceeded by the GSD of more than one-half of the workers. It is 

likely that the upper 10% in Figures 3 through 5 includes workers with many closely spaced, 

high sample values collected after “incidents.” If that were true, then the Full model would be 

bounding for the other 90% of workers, while the OPOS model regresses toward the median 

worker. 

Tritium, SRS, 1962

0

1

2

3

4

5

012345

GM (pCi/l)

GSD

SRS Workers

OPOS Model

Full Model

Figure 3. Scatter Plot of GSD vs. GM by Worker with OPOS and Full Models, 1962 
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Tritium, SRS, 1963

0

1

2

3

4

5

6

0123456

GM (pCi/l)

GSD

SRS Workers

OPOS Model

Full Model

Figure 4. Scatter Plot of GSD vs. GM by Worker with OPOS and Full Models, 1963 

Tritium, SRS, 1964

0

1

2

3

4

5

0123456

GM (pCi/l)

GSD

SRS Workers

OPOS Model

Full Model

Figure 5. Scatter Plot of GSD vs. GM by Worker with OPOS and Full Models, 1964 

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4.0 STRATIFICATION OF THE COWORKER POPULATION 

A hypothesis testing procedure is proposed for determining when there are “significantly 

different strata.” The hypothesis test procedure compares the two strata using an MCPT and the 

nonparametric Peto-Prentice test. In the analysis of previously collected data, it is necessary to 

determine if the sample size was sufficient. NIOSH has made no effort to determine sample 

sizes that allow for sufficient power to detect differences. 

More than two strata would be required to characterize properly the varied worker populations at 

many sites, including SRS. Multiple comparisons when there are more than two strata may be 

possible, but could be complex and suffer from limits imposed by small sample sizes. The 

analysis may spiral into large numbers of comparisons with inconclusive results. 

4.1 HYPOTHESIS TESTING 

In RPRT-0053, NIOSH recommends the MCPT for comparing two groups of workers. The 

permutation test (Noreen 1989) is designed to test for a statistically significant difference 

between lognormal distributions for the two groups. An incorrect variation of the MCPT was 

described in ORAUT-RPRT-0049, Discussion of Tritium Coworker Models at the Savannah 

River Site – Part 1 (ORAUT 2010a). In that report, NIOSH compared the distribution of one 

group of workers to the entire population of workers to test for a significant difference, violating 

the independence of the two samples. Historically, ORAUT-RPRT-0049 was initiated by 

ORAUT in response to SC&A comments on ORAUT-OTIB-0075 (SC&A 2010a, SCA 2010b), 

which concerned the use of stratified coworker models for CTWs at SRS. The SC&A comments 

pertained not only to the differences in tritium exposure of the CTWs as a group versus nonCTWs, but also to the varying tritium exposures within the various construction trades. SC&A 

2010a (Section 4) also looked at other radionuclides at SRS and came to a similar conclusion—

taking work area and job type into account is critical for the development of a claimant-favorable 

coworker model. 

NIOSH proposes that strong evidence (α = 0.05 or a 95% level of confidence) is necessary 

before any differences between groups of workers should be considered in the coworker model. 

In hypothesis testing, the demand for a high degree of confidence in a decision (α or Type 1 

error) is usually balanced by a requirement for adequate power (β) to ensure the test has a 

capability of detecting differences thought to be of importance. Although there is a general 

discussion of power in the literature review included in Attachment B of RPRT-0053, NIOSH 

has not provided any measure of the power of the MCPT to detect differences given the sample 

sizes and variability encountered in the available datasets. One example where a significant 

difference was found is presented in the report. This deficiency should be corrected before the 

MCPT is adopted as an appropriate testing procedure. 

In RPRT-0053, NIOSH proposes to use nonparametric hypothesis tests to determine if there are 

differences between groups of workers. NIOSH bases the sample size for these tests suggestions 

contained in the Draft ProUCL Technical Guide (EPA 2010). This general advice is contained 

within the following passages. 
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The two-sample hypothesis testing approach is used when many (e.g., exceeding 8 

to 10) site, as well as background, observations are available. For better and 

more accurate results with higher statistical power, the availability of more 

observations (e.g., exceeding 10-15) from each of the two populations is 

desirable, perhaps based upon an appropriate DQO process, as described in an 

EPA guidance document (2006). (EPA 2010, Sect 1.3) 

And later: 

As mentioned before, every effort should be made to collect as many samples as 

determined using DQO processes as described in EPA documents (2006). [EPA 

2010, Sect 1.6.2]

In addition to the general advice of 10–15 samples, the Draft ProUCL Technical Guide contains 

further advice to use the DQO process. Appendix B, Section B1.3.2, of the same document 

(EPA 2010) contains detailed instructions for determining the required sample size based on data 

variability and DQO parameters. Instructions for 1-sided and 2-sided tests are provided. NIOSH 

has made no effort to determine sample sizes that allow for sufficient power to detect differences 

given the available sample sizes and variability. 

It is well known that the application of hypothesis tests may result in two types of decision 

errors; false rejection of the null hypothesis (Type 1 error) and false acceptance (Type 2 error). 

NIOSH considers only Type 1 errors in RPRT-0053. The hypothesis testing framework 

recommended in the multi-agency document MARSSIM (EPA 2000) provides a basis for 

determining the necessary sample size for controlling decision errors of both types. The Draft 

ProUCL Technical Guide used by NIOSH was developed to implement the recommendations 

contained in MARSSIM; the companion document for Superfund sites Guidance for Comparing 

Background and Chemical Concentrations in Soil for CERCLA Sites (EPA 2002); and other 

similar EPA guidance based on the DQO process. Although the Draft ProUCL Technical Guide 

may contain useful suggestions, it should be noted that the document has been in draft form for 

several years now and has not yet received final approval from EPA for publication. MARSSIM 

and the CERCLA guidance have received approval following extensive peer review processes. 

Several discussions in the Draft ProUCL Technical Guide refer to a “revised” version of the 

2002 CERCLA guidance document, but the revised version could not be located in an EPA 

search and final approval status is unknown. 

The statistical methods developed for MARSSIM and Superfund are particularly useful in this 

discussion. The statistical problems associated with clean-up and decommissioning of NRClicensed and Superfund facilities require comparison of data from two independent populations, 

samples from the decommissioned site (Group A), and those from nearby reference areas (Group 

B), to decide if the site concentrations exceed those in the reference areas. In the coworker 

model Group A are, say, the CTWs and Group B all other workers. Under constant revision, 

MARSSIM is the product of a multi-agency effort to provide detailed guidance for using 

decision theory for comparing the two populations. 
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MARSSIM recognizes that the use of hypothesis tests for decision-making requires 

consideration of both types of decision errors; Type 1 and Type 2. MARSSIM also recognizes 

that there is a trade-off between Type 1 and Type 2 error rates. When designing data collection 

for a hypothesis test, the required sample size is determined by specifying both the Type 1 error 

rate α and the Type 2 error rate β for the decision. Lower error rates require larger sample sizes. 

A realistic assessment of the sample sizes required to achieve pre-specified error rates depends 

on knowledge of the underlying variability in the two datasets. RPRT-0053 makes no use of this 

information. 

The following EPA guidance for setting Type 1 and Type 2 error rates during the DQO process 

has survived the test of time. Formalized first in the CRCLA guidance for Superfund sites (EPA 

2002, Section 3.2), the guidance is repeated almost verbatim in Chapter 6 of the Draft ProUCL 

Technical Guide (EPA 2010). 

The selection of appropriate levels for decision errors and the resulting number of 

samples is a critical component of the DQO process that should concern all 

stakeholders. Because there is an inherent tradeoff between the probabilities of 

committing Type I or Type II error, a simultaneous reduction in both types of 

errors can only occur by increasing the number of samples. If the probability of 

committing a false positive error is reduced by increasing the level of confidence 

associated with the test (in other words, by decreasing α), the probability of 

committing a false negative is increased because the power of the test is reduced 

(increasing β). 

Typically, the following values for error probabilities are selected as the 

minimum recommended performance measures (EPA, 1990 and EPA, 2002). 

· For the Background Test Form 1, the confidence level should be 

at least 80% (α = 0.20) and the power should be at least 90% 

(β = 0.10). 

In MARSSIM terminology, Background Test Form 1 is a 2-sample test with a null hypothesis 

that there is no difference between the site and background reference areas. These 

recommendations indicate that the power of the test should be of greater importance than the 

confidence level when the test has a null hypothesis that there is no difference between the 

populations. To facilitate this goal, the confidence level may be relaxed to 80% so the test can 

achieve greater power to detect differences between the two populations. 

Finding No. 5: The methods in RPRT-0053 require a high level of confidence before deciding 

that the two worker groups are significantly different. The requirement for a high level of 

confidence in this decision is not claimant favorable when using a null hypothesis of “No 

Difference.” The power of the tests to detect differences given the limited quantity of available 

data has not been established. The Data Quality Objectives (DQO) process should be used to 

balance Type 1 and Type 2 decision errors. 
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RPRT-0053 discusses hypothesis testing as though there were only two possible outcomes of the 

test. When the sample sizes are fixed by circumstance, there are, in fact, three possible 

outcomes, not two. The three outcomes are: 

(1) Accept the Null hypothesis of No Difference 

(2) Reject the Null hypothesis of No Difference 

(3) No conclusion can be reached from these data 

This 3-way list characterizes the “win,” “lose,” or “tie” nature of the decision-making under 

uncertainty. The process is best described in terms of the gray region for the test. The gray 

region is related to item #3 in the list above. 

4.1.1 The Gray Region for a Statistical Test 

Figure 6 shows an example of the gray region for a test of the No Difference null hypothesis. In 

this figure, the probability that the test will reject the null hypothesis is plotted on the vertical 

axis. The difference between the two populations is plotted on the horizontal axis expressed as a 

multiplier. Below the gray region, the difference between the two distributions is sufficiently 

small that the test almost always will accept the null hypothesis of No Difference. Above the 

gray region, the difference between the two distributions is sufficiently large that the test almost 

always will reject the null hypothesis of No Difference. Other features shown in Figure 6 will be 

discussed in the following sections. 

Figure 6. Simulated Test Performance Plot and Gray Region for 2-Sample t-Test for 

Difference between Coworker Model Lognormal Distributions for CTW and non-CTW 

Neptunium Whole-Body Counts in 1975 

The question of the statistical significance of any observed difference depends on the sample 

sizes and underlying variability of the populations. With small sample sizes and high variability, 
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it is unlikely that the observed difference will be found significant unless the difference is very 

large. Alternatively, when the sample sizes are large and the variability is low, the same 

difference may be statistically significant. If a test concludes that there is no significant 

difference, this should not be taken as evidence that there is no difference, but rather that the data 

are insufficient to decide if there is a difference. The statistical significance issue is not actually 

a question of whether there is a difference in the two datasets, but whether the quantity of data is 

sufficient to resolve the difference given the variability in the data. The power of resolution of 

the test, given the quantity and variability of the available data, is measured by the width of the 

gray region. 

Using the somewhat cumbersome MARSSIM terminology, the gray region shown in Figure 6 is 

bounded on the left by the Lower Bound of the Gray Region (LBGR), and on the right by the 

Upper Bound of the Gray Region (UBGR). The distance between the LBGR and the UBGR is 

the width of the gray region. The gray region depicts a range of differences Δ that is too small to 

resolve with the available number of samples due to the level of variability. The width of the 

gray region defines the minimum detectable difference (MDD) for the test under the given 

conditions. Differences smaller than the MDD cannot be used to derive a conclusion about 

whether the samples are from different populations or not, given the available sample sizes. The 

pitfalls of using a statistical test to resolve differences smaller than the MDD are well known. 

They bear repeating here for the record. 

The width of the gray region depends primarily on two factors, (1) the available number of 

samples and (2) the variance of the sample values. The gray region is a useful planning tool for 

determining the required sample size for a statistical test, since the width of the gray region for 

the test is reduced as sample size is increased. If the null hypothesis of No Difference is used, 

the width of the gray region determines the power of the test to detect a difference and reject the 

null hypothesis. When the number of samples is determined in advance of data collection, the 

variability is fixed by circumstance, but the number of samples may be adjusted to achieve 

acceptable test performance given the anticipated level of variability. Instructions for doing this 

step of the data collection planning stage are contained in MARSSIM. 

In retrospective analysis of data, the gray region is also a useful tool for evaluating the 

performance of a test applied with sample sizes that are fixed and cannot be increased. When 

both the number of samples and the sample variability are fixed by circumstance, the width of 

the gray region is also fixed. In this case, it is necessary to determine if there is sufficient power 

in the available data to detect differences of the size of interest. One tool recommended in 

MARSSIM for analyzing the power of a hypothesis test is the test performance plot. This curve 

and its use in decision-making in retrospective analyses are discussed in the following section. 

4.1.2 Test Performance Plots 

In this section, we use test performance plots to explore how large the differences between the 

two groups could be for NIOSH to still conclude that there is no significant difference. The 

discussion includes examples based on the application of the RPRT-0053 hypothesis testing 

methodology to distinguish between the CTW and other onsite, non-CTW neptunium exposure 

distributions in RPRT-0056. 
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Finding No. 6: For many years, given the small number of CTW data points, the tests cannot 

reliably detect differences smaller than a factor of 4 to 10 in the CTW/non-CTW ratio of 

geometric means. Larger differences have a 95% or better chance of detection. Smaller 

differences would be in the “gray region” for the test, sometimes detected, sometimes not. 

Overall, SC&A concludes that the NIOSH method of concluding that there are no significant 

differences would often lead to very claimant-unfavorable results. 

The test performance plot of a test for differences between two lognormal distributions is another 

feature shown in Figure 6. This test performance plot is for a 1-sided, 2-sample t-test1

 applied to 

test for differences between two lognormal distributions. The intersection points where the test 

performance curve crosses the left and right boundaries of the gray region define the test 

performance parameters α and β for the test. The Type 1 error rate for the test (α) is measured by 

the value of the test performance curve at the left edge of the gray region where Δ is equal to the 

LBGR. NIOSH has set the value of α at 5% by the decision to use a hypothesis test at the 95% 

level of confidence. This ensures that the Type 1 percentage error rate α is controlled at a 

maximum of 5% when there are, in fact, no differences between groups. This means that the null 

hypothesis will be falsely rejected in less than 5% of applications of the test procedure. 

A higher Type 1 error rate will result in a lower Type 2 error rate and vice versa. If the Type 1 

error rate is controlled at no more than 5%, it is likely that the Type 2 error rate will be large, 

unless an adequate number of samples are available in each group to provide sufficient power to 

detect differences. In the presence of highly variable data and many nondetects, a small sample 

size may result in unacceptably high Type 2 error rates. 

The Type 2 error rate for the test (β) is measured by 100 minus the value of the test performance 

curve when Δ is at the UBGR at the right edge of the gray region. The value of β is of greater 

interest in this analysis as it defines the power of the test to reject the null hypothesis. For a 

given sample size and test level α, the power of the test depends on the variability in the data. 

Due to this dependency, it is not possible to define a single sample size that will be adequate for 

all problems. NIOSH does not report the Type 2 error rate when the tests recommended in 

RPRT-0053 are applied to the neptunium CTW/non-CTW comparison in RPRT-0056. 

The sample sizes used by NIOSH in the preparation of RPRT-0056 are quite small. As few as 6 

detected values were available for CTW modeling in some years. RPRT-0056 compares the two 

groups of workers using annual datasets containing values for as few as 11 CTWs in the 1977 

neptunium coworker model comparison. Three OPOS values in this year are nondetects, leaving 

only 8 values to use in the regression. In 1985, 1986, and 1988, only 13 CTW values are 

available for the comparison, and in each year, there are 6 or 7 nondetects, representing about 

one-half of the values. These sample sizes are quite small and the gray region is expected to be 

very large in these years. 

In all years with small sample sizes, NIOSH finds no significant evidence for rejecting the null 

hypothesis at a 95% level of confidence. NIOSH concludes from these tests that there is no 

1

 In RPRT-0056, the hypothesis tests are conducted using 2-sided tests at a 95% level of confidence. In this 

discussion, only 1-sided tests are considered. The use of 1-sided tests is more relevant and claimant favorable. The 

choice of 1-sided versus 2-sided tests is discussed in Section 4.2.1. 
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 e

statistically significant difference between the two groups of workers. In truth, the lack of 

rejection in these years is due to exceedingly small sample sizes for CTWs. The test result 

provides no statistical evidence one way or the other concerning the difference between the two 

groups. In many years, the test outcomes are in the gray region. 

4.1.3 Simulated Test Performance Plots 

Due to the concerns raised by the small sample sizes used in RPRT-0056, the power of the 

recommended tests was evaluated by studying an example application of the proposed 

hypothesis testing methodology. A simulation analysis was conducted to evaluate the 

performance of the test procedures when applied to neptunium at SRS. Test performance was 

measured by examining the test performance plot for the test. Two types of tests were 

considered in this example; parametric and nonparametric. The first simulation is conducted 

using the t-test to compare the ROS-estimated lognormal distributions for CTW and non-CTW 

neptunium WBC data contained in Appendix A, Tables A-18 through A-51 of RPRT-0056. 

In the first example, samples of the appropriate sizes are drawn from the CTW and non-CTW 

distributions and compared using a two-sample t-test on the logarithms of simulated values from 

the two distributions. This simulation is based on ideal conditions—data truly are from a 

lognormal distribution, there are no nondetects, and all samples are positive, permitting 

calculation of the logarithms of the samples. The logarithms of the samples have normal 

distributions. The two-sample t-test is expected to perform well under these ideal conditions. 

The power of the two-sample t-test under these conditions represents an upper bound on the 

power of tests for comparing the two groups under less ideal conditions. Any test applied under 

more realistic conditions with data containing outliers and nondetects would be expected to have 

lower power than is observed in this parametric simulation. The second simulation is based on 

nonparametric tests. 

The test performance plot summarizes test performance by calculating the probability of 

rejecting the null hypothesis as a function of Δ, the difference in the locations of the two 

distributions. With lognormal-like data, a suitable definition of the difference in location is Δ = 

log[L(f2)/L(f1)] or a multiplicative factor L(f2)= L(f  e 1). Here, the location of a distribution 

L[f] is defined as the expected value, the median, or any upper percentile of the distribution. 

Given two lognormal distributions with the same GSD, all three definitions of location yield the 

same ratio and hence the same Δ=log(GM2/GM1). The quantity is a multiplier that 

determines the location of the CTW distribution relative to the non-CTW distribution in 

multiplicative terms. 

The lognormal distributions used in the first simulation are the distributions estimated for the 

comparison of CTW and non-CTW whole-body counts (WBCs) for 1975 shown in Figures A-22 

and A-39 in Attachment A of RPRT-0056, respectively. The lognormal distribution for the nonCTW group has a GM of 0.43 nCi with a GSD of 4.8. This distribution was estimated using 64 

OPOS values, of which 25 are nondetects, leaving 39 measured values (39 workers, 1 OPOS 

value per worker) for the ROS calculations. The lognormal distribution for the CTW group has a 

GM of 0.86 nCi with a GSD of 4.5. The CTW distribution was estimated using 21 CTW OPOS 

values, of which 4 are nondetects, leaving 17 measured values (17 workers, 1 OPOS value per 
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 e

e

worker) for the ROS calculations. These two distributions have approximately the same GSD, 

another ideal condition for the two-sample t-test. The CTW GM is 2 times higher than the CTW 

GM. Since the GSDs are about the same, the ratio of the mean values and the ratios of the 84th

and 95th percentiles have similar values. Although the distributions differ by a factor of 2, the 

results in RPRT-0053 using the Peto-Prentice test to compare these two groups in 1975 show no 

significant difference at the 95% confidence level. 

The test performance plot for the two-sample t-test used to test for differences between the two 

lognormal distributions is shown in Figure 6. The horizontal axis in Figure 6 labeled the “CTW 

Dose Multiplier” measures the difference in location of the two distributions using the location 

multiplier . The CTW multiplier would be of particular interest if an “adjustment factor” 

approach were used to ensure claimant favorability for CTW claimants. The vertical bar in 

Figure 6 is drawn at the actual CTW multiple of 1.99 in 1975. 

The vertical axis is the power of the test, i.e., the probability that the test will reject the null 

hypothesis, expressed in percentage terms. The test performance curve plotted as an ascending 

curve in the figure defines the power of the test at each value of the CTW dose multiplier eΔ

. 

The test performance curve rises from α at the LBGR to (100-β) at the UBGR. 

In sample design problems, the usual question is how large of a sample is required to detect 

differences that are as large as or larger than the size of the gray region. In this case, the sample 

variability and the desired Type 1 and Type 2 error rates α and β are fixed in advance. The width 

of the gray region is adjusted by determining the sample size required to detect the MDD of 

interest. At the selected sample size, the test performance curve will reach the desired power of 

(100-β) when the CTW dose multiplier is at the UBGR. In Figure 6, the β for the test is set at 

5%. 



In retrospective analysis of power, the sample sizes and the variability are known and the Type 1 

error rate α is specified by selecting the confidence level used for the test. In this case, the power 

(100-β) and the width of the gray region are unknown. When the Type 1 error rate is controlled 

at a maximum of α at the LBGR, it is claimant favorable to require an equivalently stringent 

maximum Type 2 error rate of β at the right edge of the gray region when the difference Δ is as 

high as or higher than the UBGR. Then the test performance curve is used to determine the 

UBGR, which is equal to the value of Δ where the test performance curve equals (100-β). Since 

the β for the test is set at 5%, this ensures that there will be a high chance of rejecting the null 

hypothesis if the difference Δ is at or above the UBGR. 

The test performance curve is estimated by simulation and used to determine the UBGR for the 

test, i.e., the magnitude of difference that can be detected reliably with an error rate of less than β

given the available sample sizes. The parametric simulation is summarized by asking the 

question: How much higher would the CTW lognormal distribution have to be for the test to 

have sufficient power to reject the null hypothesis of No Difference? When the sample size in 

one or both groups is small, the difference between the distributions must be large before the null 

hypothesis will be rejected. 
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 The simulation was conducted by scaling the CTW lognormal distribution by e , while leaving 

the non-CTW distribution unchanged, then using the t-test to test for a significant difference 

between the two distributions at each selected value of Δ. The simulation conducted 3,000 

iterations of the test at each value of Δ, and then calculated the percentage of iterations where the 

null hypothesis was rejected by the test. This percentage is an estimate of the test performance 

when the difference is Δ. The width of the gray region is defined by the value of Δ when the test 

performance curve reaches the desired power of (100-β). 

Table 4 shows the results of the analysis of differences between the CTW and non-CTW 

neptunium WBC OPOS datasets for all years with coworker model lognormal distributions 

reported in RPRT-0056. The two-sample t-test and the WRS test were used to test for 

differences between the two distributions. The table shows the number of OPOS values in each 

group in each year, the number of samples above the detection limit (detects) used to fit the 

lognormal models, and the observed ratio of the GMs. The right-hand column shows the upper 

bound of the gray region for the tests for the given sample sizes. In most years, the WRS test has 

slightly less power (and thus larger UBGRs) than the t-test. This is to be expected given the 

normality of these ideal datasets. The smallest upper bounds occur in the earliest years when the 

sample sizes were large. In the years 1961 and 1962, there are 47 and 40 CTW samples, 

respectively. Here the sample sizes are sufficiently large that the tests reliably detect differences 

larger than a factor of 1.5 (i.e., differences of 50% or larger). In 1963, the number of CTW 

OPOS values is 28. This smaller sample size results in an increase of the UBGR from 1.5 to a 

factor of 2. In this year, differences larger than 100% can be reliably detected. Differences 

smaller than 100% would not be reliably detected. 

NIOSH did not do a hypothesis test in RPRT-0056 for the first 3 years shown in Table 4. In 

1962 and 1963, the observed ratio of GMs significantly exceeds the upper bound of the gray 

region indicating a significant difference in these 2 years that was not analyzed by NIOSH. 

Later years in Table 4 have much smaller sample sizes and much higher values for the UBGR. 

In all years after 1963, the difference in GMs would have to exceed the UBGR to indicate a 

significant difference. In approximately one-half of the years after 1963, the difference would 

have to exceed a factor of 3 to 4 for a significant difference with these sample sizes. In all 

remaining years, except the anomaly in 1985, the difference would have to be as large as a factor 

of 4 to a factor of over 10 before the WRS test will indicate a significant difference. The UBGRs 

shown in Table 4 are for tests with lognormal data with no nondetects or extreme outliers. The 

UBGRs for the nonparametric Peto-Prentice test with nondetects are expected to be higher than 

the bounds shown in Table 4. Factors as large 10 may be required to show a significant 

difference. 
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Table 4. Sample Sizes, Ratio of Geometric Means, and Upper Bound of the Gray 

Region (UBGR) for Tests of the No Difference Hypothesis 

 Number of Samples Number of Detects Ratio Upper Bound of Gray 

Region (UBGR) 

Year non-CTW CTW non-CTW CTW 

GMCTW/ 

GMnonCTW

t-Test WRS 

Test 

1961 252 57 47 6 1.0 1.5 1.5 

1962 734 175 40 8 4.9 1.5 1.5 

1963 362 82 28 11 3.2 2.0 2.1 

1974 58 10 54 9 1.0 3.5 3.8 

1975 64 21 39 17 2.0 3.4 3.8 

1977 43 11 27 8 0.6 8.4 10.2 

1978 73 19 49 10 0.6 3.9 4.6 

1979 55 12 39 7 2.7 4.9 4.6 

1980 87 19 30 6 1.1 3.8 4.3 

1981 99 23 36 7 1.6 4.4 4.5 

1983 82 24 23 12 1.1 3.2 3.4 

1984 92 25 31 9 1.0 3.8 4.1 

1985 62 13 23 6 0.2 29.0 57.4 

1986 65 13 22 7 2.7 5.5 5.6 

1987 81 15 51 7 3.4 6.4 8.6 

1988 77 13 31 7 3.7 5.0 5.0 

1989 69 17 31 9 0.3 7.9 11.0 

One improvement that should be noted; the MCPT approach proposed in RPRT-0053 is based on 

samples from two mutually exclusive populations of workers. In RPRT-0049, the MCPT 

procedure compared coworker samples for one group of workers with samples drawn from the 

set of all workers. The current report properly compares the parameters of the lognormal 

distributions estimated separately for each group of workers. 

There are problems with implementation of the hypothesis testing strategy. Examples to 

illustrate these problems are found in the derivative publications that implement the RPRT-0053 

methodology. For example, on page 8 of RPRT-0056, NIOSH states: 

CTWs are potentially subject to different bioassay practices than other workers. 

CTWs, many of whom are contractors, commonly submit bioassay samples after 

suspected uptakes and at the completion of jobs. This is in contrast to other 

workers, especially those employed directly by the prime contractor, who are 

more likely to be on a routine bioassay program in addition to submitting 

bioassay samples after suspected uptakes. A post-job bioassay is more likely to 

be soon after an uptake, either suspected or unidentified, than is a routine 

bioassay sample and thus more likely to have a larger result. This potential 

difference in how the strata are monitored for intakes would result in higher 

results for CTWs compared to the other strata. [Emphasis added.] 
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Essentially the same comment appears on page 9 of RPRT-0058. Although the two groups are 

defined to be mutually exclusive, the bioassay program for the two groups should be the same. 

This is in direct contrast to the above quote, which clearly indicates the CTW group had more 

results from accidents and the non-CTW group had more routine results. If a worker had a 

suspected intake, it is likely that his/her monitoring would be geared to detect exposures from the 

particular radionuclide that caused the potential exposure. Hence, the entire dose reconstruction 

of a CTW would be different from a non-CTW if this sampling protocol was followed, since the 

CTW samples should not be construed as routine. 

The final sentence in the quote above suggests that the CTW bioassay results should be 

considered as bounding. If this were true, the mixture of bounding results for CTWs and routine 

results for non-CTWs in the MCPT is questionable, as it raises the question of exactly what the 

parameters estimated in the 10,000 permutations represent. Each permutation contains a varying 

proportion of bounding and routine assay results. 

A second concern with the hypothesis test strategy is that cases may arise when both groups 

contain the same worker. For example, in the derivative report RPRT-0056 (p. 12), NIOSH 

states the following [essentially the same passage appears in RPRT-0058 (page 12)]: 

Because it was possible for a worker to change jobs during the course of a single 

evaluated period, it is possible that a worker would have some samples identified 

as nonCTW and others as CTW in the same period. Therefore, one person might 

have as many as four different OPOS results, one each for the AMW, CTW, 

nonCTW, and nonCTW+unk strata. 

When the radionuclide is long-lived, the OPOS values generated in each group for that worker 

will be strongly correlated. For example, Np has a half-life of 7.8 E8 days and is Type M. If the 

worker changes jobs during the time period, and if some of his/her bioassay results are for the 

CTW group and other results are for the non-CTW group, there will be an influence of Np 

exposures in one job on the results from the other job. This happens because Np will stay in the 

body for a long period after the first intake. 

Table 5 shows the retention of Np-237 in the body after a single intake of the nuclide as a 

function of time after the intake. Over the course of a year, the body burden is reduced by less 

than half. The bioassay results for this worker are not independent. For example, if a worker in 

the CTW group was exposed then changes jobs and becomes part of the non-CTW group in the 

same year, the non-CTW results for this worker will carry the influence of the previous exposure 

as a CTW. This means that the bioassays recorded for this worker in each group will be strongly 

correlated, as will be the MPMs calculated from these assays. 

The statistical tests for comparing the CTW strata and non-CTW strata require that the samples 

in each group be independent and they are not in this case. This correlation not only violates the 

assumptions of the tests, but also creates a bias toward a decision of “No Difference” between 

the two groups. 
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Table 5. Retention of Np-237 in the Body after a Single Intake 

Time(days) Whole Body 

10 7.15E-02

20 6.63E-02

30 6.24E-02

40 5.92E-02

100 4.95E-02

180 4.46E-02

300 4.10E-02

Finding No. 7: The statistical tests for comparing two strata require that the samples in each 

group be independent. If a worker in one group is exposed to radionuclides with long retention 

in the body, then changes jobs and becomes part of the other group in the same year, the OPOS 

values are correlated for this worker. This correlation not only violates the assumptions of the 

tests, but also creates a bias toward a decision of “No Difference” between the two groups. 

4.2 DESCRIPTION OF THE MONTE CARLO PERMUTATION TEST 

An example of the MCPT procedure is shown in Figures A-2 through A-4 of RPRT-0053. 

Figures A-2 and A-3 show ROS plots for two groups of workers with two different job 

classifications and their estimated lognormal distribution parameters. There are 219 workers in 

Group A and 113 in Group B. Approximately 40% of the values in each group are nondetects. 

The ROS plots of the ordered data approximately follow the regression line in both figures 

except in the extreme upper tails, where the data points fall below the regression line, indicating 

that the lognormal distribution may be an appropriate and claimant-favorable probability model 

for these datasets. As shown in Table 6, the GM is 0.66 for Group A and 0.93 for Group B, with 

a GSD of 4.3 for Group A and 3.8 for Group B. Based on these lognormal distributions, Group 

A has a mean of 1.94 and a standard deviation of 5.3, while Group B has a mean of 2.23 and a 

standard deviation of 4.9. The 95th percentiles are 7.4 and 8.2 for Groups A and B, respectively. 

In this example, Group A has a larger GSD and standard deviation, but a smaller GM, mean, and 

95th percentile. The largest percentage difference is for the GM, but all parameters are within a 

range of ±30%. This is a first indication that it will be difficult to distinguish significant 

differences between the two distributions. 

Table 6. Comparison of Lognormal Distributions for Group A and Group B 

Lognormal Parameter Group A Group B Difference (%) 

GM 0.66 0.93 -29.0 

GSD 4.33 3.75 15.4 

Mean 1.94 2.23 -13.3 

Standard Deviation 5.33 4.86 9.5 

95th Percentile 7.37 8.19 -10.1 

A Monte Carlo simulation was conducted to examine the differences between these two 

lognormal distributions when used in the coworker model. Although the presence of nondetects 

is an important consideration when estimating the lognormal distributions for each group, the 

application of the fitted distributions within the coworker model would not include nondetects. 
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Hence, the simulation compares the fitted lognormal distributions with and without nondetects in 

the simulated sample values. While simulation with nondetects would be useful for examining 

the estimation process, simulation without nondetects is of greater interest, as it addresses the 

question of whether there will be differences in the predicted values when the estimated 

lognormal distributions are used to simulate worker exposures. 

In the simulation, a random sample of the appropriate size was drawn from each of the two 

lognormal distributions: for Group A; and for Group B. Here, n A n ,..., xx1 Bn ,..., yy1 A represents 

the number of workers in Group A and nB the number in Group B. The ROS method was used 

then to estimate the GM and GSD of the two samples using the ROS procedures described in 

RPRT-0053. Although use of the ROS procedure is necessary when there are nondetects present 

in the sample, it may also be used with no nondetects. In this case, the estimates of the slope and 

intercept of the regression line are uncorrelated, since the sum of the independent variable values 

in the regression is zero. 

The experiment was then repeated for 1,000 iterations to simulate the range of uncertainty in the 

lognormal parameter estimates for the given sample sizes. The results are shown in Figure 7, 

which contains scatter plots of the estimated GM and GSD for each group in each iteration. 

With no nondetects in the samples, the uncertainty distributions of the lognormal parameters 

appear to be different, but distributions of the GM and GSD clearly do overlap to a small degree. 

When a hypothesis test is applied to test whether there is a significant difference between the two 

distributions, the test results will be determined by the level of confidence required of the test. 

Setting a high level of confidence would result in the conclusion that, for the given sample sizes, 

no significant difference is observed, while a lower level of confidence would indicate a 

significant difference between the groups is observed. Since there is always a trade-off between 

Type 1 and Type 2 errors when conducting a hypothesis test with fixed sample sizes, setting a 

higher level of confidence would reduce the power of the test to detect a significant difference, 

while setting a lower level of confidence would increase the power of the test to detect a 

significant difference. 
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2.5

3.5

4.5

5.5

0 0.511

GM

GSD

.5

Group A Group B

Figure 7. Scatter Plot of ROS Estimates of GM and GSD for Samples of Size nA and 

nB from the Lognormal Distributions for Group A and Group B 

(1,000 iterations) 

Claimant favorability is always of concern when setting the standards for the level of 

significance. NIOSH has proposed that strong evidence is necessary before any differences 

between groups of workers should be considered in the coworker model. In the examples in 

Sections 5.1 and 5.2 of RPRT-0053, and in subsequent applications to neptunium (ORAUT 

2012b), mixed fission and activation products (ORAUT 2012c), and exotic trivalent 

radionuclides (ORAUT 2012a) at SRS, NIOSH conducts the statistical tests for a significant 

difference at the α = 0.05 probability level requiring a 95% level of confidence. A higher level 

of confidence makes it more difficult to decide if there are differences between the two groups. 

A 90% level of confidence for the MCPT would be more claimant-favorable. The issue of 

confidence levels and power are further addressed in Sections 4.1 and 4.2. 

A high level of confidence in the test for differences requires a high standard of proof before 

accepting the conclusion that there are differences within the worker population. Conversely, a 

high standard reduces the power to detect differences of any magnitude. NIOSH has not 

provided any measure of the power of the MCPT to detect differences, although one example 

where a significant difference is found is presented in the report. This deficiency should be 

corrected before the MCPT is adopted as an appropriate testing procedure. To provide more 

information to decision makers, NIOSH also should report the p-level for each test, rather than 

only providing the test outcome for a 95% level of confidence. This would permit discussion of 

exactly what level of certainty is required before admitting to differences. 

Finding No. 8: Although one example where a significant difference is found is presented in the 

report, NIOSH has not provided any measure of the power of the hypothesis test procedure to 

detect differences within the worker population. This deficiency should be corrected before the 

test is adopted as an appropriate procedure for coworker models. Conducting the tests at a 90% 

level of confidence would be claimant favorable. 
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The distribution of ROS estimates of the GM and GSD for each group are shown in Figures 8 

and 9. In both cases, the distributions of the parameters overlap, although the distributions of the 

GMs have better separation. 

0

50

100

150

200

250

300

0 0.5 1 1.5 2

GM

Frequency

Group A

Group B

Figure 8. Distribution of ROS Estimates of GM for Samples of Size nA and nB from 

the Lognormal Distributions for Group A and Group B 

(1,000 iterations) 

0

50

100

150

200

250

300

350

234567

GSD

Frequency

Group A

Group B

Figure 9. Distribution of ROS Estimates of GSD for Samples of Size nA and nB from 

the Lognormal Distributions for Group A and Group B 

(1,000 iterations) 

When there are no nondetects present, there are many ways to determine if the parameter 

distributions shown in Figures 7, 8, and 9 are different. Figure 10 shows a scatter plot of the 

differences (Group A minus Group B) of the simulated GM and GSD values in Figure 7. The 

difference in each iteration in the estimated GM of the two samples is plotted on the horizontal 
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axis and the difference in the GSD on the vertical axis. The actual value of the difference in the 

GM and GSD of the lognormal distributions is shown as a triangle in this figure and the origin of 

the plot is shown as a circle. The uncertainty distribution of the parameter estimates is centered 

around the true value and clearly includes the origin, indicating that the observed differences are 

not significantly different from the origin at (0,0). The simulation is found to agree with 

NIOSH’s conclusion that there is no significant difference between the two groups. 

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.8 -0.6 -0.4 -0.2 0 0.2

Difference in GM

(Group A - Group B)

Difference in GSD

(Group A - Group B)

Figure 10. Distribution of ROS Estimates for Differences in GM and GSD for Samples 

of Size nA and nB from the Lognormal Distributions for Group A and Group B 

(1,000 iterations) 

NIOSH has selected to use a different approach to test for a significant difference, one that is not 

based on simulation. The NIOSH approach is data-driven, based on repeated permutations of the 

original data values (including the nondetects). Two examples are provided demonstrating the 

application of the test when two groups of workers are compared. One of these examples with a 

borderline decision was examined in this review using a simulation approach to illustrate and 

validate the permutation test results. 

The MCPT is applied to test for a significant difference in the ROS lognormal parameters 

estimated for the two groups. In this permutation test, the combined original samples from the 

two groups are arranged in 10,000 permutations filling the two samples without regard to job 

classification. The distribution of parameter differences from the repeated permutations forms 

the null distribution, i.e., the distribution of parameter values that would result from samples of 

the given sizes drawn without knowledge of the job classification. The actual difference in 

parameters is then compared with the null distribution to see if the observed difference using the 

job classification information is significant. The null hypothesis for this test is that the 

distribution of the OPOS bioassay data is the same in Group A and Group B, and the alternate 

hypothesis is that the distribution of data is not the same. The null hypothesis is rejected at level 
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α as the observed difference lies outside of an elliptical region containing 100(1-α)% of the 

permutations. 

To continue with the Group A/B example above, the MCPT was applied first with no nondetects 

in either sample, then with nondetects in both samples. In the previous simulation, all samples 

were selected randomly from the two lognormal distributions. In permutation sampling, the 

samples are obtained by repeatedly drawing the samples from one set of urinalysis samples, 

which includes both Group A and Group B workers. 

Figures 11 and 12 show the results of the permutation test with no nondetects and with 

nondetects, respectively. The difference in the estimated GM of the two samples is plotted on 

the horizontal axis, and the difference in the GSD on the vertical axis. The triangular point 

plotted in each figure represents the difference between the parameters of the two lognormal 

distributions shown in Table 6. The shape of the uncertainty distribution changes to an elliptical 

shape when nondetects are added. This is an indication of the correlation between the parameter 

estimates due to the unbalanced design when there are censored data. The presence of a large 

proportion of nondetects makes it more difficult to find any significant difference between 

groups. 

In the MCPT, the distribution of the estimates of parameters from the permutation samples is 

centered at the origin (under the null hypothesis), while the observed difference lies near the 

edge of the null region. As expected, the difference between the two groups has only borderline 

significance both with and without nondetects. 

-2

-1

0

1

2

-0.5 -0.25 0 0.25 0.5

Difference in GM

(Group A - Group B)

Difference in GSD

(Group A - Group B)

Figure 11. Permutation Test for a Significant Difference in ROS Estimates of GM and 

GSD with No Nondetects 

 (1,000 permutations) 
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-2

-1

0

1

2

-0.8 -0.4 0 0.4 0.8

Difference in GM 

(Group A - Group B)

Difference in GSD 

(Group A - Group B)

Figure 12. Permutation Test for a Significant Difference in ROS Estimates of GM and 

GSD with Approximately 40% Nondetects 

(1,000 permutations) 

If there are many nondetects in the datasets, the MCPT may fail when one or more of the 

permutations results in a sample containing only nondetects. The ROS method does not apply in 

this case, and other methods must be applied. 

4.3 OTHER NONPARAMETRIC METHODS 

In addition to the use of the MCPT for comparing the two groups by fitting lognormal 

distributions, RPRT-0053 discusses the use of more general hypothesis tests for comparing the 

groups. These nonparametric methods are applicable to a broader range of distributions than the 

lognormal distribution and will give results with only a small number of values above the 

detection limit. Again, the goal of the test is to determine if there is a significant difference 

between the two groups. 

Many nonparametric methods have been developed for comparing two independent samples. 

Nonparametric methods do not require the assumption that data follow the lognormal 

distribution. Many of these methods are based on the relative ranks of the two datasets when 

samples from both groups are ranked in a single list. The two-sample rank tests determine if one 

group tends to have higher ranks than the other. One of the most commonly used rank tests is 

the WRS test. This test is based on a comparison of the sum of the ranks of the workers in each 

group. RPRT-0053 considers several nonparametric tests based on ranks, which are 

generalizations of the WRS test for use with nondetects. 
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4.3.1 Peto-Prentice Test 

When there are nondetects present in either dataset or both, the ranks for the nondetects are 

assigned scores. There are many generalizations of the WRS test that differ in the manner these 

scores are assigned. Generalized WRS tests reviewed in RPRT-0053 include the Gehan test, the 

generalized Wilcoxon-Gehan test, and the Peto-Prentice test. These three generalized WRS tests 

are identical to the WRS test when there are no nondetects in the data. 

The Gehan Test is the most commonly used generalized WRS test for comparing two datasets 

containing nondetects with the same detection level. Attachment B to RPRT-0053 reviews the 

discussion of the generalized WRS tests found in Helsel (2005). After review of the available 

generalized WRS tests, RPRT-0053 recommends the Peto-Prentice test as most powerful if there 

are nondetects with varying levels of detection in the dataset. This conclusion agrees with the 

evaluations by Helsel (2005, p. 150) and Latta (1981). The literature search does not include 

reference to the Brunner-Munzel test (Brunner and Munzel 2000). This nonparametric test is 

another generalization of the WRS test designed for comparisons of populations with different 

variances. 

The Peto-Prentice test typically leads to the same conclusion as the MCPT when both are 

applicable. The Peto-Prentice test is recommended by NIOSH for use when the MCPT is not 

applicable. The null hypothesis proposed by NIOSH for this test is that the distribution of the 

OPOS bioassay data is the same in Groups A and B. The alternative hypothesis is that the 

distributions are not the same. 

As noted above, the MCPT test fails when one or more of the permutations contains all 

nondetects. When the data contain a large proportion of nondetects, the MCPT is likely to fail 

and the Peto-Prentice test must be used. In the application of the RPRT-0053 methodology to 

neptunium (ORAUT 2012b), mixed fission and activation products (ORAUT 2012c), and exotic 

trivalent radionuclides (ORAUT 2012a) at SRS, only the Peto-Prentice test was used due the 

high proportion of nondetects in these datasets. 

The Peto-Prentice test has several advantages over the MCPT: 

(1) The Peto-Prentice test is a nonparametric test and does not require the assumption of a 

lognormal distribution necessary in the parametric models underlying the MCPT 

(2) The Peto-Prentice test may be used in cases when the MPCT is not applicable due to a 

high proportion of nondetects 

(3) The Peto-Prentice test may be applied to test for several different hypotheses, rather than 

only a test for a significant difference 

The Peto-Prentice test is a generalization of the WRS test which is a test for the location of one 

distribution relative to the other. Tests of location may be applied using three different forms of 

the hypothesis test, which differ in terms of the null hypothesis (H0). Three hypothesis test 

forms may be tested using the Peto-Prentice statistic z: 
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(A) H0: The distribution of the bioassay data is the same for CTW and non-CTW 

vs. HA: the distribution of data is not the same for CTW and non-CTW 

(B) The distribution of the bioassay data non-CTW is higher than for CTW 

vs. HA: the distribution of data for CTW is higher than for non-CTW 

(C) H0: The distribution of the bioassay data for CTW is higher than for non-CTW 

vs. HA: the distribution of data for non-CTW is higher than for CTW 

Although the three test forms may appear similar, in practice, there are large differences between 

the three test forms in terms of claimant favorability. The differences arise because the null 

hypothesis is assumed true until the data provide sufficient evidence to reject the null hypothesis. 

If the sample size for one or both groups is too small, the test would not have sufficient power to 

reject the null hypothesis. Test form A is a 2-sided test. With a 2-sided test, the null hypothesis 

of “No Difference” is rejected if the CTW data are either significantly higher or lower than the 

non-CTW data. If the sample size is too small, the test may have insufficient power to reject the 

null hypothesis of No Difference. Using this test form, the null hypothesis is accepted due only 

to a lack of evidence in the data that proves the CTW are different. This is not claimant 

favorable, as it places the burden of proof on the claimants despite the known lack of sufficient 

data to provide such proof. 

Test forms B and C are both 1-sided tests. In test form B, the null hypothesis is that the nonCTW data are higher than the CTW data. In this form of a 1-sided test, the null hypothesis is 

rejected if the CTW data are significantly higher than the non-CTW data. If the sample size is 

too small, the test may have insufficient power to reject the null hypothesis that the non-CTW 

distribution is at least as high as the CTW distribution. As with test form A, the null hypothesis 

may be accepted due only to a lack of evidence in the data to prove the CTWs are different from 

non-CTWs. Test form B is also not claimant favorable, as it places an unreasonable burden of 

proof on the claimant to show that the CTW data are higher than the non-CTW data despite the 

known lack of sufficient data. The 1-sided test form B is more relevant than the 2-sided test 

form A. Unlike test form A, test form B at least provides a clear answer as to whether the CTW 

are higher than the non-CTW data, which is the issue in question. 

Test form C is also a 1-sided test. In test form C, the null hypothesis is that the CTW data are 

higher than the non-CTW data. In this form of a 1-sided test, the null hypothesis is rejected if 

the non-CTW data are significantly higher than the CTW data. If the sample size is too small, 

the test may have insufficient power to reject the null hypothesis that the CTW distribution is 

higher than the non-CTW distribution. Of the three test forms, only test form C is claimant 

favorable when the sample sizes are too small to provide clear evidence. Unless there is 

significant statistical evidence to the contrary, the null hypothesis that the CTW samples are 

higher than non-CTW should be accepted as claimant favorable. 

In RPRT-0053, NIOSH applies test form A for both the MCPT and the Peto-Prentice test. The 

MCPT is not a test of location and it may be difficult to use test forms B and C for the MCPT. 

The Peto-Prentice test is a test of location and may be used with all three hypothesis test forms. 
Effective Date: 

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NOTICE:

RECOMMENDATION: 

NIOSH might consider reversing the null hypothesis for the Peto-Prentice test. The hypothesis 

tests applied by NIOSH to test for differences between CTWs and non-CTWs use a null 

hypothesis that is not claimant favorable, as it would place the burden of proof on the CTW 

claimants to prove a significant difference. The Peto-Prentice test is more generally applicable 

and may be applied using a claimant-favorable null hypothesis. The groups of workers with high 

suspected exposures should be considered different in the absence of strong evidence that they 

are not. This is more likely to result in a claimant-favorable model. Moreover, there is 

persuasive evidence provided by the analysis of SRS CTWs by job type and by area of work 

(SC&A 2010a, 2010b) that subgroups of CTWs are not drawn from the same distribution as nonCTWs. When the distributions of CTW subgroups are different from non-CTWs, CTW data by 

job type and area can be used to construct coworker models for their CTW peers. Of course, this 

requires sufficient data in each job/area category for which a coworker model is to be 

constructed.
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5.0 REVIEW CHECKLIST 

Table 7. Procedure Review Outline/Checklist 

Document No.: ORAUT-RPRT-0053 Rev. 01 Effective Date: 7/26/2012

Document Title: Analysis of Stratified Coworker Datasets

Reviewer: Harry J. Chmelynski

 

No. Description of Objective Rating

1-5* Comments

1.0 Determine the degree to which the procedure supports a process that is expeditious and 

timely for dose reconstruction.

1.1 Is the procedure written in a style 

that is clear and unambiguous?

4

1.2 Is the procedure written in a 

manner that presents the data in a 

logical sequence?

4

1.3 Is the procedure complete in 

terms of required data?

2 Data are reduced to one statistic per worker per 

time period.

1.4 Is the procedure consistent with 

all other procedures that are part 

of the hierarchy of procedures 

employed by NIOSH for dose 

reconstruction?

4

1.5 Is the procedure sufficiently 

prescriptive in order to minimize 

the need for subjective decisions 

and data interpretation?

3

2.0 Determine whether the procedure provides adequate guidance to be efficient in instances 

where a more detailed approach to dose reconstruction would not affect the outcome.

2.1 Does the procedure provide 

adequate guidance for identifying 

a potentially high probability of 

causation as part of an initial 

dose evaluation of a claim?

N/A

2.2 Conversely, for claims with 

suspected cumulative low doses, 

does the procedure provide clear 

guidance in defining worst-case 

assumptions?

3 Worst-case analysis is not addressed. 

Recommended approach is “one size fits all.”
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No. Description of Objective Rating

1-5* Comments

3.0 Assess the extent to which the procedure accounts for all potential exposures and ensures 

that resultant doses are complete and based on adequate data in instances where the POC 

is not evidently clear.

3.1 Assess quality of data sought via 

interview:

 ---- 

3.1.1 Is scope of information 

sufficiently comprehensive?

N/A

3.1.2 Is the interview process 

sufficiently flexible to permit 

unforeseen lines of inquiry?

N/A

3.1.3 Does the interview process 

demonstrate objectivity and is 

free of bias?

N/A

3.1.4 Is the interview process 

sensitive to the claimant?

N/A

3.1.5 Does the interview process 

protect information as required 

 under the Privacy Act?

N/A

3.2 Assess whether the procedure 

adequately addresses generic as 

well as site-specific data

pertaining to:

---- 

3.2.1 Personal dosimeters (e.g., film, 

TLD, PICs)

N/A Site-specific data are not addressed.

3.2.2 In vivo/In vitro bioassays N/A

3.2.3 Missing dosimetry data N/A

3.2.4 Unmonitored periods of 

exposure

N/A

4.0 Assess procedure for providing a consistent approach to dose reconstruction regardless of 

claimants’ exposures by time and employment locations.

4.1 Does the procedure support a 

prescriptive approach to dose 

reconstruction?

3 Specific methods are recommended for 

determining if exposures differ by job type or work 

area.

4.2 Does the procedure adhere to the 

hierarchical process as defined in 

42 CFR 82.2?

4
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No. Description of Objective Rating

1-5* Comments

NOTICE:

5.0 Evaluate procedure with regard to fairness and giving the benefit of the doubt to the 

claimant.

5.1 Is the procedure claimant 

favorable in instances of missing 

data?

2 RPRT-0053 recommends a one person - one 

sample (OPOS) approach to derive a single value 

for each worker by averaging over all urine 

samples collected in each time period. Time 

periods may be as long as 3 years. This procedure 

ignores variation within each individual worker’s 

bioassay samples in the period and may result in 

underestimation of the geometric standard 

deviation (GSD) used in the coworker model.

5.2 Is the procedure claimant 

favorable in instances of 

unknown parameters affecting 

dose estimates?

2 Dose estimation requires a large number of 

parameters other than urine concentration 

estimates. The recommended procedures are not 

radionuclide specific, hence ignore these 

differences.

5.3 Is the procedure claimant 

favorable in instances where 

claimant was not monitored?

2 Requirement of 95% confidence before deciding 

that there are differences in the worker population 

is not claimant favorable.

6.0 Evaluate procedure for its ability to adequately account for the uncertainty of dose 

estimates.

6.1 Does the procedure provide 

adequate guidance for selecting 

the types of probability 

distributions (i.e., normal, 

lognormal)?

2 MCPT procedure is based on the lognormal 

distribution. The nonparametric Peto-Prentice test 

is recommended for cases when MCPT cannot be 

run.

6.2 Does the procedure give 

appropriate guidance in the use 

of random sampling in 

developing a final distribution?

2 Procedure may be used to derive a single coworker 

distribution for all workers, regardless of work 

location or job type. Differences between worker 

groups are ignored in this approach.

7.0 Assess procedure for striking a balance between the need for technical precision and 

process efficiency.

7.1 Does the procedure require levels 

of detail that can reasonably be 

accounted for by the dose 

reconstructor?

4

7.2 Does the procedure avoid levels 

of detail that have only limited 

significance to the final dose 

estimate and its POC?

N/A

7.3 Does the procedure employ 

scientifically valid protocols for 

reconstructing doses?

2 See Sections 3 and 4.

______________________ 

* Rating System of 1 through 5 correspond to the following: 1=No (Never), 2=Infrequently, 

 3=Sometimes, 4=Frequently, 5=Yes (Always). N/A indicates not applicable 
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6.0 CONCLUSIONS 

In conclusion, the statistical methods proposed in ORAUT-RPRT-0053 are based on sound 

statistical methodologies, and the material is well presented. Several previously published 

statistical procedures for estimating the GM and GSD of coworker urinalysis datasets are 

reviewed. 

In the application of the procedures recommended in RPRT-0053, the issue of completeness of 

the available coworker data has not been addressed. The methods proposed in RPRT-0053 for 

analyzing the coworker datasets require verification that (1) the available coworker data are 

representative of all groups of workers, and (2) the manner of use of the data is claimant 

favorable for the specific datasets to which the method is applied. A sound statistical 

methodology is subject to these two important caveats. 

Due to the dependencies that exist in the ranked data, the R2

 for ROS does not have the usual 

interpretation. The recommendations in RPRT-0053 for using ROS do not address this concern. 

The use of average values (OPOS) does not account for variability of the samples within the time 

period, and the procedure may result in a lower GSD used in the coworker models. This 

procedure may not be appropriate for certain radionuclides with long half-lives or long retention 

times. 

The statistical tests for comparing the strata require that the samples be collected using the same 

or a similar protocol. However, there is evidence presented by NIOSH that the sampling 

protocol for CTWs at SRS was different than the protocol used for non-CTWs. 

More than two strata would be required to properly characterize the varied worker populations at 

many sites, including SRS. Multiple comparisons when there are more than two strata may be 

possible, but could be complex and suffer from limits imposed by small sample sizes. 

A high level of confidence is required before deciding that the two worker groups are 

significantly different. The requirement for a high level of confidence in this decision is not 

claimant favorable when using a null hypothesis of “No Difference.” 

The statistical tests for comparing strata require that the samples in each group be independent. 

If a worker in one group is exposed to radionuclides with long retention in the body, then 

changes jobs and becomes part of the other group in the same year, the OPOS values are 

correlated for this worker. 

NIOSH has not provided any measure of the power of the hypothesis tests to detect differences 

within the worker population. This deficiency should be corrected before the tests are adopted as 

an appropriate testing procedure. 

Given the small number of CTW data points at SRS, in many years the tests cannot reliably 

detect differences smaller than a factor of 4 to 10 in the CTW/non-CTW ratio of GMs. Overall, 
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NOTICE:

SC&A concludes that the NIOSH method of concluding that there are no significant differences 

based on the available data would often lead to very claimant-unfavorable results. 

The MCPT applied by NIOSH to test for differences between CTW and non-CTW uses a null 

hypothesis that is not claimant favorable, as it places the burden of proof on the claimants to 

prove a significant difference. The Peto-Prentice test is more generally applicable and may be 

applied using a claimant-favorable null hypothesis. 
Effective Date: 

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Health for factual accuracy or applicability within the requirements of 42 CFR 82.

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However, this report is pre-decisional and has not been reviewed by the Advisory Board on Radiation and Worker 

Health for factual accuracy or applicability within the requirements of 42 CFR 82.

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