Evaluation of Differences between Strata 

Coworker Models 

White Paper 

Rev. 0 

National Institute for Occupational 

Safety and Health 

July 11, 2014 

J.W. Neton, Ph.D., CHP 

Daniel Stancescu, Ph.D. 

Division of Compensation Analysis and Support 

Page	1	of	8

This working document prepared by NIOSH’s Division of Compensation Analysis and Support (DCAS) or its contractor for use in discussions with the 

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Introduction 

ORAUT-RPRT-0053 provides a statistical approach for the evaluation of potential stratification in 

coworker models. The concept employs a two-tiered evaluation where the stratified distributions are first 

compared on a year-by-year basis (or other selected monitoring interval) to determine if any of the 

individual distributions are significantly different. Significance in this case is evaluated using a Monte 

Carlo permutation test or a Peto-Prentice test at the 0.05 significance level. If a significant difference is 

observed in any of the modeled time intervals, then a test of practical significance is employed. This test 

compares the slopes of the chronic intake models over the time periods where a statistically significant 

difference in the modeled distributions was observed. One of the objections raised by Sanford Cohen & 

Associates (SC&A) to the use of these test statistics is that they are, in certain cases, capable of only 

detecting large differences in geometric means between datasets. This is particularly true in the situation 

where there are small sample sizes and the distributions have large standard deviations. 

The National Institute for Occupational Safety and Health’s (NIOSH) standard practice is to use the 95th 

percentile value of the distribution of all monitored workers to estimate doses for all unmonitored 

workers with a potential to be highly exposed1. If a stratum within the all monitored workers distribution 

can be identified, the worker’s dose would be represented by the lognormal distribution that defines that 

stratum. Given this, it is of interest to compare the differences between using the probability of causation 

(PC) outcomes for the 95th percentile value and the lognormal distribution for the stratified subset. 

Preliminary Evaluation 

As discussed during the April 7, 2014, Advisory Board on Radiation and Worker Health’s Work Group 

on Special Exposure Cohort (SEC) Issues meeting2, unmonitored workers who are judged to have been 

highly exposed would receive the 95th percentile of the all monitored workers coworker model. This 

value would be used as a constant to calculate the dose for the period of time covered by the coworker 

model. If there are sufficient data available to develop a stratified subset of the full model, the lognormal 

distribution of the stratified model would be used to calculate doses, rather than the 95th percentile. In 

this white paper, NIOSH explores the relationship between the PC generated for a stratified model and 

the use of the 95th percentile as a constant for the full model. 

During the April 7th Work Group meeting, NIOSH proposed to outline a possible strategy that could be 

used to make such a comparison. As part of this effort, NIOSH first evaluated the relationship that exists 

between the PC generated using either a distribution or a constant. That is, NIOSH determined the 

amount of increase in the geometric mean of a lognormal distribution required to produce a PC in 

1 For purposes of this discussion, a highly exposed worker would be one who routinely conducted work that had the possibility of
 

generating airborne radioactivity. 

2 See pages 33-59 of the meeting transcripts: <http://www.cdc.gov/niosh/ocas/pdfs/abrwh/2014/wgtr040714.pdf> 

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NIOSH-Interactive Radio Epidemiological Program (IREP) that is equivalent to the input of the 95th 

percentile of the distribution as a constant. There are, of course, a number of factors that contribute to 

the overall uncertainty of the PC calculation that will likely affect the outcome of such a comparison. 

These include: 1) the type of the exposure (alpha, beta, gamma or neutron); 2) whether the exposure is 

chronic or acute; 3) the age at exposure and the time period between exposure and the development of a 

cancer; 4) the relative uncertainties associated with the full and stratified distributions; 5) the cancer 

model being applied to the case; and 6) gender. 

Because there is substantial uncertainty associated with the radiation effectiveness associated with alpha 

exposure, this exposure type was chosen for the initial evaluation. The rationale behind this choice was 

that those parameters that tend to increase the overall uncertainty of the input dose will also tend to 

maximize the effect of the overall uncertainty in the PC outcome. This would have the effect of 

maximizing the 99th percentile of the outcome of the calculation for a given dose input. The age at 

exposure and age at diagnosis for this analysis was fixed at 27 and 68 years for solid cancers and 33 and 

49 years for leukemia. These were the median values observed for these cancers in the previous analysis 

of practically significant dose. 

Using the above parameters, the NIOSH-IREP program was used to compute the value of the increase in 

geometric mean that produces the same 99th percentile PC result as the input of the 95th percentile of the 

lognormal distribution associated with the full model. This evaluation was done for all the 33 cancers 

models in NIOSH-IREP. The distribution for all monitored workers was assumed to have a geometric 

mean (GM) of 1 and a geometric standard deviation (GSD) of 3. As indicated in Table 1 on page 6, the 

95th percentile of this distribution is equal to 6.09. This represents the value that would be used for 

unmonitored workers who were judged to be highly exposed. The last two columns of Table 1 provide 

the parameters of a lognormal distribution that produces the same 99th percentile PC result as that of 

using the constant equal to the 95th percentile of the full model. As can be seen the results vary by cancer 

model, with the lowest geometric mean (2.07) associated with the cancer model for urinary organs, 

excluding the bladder. 

If the GSDs of the all monitored worker and stratified subset models are the same, the geometric mean 

of the stratified model would have to be at least two times higher than the geometric mean of the full 

model for the stratified model to produce a more claimant favorable outcome. In other words, a stratified 

model would need to have a GM of 2.07 with a corresponding GSD of 3.0 to produce the same PC result 

as the input of the 95th percentile value of 6.09 as a constant. This is based on the urinary organ cancer 

model which, as indicated in Table 1, required the lowest multiplier. All other cancers would need to 

have an even larger increase in the geometric mean to equal the PC value produced by the 95th percentile 

as a constant. 

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ABRWH or its Working Groups or Subcommittees. Draft, preliminary, interim, and White Paper documents are not final NIOSH or ABRWH (or their 

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The above evaluations were conducted assuming a GSD of 3.0 for both the full distribution and the 

stratified subset. Preliminary analysis of this relationship using increased GSDs of 4 and 5 for both the 

full and subset distributions indicate that the factor of two is still a reasonable approximation. When the 

stratified model has an increase in GSD over the full distribution, the difference in GM for the stratified 

model is reduced. Although it has not yet been fully evaluated, observation of a few stratified 

distributions indicates that the GSD tends to increase when the stratified subset has a lower GM than the 

full distribution. The converse of this also appears to be true. That is, the GSD for stratified models tends 

to be lower as the GM increases over that of the full model. This relationship requires further evaluation. 

Example Evaluation 

The concepts outlined above were applied to the example coworker models that were provided in 

Figures A-1 and A-3 of Attachment A to ORAUT-RPRT-0053, which are reproduced in Figure 1 of this 

document. As can be seen in Figure 1 on page 8, the full distribution that includes all monitored workers 

has a GM of 0.7509 and a GSD of 4.055, while the stratified subset has GM of 0.9306 and a GSD of 

3.753. Even though the geometric mean for the stratified subset is almost 24 percent greater than that of 

the full distribution, it is likely that statistical testing would find that there is no significant difference 

between these two distributions. While it might be tempting to decide that it would be claimant 

favorable to stratify these distributions (even though they might fail the significance test) it is worth 

evaluating what effect this might have when applied to a PC calculation. 

As described previously, the 95th percentile of the full distribution will be applied to those unmonitored 

workers who are judged to have been highly exposed. In this case, the 95th percentile of the distribution 

for all monitored workers is 0.7509 x (4.0551.645) = 7.51. This value is used is to account for the fact that 

the full distribution may be comprised of several distributions and the most highly exposed unmonitored 

workers could fall into the upper tail of the all worker distribution. In this way, there is less than a 5% 

chance that the unmonitored workers exposure is greater than the value used in his or her dose 

reconstruction. Once a stratified model is produced, the distribution is considered representative of the 

stratified subset of workers and the GM of the dose associated with the bioassay value, along with its 

associated GSD, will be used to generate the NIOSH-IREP output. 

To evaluate whether the stratified subset would produce a greater PC value than the 95th percentile of the 

distribution of data for all monitored workers, each scenario was run through the NIOSH-IREP 

calculation using the same default values as those used to establish the results provided in Table 1. That 

is, the worker was considered to have been: 1) male, first exposed when 27 years old; 2) chronically 

exposed to alpha activity; 3) diagnosed when 68 years old; and 4) developed cancer of a urinary organ 

other than the bladder. The urinary organ was chosen because previous testing indicated that this cancer 

model produced the most claimant favorable result. Although the input to NIOSH-IREP requires values 

in units of dose, the bioassay values observed were used as NIOSH-IREP inputs for this exercise. This 

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ABRWH or its Working Groups or Subcommittees. Draft, preliminary, interim, and White Paper documents are not final NIOSH or ABRWH (or their 

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is acceptable because this analysis is only interested in the relative PC outcomes between the two 

models. Thus, the first NIOSH-IREP run used 7.51 as the input term, while the second run used the full 

lognormal distribution with a GM of 0.9306 and a GSD of 3.753. At the 99th percentile, the NIOSHIREP output results were 12.2% for the stratified subset and 20.0% for the 95th percentile of the all 

monitored workers distribution. 

Summary and Conclusions 

Because of large uncertainties associated with coworker model distributions, it is not possible to 

statistically detect small differences between geometric means of a coworker model based on all 

monitored workers and one based on an identified subset (strata) of data from the full model. This white 

paper has explored an alternative method of evaluating the significance of differences between coworker 

models that was not based on statistical considerations, but based on the probability of causation 

outcome. For heavily exposed, unmonitored workers it was determined that fairly large differences in 

geometric means between the stratified subset and the all monitored worker distributions were required 

to produce PC results that exceeded those produced using the 95th percentile of the all monitored worker 

distribution. 

Under the test parameters used in this analysis, it was found that this difference was approximately a 

factor of two when the GSDs of the distributions being compared were the same. Although attempts 

were made to ensure that the comparisons made were conservative (e.g., the magnitude of the 

differences required was minimized), further analysis is required to evaluate the concepts explored in 

this white paper more fully. Nonetheless, it does appear that the inability to statistically detect small or 

even somewhat large (i.e., a factor of 2) differences in geometric means between distributions may be 

mitigated by NIOSH’s claimant favorable practice of using the 95th percentile of the all monitored 

workers distribution. Unless a statistically significant difference is detected using the methods outlined 

in ORUAT-RPRT-0053, it might be more claimant favorable to continue to use the 95th percentile of the 

all monitored workers distribution as a constant to represent exposures to unmonitored workers who 

may have been highly exposed. If a statistically significant difference is detected, the subset should be 

stratified, regardless of the effect on the outcome of a dose reconstruction. 

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This working document prepared by NIOSH’s Division of Compensation Analysis and Support (DCAS) or its contractor for use in discussions with the 

ABRWH or its Working Groups or Subcommittees. Draft, preliminary, interim, and White Paper documents are not final NIOSH or ABRWH (or their 

technical support and review contractors) positions unless specifically marked as such. This document represents preliminary positions taken on technical 

issues prepared by NIOSH or its contractor. NOTICE: This report has been reviewed to identify and redact any information that is protected by the Privacy 

Act 5 USC §552a and has been cleared for distribution. 
 

		

               

   

     

       

   

     

   

   

     

     

       

   

     

   

     

     

       

       

   

Table 1 

Parameters of the Lognormal dose distribution for a Stratified Model that are needed to get the same PC result in 

IREP, as the PC result obtained by using the constant dose equal to the 95th percentile of the Full Model 

(continued on next page). 

IREP Cancer Model Gender Age at

Exposure

Age at

Diagnosis

Full Model Stratified Model

95th percentile

of Lognormal (1,3)

GM GSD

Female Genitalia, excl. ovary Female 27 68 6.09 4.11 3

Non‐melanoma skin‐Squamous Cell Male 27 68 6.09 3.05 3

Leukemia, excl. CLL Male 27 68 6.09 2.62 3

Other respiratory Male 27 68 6.09 2.53 3

Chronic Lymphocytic Leukemia Male 27 68 6.09 2.51 3

Gallbladder Male 27 68 6.09 2.48 3

All Male Genitalia Male 27 68 6.09 2.46 3

Chronic Myeloid Leukemia Male 33 49 6.09 2.46 3

Lymphoma & multiple myeloma Male 27 68 6.09 2.45 3

Stomach Male 27 68 6.09 2.45 3

Thyroid Male 27 68 6.09 2.42 3

Malignant melanoma Male 27 68 6.09 2.34 3

Non‐melanoma skin‐Basal Cell Male 27 68 6.09 2.34 3

Nervous system Male 27 68 6.09 2.31 3

Pancreas Male 27 68 6.09 2.31 3

Rectum Male 27 68 6.09 2.31 3

Acute Myeloid Leukemia Male 33 49 6.09 2.29 3

Leukemia, excl. CLL Male 33 49 6.09 2.26 3

Liver Male 27 68 6.09 2.26 3

Esophagus Male 27 68 6.09 2.22 3

Lung Male 27 68 6.09 2.22 3

Ovary Female 27 68 6.09 2.22 3

Oral Cavity and Pharynx Male 27 68 6.09 2.21 3

Other and ill‐defined sites Male 27 68 6.09 2.16 3

Bladder Male 27 68 6.09 2.15 3

Breast Female 27 68 6.09 2.14 3

Connective tissue Male 27 68 6.09 2.14 3

Eye Male 27 68 6.09 2.14 3

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Act 5 USC §552a and has been cleared for distribution. 
 

		

               

   

     

   

   

     

       

 

IREP Cancer Model Gender Age at

Exposure

Age at

Diagnosis

Full Model Stratified Model

95th percentile

of Lognormal (1,3)

GM GSD

Acute Lymphocytic Leukemia Male 33 49 6.09 2.12 3

Bone Male 27 68 6.09 2.12 3

All digestive Male 27 68 6.09 2.11 3

Colon Male 27 68 6.09 2.11 3

Other endocrine glands Male 27 68 6.09 2.11 3

Breast Male 27 68 6.09 2.09 3

Urinary organs, excluding bladder Male 27 68 6.09 2.07 3

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Figure 1 

Examples of a Full and Stratified Model 

Distribution for All Monitored Workers 

Distribution of a Stratified Subset 

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