Memo to SEC Work Group 1 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

MEMO 

TO: SEC Issues Work Group 

FROM: SC&A SEC Issues Team 

SUBJECT: SC&A’s Preliminary Review and Comments on Three NIOSH White Papers 

Related to Coworker Modeling 

DATE: July 25, 2014 

SECTION 1. EXECUTIVE SUMMARY 

NIOSH has provided SC&A and the SEC Issues Work Group with three new white papers 

related to coworker modeling in an SEC context entitled: 

(1) Draft Criteria for the Evaluation and Use of Internal Exposure Coworker Datasets

(referred to as ‘Draft Coworker Criteria’ in this memo). Dated June 17, 2014 (NIOSH 

2014a) 

(2) Evaluation of Differences between Strata Coworker Models. Dated July 11, 2014 

(NIOSH 2014b) 

(3) NIOSH’s Reconsideration of the Application of the OPOS Methodology: Allowance for 

Time-Weighted Averaging. Dated June 17, 2014 (NIOSH 2014c)

SC&A’s evaluation of each of these white papers is discussed in Sections 2–4, and represents a 

preliminary review to facilitate discussion during the upcoming SEC Issues Work Group meeting 

on July 28, 2014. 

It is SC&A’s view that the overarching issues can be grouped into two separate topics of 

discussion: 

 The ability to establish and compare different worker strata in order to evaluate the 

representativeness of a proposed coworker model(s) and its application to workers with 

varying exposure potential. 

 The appropriateness of the mechanism by which resultant coworker intakes are calculated 

[One Person-One Sample (OPOS), Time-Weighted OPOS, “Pooled Data” approach] 

It is SC&A’s contention that the former topic is essential in order to demonstrate that a given 

coworker model will represent those workers who may have had higher exposure potential, and 

that any application of resultant coworker intakes will bound such exposures. In order to 

accomplish this comparison, NIOSH developed the OPOS statistic and related strata comparison 

methodologies as outlined in ORAUT 2012a. NIOSH then modified the process of calculating 

the OPOS statistic (NIOSH 2014b) in order to better account for the time weighting between a 

given sampling result and the subsequent observed sample. In this way, samples with long 
Memo to SEC Work Group 2 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

periods between the next sample would be given more “weight” in the OPOS calculation than 

samples with very short temporal duration to the next sample (such as would be expected for 

incident-based sampling). 

SC&A acknowledges that utilizing a temporal weighting criteria represents a technical 

improvement over the original OPOS statistic, which gave equal weight to each sample in a 

given evaluation period. However, SC&A does not feel that this improvement obviates the 

concern over comparing two groups of worker strata that do not have sufficiently similar 

monitoring protocols. It is SC&A’s opinion that without a clear connection between the 

sampling protocol of two worker strata, then a scientifically accurate and defensible 

comparison is not feasible. SC&A further acknowledges that this important issue is independent 

of whether the comparative distributions are calculated using the original unweighted OPOS 

statistic, time-weighted OPOS statistic, or the “Pooled Data” approach.

The second main topic for discussion relates to how the coworker intake values are calculated, or 

more specifically, how the distribution of excreta values is obtained for a given time period. The 

OPOS mechanism (both unweighted and time-weighted) was mainly created to diminish the 

confounding factors of “data dominance” and “correlation.” The former term refers to situations 

where a single worker or small groups of workers have significantly more sampling results than 

the overall worker population. The latter term refers to the fact that many radionuclide intakes 

take significant time to clear the body and thus consecutive bioassay samples may reflect a single 

intake scenario and therefore are not independent. SC&A, in our February 2014 report on OPOS 

(SC&A 2014) notes that the problem of correlation is not obviated by OPOS. Furthermore, the 

OPOS mechanism represents a data reduction technique and thus reduces the number of data 

points available for comparison, which in turn reduces the power of the statistical tests employed 

to test for differences in strata. OPOS also removes an element of uncertainty when compared to 

the traditional pooled data models, which reduces the geometric standard deviation (GSD) of the 

OPOS distribution. While alleviating any observed issues with data dominance, this will likely 

result in lower calculated coworker intake values. Therefore, SC&A’s position remains that the 

OPOS mechanism (whether unweighted or time-weighted) for calculating coworker 

distributions should only be used in cases of clear data dominance. A typical example would 

be a worker involved in an incident/accident for which many follow-up samples were taken over 

a short period of time. In such a case, it would be appropriate to average these results into a 

single value for inclusion in the overall coworker distribution. 

SECTION 2. SC&A REVIEW COMMENTS FOR NIOSH WHITEPAPER ‘DRAFT 

COWORKER CRITERIA’ (NIOSH 2014a) 

SC&A had the following seven specific review comments based on the noted sections of the 

NIOSH white paper ‘Draft Coworker Criteria (NIOSH 2014a).

SC&A Comment 1: Data Completeness and Representativeness 

From the Introduction (page 1, paragraph 1): 
Memo to SEC Work Group 3 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

While the use of individual personnel monitoring is preferred in the completion of 

dose reconstructions, these data are oftentimes not available because either the 

worker was monitored and the data have been lost or the worker was potentially 

exposed and not monitored. In the latter case, NIOSH has observed that, in 

accordance with the practices in effect at the time, only workers with the highest 

exposure potential were monitored or, in some cases, monitoring was conducted 

on representative members of the exposed population. [Emphasis added] 

SC&A has found during previous coworker evaluations that it is not always the case that the 

highest exposed classes of worker were targeted by the bioassay program. One particularly 

notable example was the Nevada Test Site coworker evaluation in which it was found that health 

physics monitors and security guards comprised the majority of the sampled worker population,

yet these workers often stayed at the radiological checkpoints and seldom entered the forward 

areas for any appreciable amount of time. Higher risk job types, such as miners and drillers,

were not sampled nearly as often and thus were severely under-represented in the proposed 

coworker model. 

Therefore, SC&A believes that for each coworker model, the exposure potential of the monitored 

worker population must be evaluated to assure that the higher risk job types, temporal periods 

and areas are adequately represented in the resultant distribution. This can be accomplished by 

utilizing strata comparison techniques; secondary source term data, such as air and surface 

contamination monitoring; worker interviews; and campaign-specific information. 

SC&A Comment 2: Data Completeness and Representativeness 

From the Introduction (Page 1, Paragraph 2): 

For dose reconstructions under EEOICPA, it is often difficult to locate a worker 

in a specific job at a specific location. Because of this, NIOSH has chosen to 

develop coworker models that cover a wide range of workers for a specific 

radionuclide at a specific time. 

SC&A acknowledges that often times the available datasets lack the granularity to identify and 

apply coworker intakes that are specific to an individual place, time, and job type, and more 

wide-ranging application of coworker intakes is necessitated. We also understand that in many 

cases (e.g., many AWEs) a single “all monitored worker” (AMW) distribution can be 

representative of all exposure categories. However, SC&A has also demonstrated instances 

where certain job types have a markedly different exposure potential than the general worker 

population (for example ‘pipefitters,’ who may have performed maintenance work on 

contaminated piping or ventilation equipment). 

As a follow-on to SC&A comment 1, the exposure potential among different worker types must 

be carefully evaluated to assure that the application of a site-wide coworker model, or even a 

stratified model, adequately captures the intake potential to the highest exposed workers. One 

potential method would be to evaluate a subset of individual worker intakes for the highest 
Memo to SEC Work Group 4 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

exposed job types and compare those exposures to the recommended intakes based on the 

proposed coworker model. 

SC&A Comment 3: Data Completeness and Representativeness 

From Section 2.2 (Page 3, Paragraph 2): 

It must be established who was monitored and why they were monitored. In this 

evaluation there must be some demonstration that the monitored population 

consisted of: 1) a representative sample of the exposed population or 2) the 

workers with the highest exposure potential. In these cases, the assignment of a 

coworker dose from the distribution of measured values would either be claimant 

favorable in the first case or representative of the worker’s exposure in the 

second case.

SC&A assumes that the third and final sentence shown above was an editorial error and the 

author intended to say that “case 2” would be claimant favorable, while “case 1” would be 

representative of the worker’s exposure. Nonetheless, SC&A agrees that a positive review and 

finding that one of these two cases applies is essential for an acceptable coworker model. An 

explicit corollary is that one of these two should apply across all exposed job types. In other 

words, representativeness must be shown for job types when working conditions indicate that 

exposures differ by location. For instance, exposures to fission products are likely to be higher 

around a high-level waste tank farm than in a reactor building during normal operation. 

SC&A Comment 4: Coworker Models based on Incident Sampling 

From Section 2.2 (Page 3, Paragraph 3): 

If one can demonstrate that the effectiveness of workplace administrative and/or 

engineering controls was adequate to prevent exposures, except during upset 

conditions, it may be possible to use incident-based sampling in a coworker 

model.

SC&A questions the extent and feasibility to which such a concept could be adequately 

demonstrated. “Prevent[ing] exposures” is a pretty high bar to establish. It intimates that air 

contamination should be at background and not just below a given MDA that is above 

background. This would essentially be setting up to prove a negative—that there were no routine 

exposures. For instance, SC&A feels that definitive evidence would be needed that sources were 

sealed, etc. If such information is available and sufficient, SC&A could agree that exposures 

would be incident-related only. 

However, an incident-related approach requires a demonstration that all incidents were actually 

documented, and that comprehensive and appropriate follow-up monitoring data 

(urinalysis/fecal/in-vivo sampling) was performed and is available. SC&A notes that 

interviewed workers have often stated that incidents were deliberately not documented or 

reported for various reasons. Additionally, construction of an incident-based coworker model is 
Memo to SEC Work Group 5 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

further complicated, because the line between “incidents” and recurring off-normal conditions is 

difficult to define and must be addressed on a case-by-case basis. 

SC&A Comment 5: Strata Comparison Issues and Variability among SRS Trivalent 

Actinide Data 

From Section 3.0 (Page 4, Paragraph 3):

NIOSH is considering a modification of the OPOS approach to include a timeweighted average analysis. We have conducted an analysis of the SRS americium 

coworker model using a time-weighted averaging technique and have determined 

that this method more appropriately accounts for the variability in excretion 

patterns, including this issue associated with carry-over from positive bioassay 

results in previous years. 

SC&A would like to note that the application of a time-weighted OPOS approach does not 

address the main concern that the ability to accurately compare different worker strata 

necessitates that the monitoring protocols for the two groups of workers be the same. The ability 

to accurately compare strata is essential to establish the representativeness of any proposed 

coworker model. 

Furthermore, SC&A notes that the application of a time-weighted OPOS approach would not 

address the observed variation in measurement values among aliquots of the same trivalent 

bioassay sample at SRS. The observed variability, including samples indicating results both 

above and below the MDA, must be technically addressed to assure the accuracy and adequacy 

of the underlying dataset.

SC&A Comment 5: Combination of Multiple Exposure Periods into a Single Evaluation 

Regime 

From Section 3.1 (Page 4, Paragraph 4):

If, because of data limitations, it is necessary to consider time intervals beyond 

one year in the coworker model, any changes in site practices or operations 

should be evaluated to ensure that the data can be validly combined.

SC&A strongly agrees with this concept and notes that it is directly applicable to the thorium and 

trivalent coworker models at Savannah River Site (SRS). In those instances, the following years 

were combined: 1966–1968, 1981–1982, and 1987–1989. Based on RPRT-0055, it appears that 

these years were grouped together solely to gain the requisite number of samples for strata 

comparison. Specifically, RPRT-0055 states: 

To have enough data to perform the comparisons, 1966 to 1968, 1981 to 1982, 

and 1987 to 1989 were combined to form three merged periods. This was 

necessary due to the small population size of the CTW stratum. (ORAUT 2012a) 
Memo to SEC Work Group 6 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

Therefore, a detailed investigation and analysis of exposure potential for these combined periods 

is warranted to establish that the year included in the combined grouping is sufficiently similar to 

enable the combination into a single evaluation period. This would be in accordance with the 

noted section from ‘Draft Coworker Criteria’ noted above. 

SC&A Comment 6: Application of Coworker Intakes to Different Worker Strata 

From Section 4.0 (Page 5, Paragraph 2):

As described above, workers with a higher potential for exposure would be 

considered to have been exposed at the 95th percentile of the general worker 

distribution. Thus, the geometric mean and standard deviation of the stratified 

subset should be compared to the 95th percentile of the general distribution. If it 

can be shown that the use of the full distribution in the stratified subset is more 

favorable than using the 95th percentile of the general distribution, the full 

distribution of the stratified subset should be used for those workers that fall into 

this category. 

The above narrative appears to assume the following: 

(1) A valid comparison among different strata is feasible 

(2) There is sufficient data in the subsets (or worker strata) to construct a separate coworker 

model

These two conditions must be met in order to construct an acceptable coworker model, either 

stratified or site-wide. 

Often times, the coworker model is based on a very large number of workers with little to no 

exposures and only a comparatively small subset of the population has bioassay results > MDA. 

Therefore, the 95th percentile can be very low (<MDA) if the number of unexposed monitored 

workers is very high. In these cases, significant care must be taken when comparing the results 

of a given subset of workers to the upper tail of a site-wide (all worker) model. 

SC&A Comment 7: Comparison of the “Full Distribution” of Stratified Coworker Intakes 

to the Upper Percentiles of a Site-Wide Model 

From Section 4.0 (Page 5, Paragraph 3):

Preliminary results seem to indicate that PC outcome associated with the full 

distribution can be generated by using a constant value that is around the 84th

percentile. If this were true, then it would make sense to stratify distributions only 

if the ~84th percentile of the full distribution of the stratified dataset is larger than 

the 95th percentile of the general distribution of all monitored workers.
Memo to SEC Work Group 7 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

There is a monotonic relationship between the expected value and the percentiles of a lognormal 

distribution. This relationship does not depend on the geometric mean (GM) of the distribution, 

only on the GSD = eσ. Any percentile of a lognormal distribution may be expressed as 

p = GM∙exp(zpσ), where zp is the pth percentile of the standard normal distribution. The expected 

value of the lognormal distribution is E(X) = GM∙exp(σ2

/2). By inspection, the expected value is 

equal to the percentile p* located at z*=σ/2. The corresponding percentile is p* = 100Φ(z*),

where Φ(z) is the value of the standard normal cumulative distribution function at z. 

The percentile p* that equals the expected value at each value of the GSD is shown in the table 

below. For the typical GSDs encountered in exposure assessment, the expected value ranges 

from the 70th percentile to the 85th percentile, with a central value of approximately the 80th

percentile at a GSD of 5. Hence, it is not unexpected that the PC obtained using a single intake 

near the 80th percentile will be nearly the same as the PC generated using the full distribution. 

GSD σ=ln(GSD) z

*

=σ/2 p

*

=100Φ(z*)

2 0.69 0.35 64

3 1.10 0.55 71

4 1.39 0.69 76

5 1.61 0.80 79

6 1.79 0.90 81

7 1.95 0.97 83

8 2.08 1.04 85

What does this have to say about the comparison of the construction trades worker (CTW) 84th

percentile with the all monitored worker (AMW) 95th percentile? It’s much the same as saying 

that a subgroup (like CTW) will be treated differently if their mean value exceeds the AMW 95th

percentile. The OPOS/ maximum possible mean (MPM) procedure could be used to calculate 

the mean value, so it would be as easy to implement. This appears less arbitrary than using a 

rule that the CTW 84th percentile exceeds the AMW 95th percentile. However, neither method 

for selecting who gets special treatment considers uncertainty in estimating the percentiles or the 

mean value. The paper is expressed in terms of point estimates of the 84th or 95th percentile. 

There are usually large uncertainties involved in the estimation of upper percentiles using a small 

sample size in one or both groups. Comparisons based on the difference between two point 

estimates will have large decision errors. 

Given that the white paper ‘Draft Coworker Criteria’ focuses attention on point estimates for 

comparing the upper percentiles of two populations, other ways to look at this problem should be 

considered. Perhaps a better method would be to use a formal statistical test. Hypothesis tests 

explicitly account for uncertainty when making a decision of this type. For example, a nonparametric quantile test could be used here to test if a larger than expected proportion of CTW is 

found among the workers above the 84th percentile of the AMW distribution. If so, then the 

group should be treated differently. The quantile test is also easy to implement, and avoids many 

of the problems associated with evaluating the confidence intervals for comparing the estimated 

upper percentiles and/or expected values. The test may be used with up to 84% non-detects in 

the data. 
Memo to SEC Work Group 8 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

In addition, looking only at the workers above the 84th percentile (top 1 out of 6) is somewhat 

arbitrary here. The 75th or 80th percentile would work as well, and would provide a larger sample 

size and greater power for the quantile test. But the 84th is at the “+1-sigma” mark on the normal 

distribution, and it seems to have some favor historically with NIOSH. To consider a percentile 

any higher than the 84th is likely infeasible, because the number of workers in the upper tail 

would be too small for evaluation. 
Memo to SEC Work Group 9 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

SECTION 3. PRELIMINARY REVIEW OF THE WHITE PAPER “EVALUATION OF 

DIFFERENCES BETWEEN STRATA COWORKER MODELS”

3.1 Introduction 

ORAUT-RPRT-0053 (ORAUT 2012b) provided a statistical approach for the evaluation of 

stratified coworker models. A two-tiered evaluation was proposed where the stratified 

distributions are first compared on a year-by-year basis to determine if any of the individual 

distributions are significantly different based on the Monte Carlo permutation test or the PetoPrentice test. If a significant difference is observed in any time interval, then a test of practical 

significance was proposed to determine if there is a practical difference in these cases. This test 

compares the slopes of the chronic intake models in the time periods with a statistically 

significant difference. SC&A 2013 noted that these tests only detect relatively large differences 

in the GM, particularly when the small sample sizes in one or both strata are small and the 

distributions have large GSDs.

The recent NIOSH white paper titled, Evaluation of Differences between Strata Coworker 

Models (NIOSH 2014b) presents an alternative approach to coworker modeling based on the 95th

percentile of the AMW distribution. In this approach, the 95th percentile of the full AMW 

distribution would be applied in IMBA for those “unmonitored workers who are judged to have 

been highly exposed.”

Although the approach presented appears reasonable, a major short-coming is that the paper does 

not provide a specific method for determining which unmonitored workers meet the italicized 

criterion in the statement above. As noted by NIOSH, the statistical tests may fail to detect 

differences due to inadequate power with the small number of OPOS values available for some 

strata. If the statistical tests have inadequate power in these cases, what procedure will be used 

to “judge” which unmonitored workers require use of the AMW 95th percentile? 

An example evaluation is provided in the white paper comparing the IMBA PC results obtained 

using either: 

 The 95th percentile of the AMW lognormal distribution 

 The full lognormal distribution observed for the stratum 

In the selected example, the GM of the selected stratum is higher than that of the AMW 

distribution, so there is some reason to suspect that the stratum may require special attention. 

However, the GSD is lower than that of the AMW distribution, so this example does not provide 

a clear example of how to judge when to use the recommended procedure. Other general issues 

raised by the example evaluation are discussed in the following section. 

3.2 Interpretation of the Results of the Example Evaluation 

In the white paper, the AMW 95th percentile approach was applied to the example coworker 

models provided in Figures A-1 and A-3 of Attachment A to ORAUT-RPRT-0053 (ORAUT 
Memo to SEC Work Group 10 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

2012b). In this example, the full distribution that includes AMWs has a GM of 0.7509 and a 

GSD of 4.055, while the stratified subset has a GM of 0.9306 and a GSD of 3.753. NIOSH 

provides the following motivation for this approach: 

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 × (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. [Emphasis added.] 

The example given in the paper shows that the AMW 95th percentile generates a higher 

probability of causation (PC) than when the full distribution of the stratified subset is used to 

generate a PC, and it is a factor of 1.6 times higher. However, it should be noted that the value 

of the 95th percentile of the AMW distribution (7.51) is equal to the 94.3 percentile of the 

stratified distribution. Thus, the example suggests an alternative explanation: that the increase 

in PC is systematic, i.e., when the 94th or 95th percentile of any distribution is used is used in 

IMBA, this will generate a PC that is approximately 11⁄2 times higher than if the full distribution 

were used. Given this possible alternative explanation, it is not clear that the example provides a 

valid comparison of the AMW and stratified datasets. Unfortunately, the paper does not report 

what happens when the full AMW distribution is applied. Another IMBA run using the full 

AMW distribution may shed light on this issue. 

The bolded section of the passage above also raises questions. In the example evaluation, we 

found that slightly over 5% of the stratified distribution exceeds the AMW 95th value of 7.51. 

Thus, it is approximately true (in that example only) that 5% of the unmonitored workers in the 

more highly exposed stratum would have exposures greater than the value used in his or her dose 

reconstruction. To determine if this statement is true in the general case, it is necessary to 

determine what fraction of the stratified dataset lies below the AMW 95th percentile. That issue 

is addressed in the following section. 

3.3 Coverage of the All Monitored Worker 95th Percentile 

NIOSH proposes that the 95th percentile of the AMW distribution is a claimant-favorable value 

to use in IMBA for unmonitored workers in a stratified subset of workers (say Group B) who 

may have been more highly exposed. If the AMW data follow a lognormal distribution with a 

geometric mean GMAMW and geometric standard deviation GSDAMW, then the 95th percentile of 

the AMW distribution is: 
Memo to SEC Work Group 11 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

Here μAMW = log(GMAMW), σAMW = log(GSDAMW) and z.95 = 1.645 is the 95th percentile of the 

standard normal distribution. 

The claimant favorability of this approach hinges on whether the AMW95 value will “cover” a 

high proportion of the Group B distribution. To measure the amount of coverage that the AMW

95th percentile value provides, we determine what fraction of Group B workers are at or below 

this value. Let μB = log(GMB), σB = log(GSDB) and zc be the c

th percentile of the standard normal 

distribution. The coverage c is found at the point yc =AMW95 on the Group B distribution 

function where: 

To solve for c, we first obtain: 

Then the coverage is: 

The function Φ represents the cumulative distribution function of the standard normal 

distribution. 

As an example of the use of coverage to assess claimant favorability of the AMW95 approach in 

specific applications, an assessment was conducted using the exotic trivalent radionuclide 

bioassay data for AMWs and CTWs at SRS reported in Appendix A of ORAUT-RPRT-0055 

(ORAUT 2012a). Table 1 shows the coverage of the 95th percentile of the AMW distribution 

when applied for CTW at the SRS site from 1968 to 1988. In several time periods, the CTW 

distribution was estimated using more than one year of data. In these cases, a representative year 

was selected for the AMW distribution. 

The coverage ranges from a minimum of 83.8% to a maximum of 99.6% with a mean of 93.3%. 

These data do not support the claim that the AMW 95th percentile is only exceeded by 5% of the 

unmonitored CTWs, but this may hold approximately on average for these specific datasets. The 

proportion of CTWs that exceed the AMW95 value ranges from approximately 16% down to 

0.5%. On average over all years, 6.7% of the CTWs exceed the AMW 95th percentile for these 

SRS exotic trivalent radionuclide datasets. 
Memo to SEC Work Group 12 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

Table 1. Coverage of the AMW 95th Percentile 

AMW CTW μ=log(GM)* σ=log(GSD)* Coverage

Period Period AMW CTW AMW CTW z(c) c (%)

1968 1966–1968 -1.4 -2.0 0.9 1.7 1.2 89

1969 1969 -1.2 -0.6 1.1 0.6 2.0 98

1970 1970 -1.5 -1.4 0.8 0.5 2.6 99.6

1971 1971 -1.8 -1.8 0.9 0.7 2.0 98

1972 1972 -2.6 -2.6 1.2 1.0 1.9 97

1973 1973 -4.8 -4.7 2.1 2.2 1.5 93

1974 1974 -4.7 -4.3 2.3 1.8 1.9 97

1975 1975 -4.6 -4.7 2.0 2.1 1.6 95

1976 1976 -4.3 -4.2 1.8 1.7 1.7 96

1977 1977 -5.6 -5.9 2.4 2.6 1.6 95

1978 1978 -3.7 -4.2 2.3 2.2 2.0 97

1979 1979 -3.7 -3.6 2.4 2.6 1.5 93

1980 1980 -4.7 -4.7 2.0 2.4 1.4 92

1981 1981–1982 -7.0 -5.8 3.2 4.0 1.0 85

1983 1983 -5.2 -4.4 2.1 2.0 1.3 91

1984 1984 -5.1 -5.3 2.4 4.2 1.0 84

1985 1985 -4.4 -3.0 2.3 1.7 1.3 91

1986 1986 -5.6 -6.5 2.4 4.1 1.2 88

1988 1987–1989 -4.0 -4.7 2.0 2.4 1.7 95

Mean 93.3

Minimum 83.8

Maximum 99.6

*Source: ORAUT 2012b, GMs and GSDs reported in Figures A-39 to A-57 and A-72 to A-90.
Memo to SEC Work Group 13 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

SECTION 4. PRELIMINARY REVIEW OF THE WHITE PAPER “NIOSH’S 

RECONSIDERATION OF THE APPLICATION OF THE OPOS 

METHODOLOGY: ALLOWANCE FOR TIME-WEIGHTED 

AVERAGING 

4.1 Summary 

Although the best approach to coworker modeling would be to calculate actual intakes for all 

monitored workers in the intake regime, and to use that distribution for coworker modeling, 

NIOSH has stated they do not have the resources to do these calculations, and a more expedient 

approach is required based on excretion rates, not intakes. The concept of aggregating the 

bioassay data used for coworker modeling to create an OPOS statistic for each time period was 

proposed by NIOSH in the report, Analysis of Stratified Coworker Datasets (ORAUT 2012a). 

Current procedures fit a probability distribution to the full set of bioassay results from all 

workers with samples to derive the 50th and 84th percentile excretion rates used for coworker 

intake modeling. 

The OPOS proposal was extensively discussed during the meeting of the Special Exposure 

Cohort (SEC) Work Group on September 26, 2013 (ABRWH 2013). SC&A was tasked at that 

meeting to review the various reports that have been prepared by NIOSH and SC&A on the 

topic, as well as the discussion during the Work Group meeting. SC&A findings (SC&A 2014) 

recommended a weighted approach to the mean value problem posed by OPOS. In this 

approach, the mean annual excretion rate is defined as a time-weighted average obtained by 

integrating excretion rates over the time period. This approach requires that a time-weighted 

average be used to estimate the mean excretion rate. 

NIOSH recently proposed (NIOSH 2014c) a revised version of the OPOS procedure named 

Time-Weighted OPOS. Time-Weighted OPOS is the weighted average of the bioassay results 

using the number of days between the measurements as weights. If the samples were collected at 

equally spaced times, the Time-Weighted OPOS statistic reduces to the same result as the 

original un-weighted version of OPOS. 

NIOSH applied the weighted OPOS methodology to the americium bioassay data collected at the 

SRS. The results of the comparison of the original OPOS to the Time-Weighted OPOS approach 

showed that the two statistics are the same in about 83% of the cases. In about 15% of the cases, 

the difference between the two statistics is less than 1 dpm/day in absolute value, and only 2% of 

the cases show differences between the two statistics of more than 1 dpm/day in absolute value, 

with some extreme cases where the two statistics are very far apart. NIOSH concluded that there 

is no evidence that one of the two methods is more claimant favorable than the other for 

americium at SRS. 

Evidence should be provided to support this conclusion. While a difference of 1 dpm/d does not 

sound like much at face value, it could make a significant difference in the calculated intake. 

Considering that most measured urinalysis samples are below the detection limit of 0.3 dpm/d, a 

change of 1 dpm/d could have a large effect in some cases. For example, the difference in the 
Memo to SEC Work Group 14 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

calculated intake rate based on 0.3 dpm/d and 1.3 dpm/d is a roughly a factor of 4. If lower 

actual measurement values were used in calculating the OPOS result, this factor will be larger. 

SC&A notes that there are a variety of ways to assign the number of days used as weights. 

NIOSH currently uses a “post-weighted” procedure, where the weight for bioassay result j is the 

number of days that elapse after result j up to the time of the next result. The final result is then 

assigned the number of days up to the end of the year. This “post-weighted” procedure does not 

account for the period of time at the beginning of the year before the first excretion result. To 

account for this period, NIOSH introduces an initial term at j = 0, and specifies several rules to 

define the result used for the initial time period. If there is a sample in the previous year, it is 

used for the for the excretion rate in the initial period. If there is no sample in the previous year, 

then the first result of the year is used for the initial period (and the one following). 

SC&A’s original recommendation used the number of days in the period before the result j for its 

weight, reasoning that the intakes reflected in the excretion occurred before the sample was 

collected, not after. This “pre-weighted” procedure assigns the number of days in the initial 

period as the weight for the first excretion result, but does not account for the final period of time 

from the last sample to the end of the year. This period could be addressed by using the first 

excretion result in the following year, in mirror image to what is done with the NIOSH postweighted procedure. 

On the surface, the “pre-weighted” and “post-weighted” methods appear to be quite similar, but 

may lead to quite different results for years with an incident. If the incident occurs before any 

other results that year, then the first excretion result of the year is a very high number and the 

weight assigned to this initial will have a high degree of influence on the Time-Weighted OPOS 

result. Since incidents almost always include follow-up samples soon after the initial result, the 

time weight assigned to the high initial result will be very small, often only a day or two, if the 

post-weighted procedure recommended by NIOSH is used.

Since incidents are rare events, it is most likely that the excretion result for that worker in the 

previous year will be much lower than the initial incident result and will be applied to the entire 

initial period if post-weighting is used. If there is no result in the previous year, then the initial 

incident result will be assigned for the entire initial period. Thus, the first result may be assigned 

a relatively high weight or a very small weight, depending solely on whether an (unrelated) 

excretion result was or was not collected in the previous year. SC&A suggests that this arbitrary 

weighting outcome be avoided by using the “pre-weighted” approach.

4.2 Background 

The concept of aggregating the bioassay data used for coworker modeling to create an OPOS 

statistic for each time period was proposed by NIOSH in the report, Analysis of Stratified 

Coworker Datasets (ORAUT 2012a). Although the best approach to coworker modeling would 

be to calculate actual intakes for AMWs in the intake regime and to use that distribution for 

coworker modeling, NIOSH stated they did not have the resources to do these calculations and a 

more expedient approach was required. Current procedures fit a probability distribution to the 

full set of bioassay results from all workers with samples in the time period to derive the 50th and 
Memo to SEC Work Group 15 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

84th percentile excretion rates used for coworker modeling. These percentiles are used to 

calculate intakes corresponding to the 50th and 84th percentile excretion rates. This procedure 

uses the distribution of all bioassay results from all workers and is referred to as the pooled-data 

approach. 

As an alternative to the pooled-data approach, the OPOS approach to coworker modeling was 

recommended by NIOSH as introducing a new scientific credibility to the intake modeling 

process that did not exist in the previous pooled-data approach. As originally proposed, the 

OPOS method calculates the arithmetic average of all urine samples for one individual in one 

year (or other specified time period). The resulting set of OPOS values is then used to calculate 

the percentiles needed for calculating intakes. NIOSH has argued that, under certain 

assumptions, the OPOS mean excretion rate will be proportional to the intake for that individual 

and thus serves as the best surrogate for the intakes of the individual worker. 

The OPOS approach also was designed to address problems of data dependence and data 

dominance when statistical hypothesis tests are applied for comparing two strata of workers. In 

the former case, a number of bioassay samples following a single intake will be correlated if the 

radionuclide persists in the body; hence, the samples are not independent. Data dominance is 

when a few workers have provided such a large number of samples, as for instance following 

incidents, that those samples would skew the distributions used for coworker modeling. There 

is, of course, some overlap between data dependence and data domination, since samples 

following incidents are not independent. 

The OPOS proposal was extensively discussed during the meeting of the SEC Work Group on 

September 26, 2013 (ABRWH 2013). SC&A was tasked at that meeting to review the various 

reports that have been prepared by NIOSH and SC&A on the topic, as well as the discussion 

during the Work Group meeting. SC&A was also asked (NIOSH 2013, p. 3) to be more explicit 

about its position on the use of the OPOS approach in coworker modeling and comparison of 

bioassay data of two worker strata. 

SC&A presented its OPOS findings to the Work Group in the report Draft Review of Proposed 

One Person-One Sample (OPOS) Approach to Coworker Modeling (SC&A 2014). Section 7.4 

of that report introduced a general approach to the mean value problem posed by OPOS. In this 

approach, the mean annual excretion rate is defined as a time-weighted average using integration 

over the year. A physical model of the integration process was proposed to motivate this 

approach. The true mean concentration is defined as the concentration obtained if all of the 

worker’s excretions over the year were pooled together. If the volume excreted per day is 

roughly constant, then the mean concentration in the resulting mixture is the time-weighted 

average of all urine concentrations collected over the year. 

4.3 Time-Weighted OPOS 

In their most recent white paper on OPOS, NIOSH has suggested a revision to the approach for 

calculating the mean value of a worker’s bioassay results (NIOSH 2014c). NIOSH proposes a 

new version of the OPOS procedure named Time-Weighted OPOS. Time-Weighted OPOS is 

the weighted average of the bioassay results using the number of days between the measurements 
Memo to SEC Work Group 16 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

as weights. If the samples were collected at equally spaced times, the Time-Weighted OPOS 

statistic reduces to the same result as the originally proposed un-weighted version of OPOS. 

The mathematical details of the computation of the Time-Weighted OPOS are provided in 

Attachment A to NIOSH 2014c. To implement The Time-Weighted OPOS procedure, NIOSH 

has introduced three rules that apply in special circumstances: 

(1) For an individual with more than one measurement in the same day, all the values 

(detects and non-detects) from the same day are averaged to arrive at an average daily 

excretion. 

(2) For an individual that had a sample in the previous year, it is assumed that the last sample 

from the previous year is representative of the excretion from the beginning of the current 

year until the first sample in the current year. 

(3) For an individual that had no sample in the previous year, it is assumed that the first 

sample from the current year is the exposure from the beginning of the current year until 

the first exposure observed in the current year. 

The first rule addresses the problem of multiple bioassays on the same day, while the next two 

rules address “edge effects” that occur at the beginning and end of the time period in question, 

before the first sample and after the last sample. The effects of implementing these rules are 

discussed in the following section of the report. 

NIOSH applied the weighted OPOS methodology to the americium bioassay data collected at the 

SRS. The results of the comparison of the original OPOS to the Time-Weighted OPOS approach 

showed that the two statistics are the same in about 83% of the cases. In about 15% of the cases, 

the difference between the two statistics is less than 1 dpm/day in absolute value, and only 2% of 

the cases show differences between the two statistics of more than 1 dpm/day in absolute value, 

with some extreme cases where the two statistics are very far apart. Overall, the average of the 

Time-Weighted OPOS values was about the same as the average of the OPOS values. NIOSH 

concludes that there is no evidence that one of the two methods is more claimant favorable than 

the other for americium at SRS. 

4.4 Mathematical Details of Time-Weighted OPOS 

Originally, the OPOS method was defined as the MPM. The formula given in the NIOSH paper 

for the original OPOS statistic contains an omission. The correct formula is: 

where: 

 Number of all excretion results for a person in a year 

 Individual excretion result (can be either uncensored or censored) 
Memo to SEC Work Group 17 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

NIOSH states that if there are censored excretion results, then the “face values” of these results 

are to be used in the formula above. No definition of the term “face value” is provided in the 

NIOSH paper. SC&A believes that the all measurements reported below the CL (or MDA) 

should be replaced by the CL (or MDA) as is done in the calculation of the MPM. In the 

examples in Attachment B to the paper, NIOSH does appear to use the CL for censored data, but 

the meaning of the term “face value” should be made clear.

The Time-Weighted OPOS method is weighted mean of the (censored and uncensored) excretion 

results in a year, where the results are weighted by the appropriate number of days between the 

measured values. The formula for the statistic computed using the Time-Weighted OPOS 

method is the following: 

Where m is the number of days when the person had excretion results in the year, yj is the 

average excretion result on day j, and dj is the umber of days assigned as the weight for the 

average result on day j. The use of an initial term at j = 0 in the equation above is one way to 

assign appropriate weights at the beginning and end of the year. The number of days associated 

with each result may be counted in many ways. If there are m days with excretion results, these 

days divide the year into m+1 time intervals, j = 0, 1, ... , m. The sum of these intervals is the 

sum appearing in the denominator in equation above. Yet there are only m samples in the year 

which require weights. 

This disparity introduces a variety of ways to assign the number of days used as weights. In 

Attachment B, NIOSH uses a “post-weighted” procedure, where the weight for result j is the 

number of days that elapse after result j up to the next result at time j+1. The final result is 

assigned the number of days up to the end of the year. The post-weighted procedure does not 

account for the period of time at the beginning of the year before the first excretion result. To 

resolve this, NIOSH introduces an initial term at j = 0, and specified two “Rules” to define the 

hypothetical bioassay result value used for the initial time period. The rules reduce to the choice 

of A or B: 

A) If there is a sample in the previous year, it is used for the initial period 

B) If there is no sample in the previous year, then the initial measured result at j = 1 is used 

for the initial period (and the one following) 

Mathematically, these rules are implemented by defining y0 as follows: 

 { if the individual had a bioassay in the previous year

 if the individual had no bioassay in the previous year

where: 

 last excretion result in the previous year. 
Memo to SEC Work Group 18 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

The post-weighted OPOS procedure is depicted in Figure 1. Each bioassay result is assigned a 

weight equal to the number of days elapsed after the result until the next result. The length of the 

initial period (w0 in the figure) is assigned as weight for either result A if there is a result in the 

previous time period, or result B if not. The contribution of the initial time period to the total 

integral can vary by a large amount, depending whether result A or result B is selected for this 

period. 

SC&A originally used the number of days in the period before the result j for its weight, 

reasoning that the intakes reflected in the excretion occurred before the sample was collected, not 

after. This “pre-weighted” procedure assigns the number of days in the initial period as the 

weight for the first excretion result, but does not account for the final period of time from the last 

sample to the end of the year. This, of course, could be addressed by using the first excretion 

result in the following year, in mirror image to the NIOSH post-weighted procedure. 

The pre-weighted OPOS procedure is depicted in Figure 2. Each bioassay result is assigned a 

weight equal to the number of days elapsed since the previous next result. The length of time in 

the final period (wn+1 in the figure) is assigned as weight for either result A if there is a result in 

the following time period (yp

*

in the figure), or result B if not. The contribution of the final time 

period to the total integral under these two alternative choices does not vary by as large of an 

amount as in Figure 1 with post-weighted OPOS. 

The mathematical form of the pre-weighted OPOS estimate is similar to that of the postweighted OPOS estimate: 

The weight terms dj are defined as the number of days from result j-1 to result j. For y1, the 

count of days starts at the beginning of the year. The rules A and B for the pre-weighted OPOS 

estimate are: 

A) If there is a sample in the following year, it is used for the final period 

B) If there is no sample in the following year, then the final result at j=m is used for the final 

period (and the one before) 

For pre-weighted OPOS the term ym+1 is defined as: 

 { if the individual has a bioassay in the following year

 if the individual has no bioassay in the following year

Where 

 first excretion result in the following year. 

On the surface, the “pre-weighted” and “post-weighted” methods appear to be quite similar, but 

may lead to quite different results for years with an incident. If the incident occurs before any 

other results that year, then the first excretion result of the year is a very high number and the 
Memo to SEC Work Group 19 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

weight assigned to this initial result will have a high degree of influence on the Time-Weighted 

OPOS result. Since incidents almost always include follow-up samples soon after the initial 

result, the time weight assigned to the high initial result will be very small, often only a day or 

two.

Since incidents are rare events, it is most likely that yp, the excretion result in the previous year, 

will be much lower than the initial incident result y1 and yp will be used for the entire initial 

period. If there is no result in the previous year, then the initial incident result will be assigned 

for the entire initial period. Thus, the first result may be assigned a relatively high weight or a 

very small weight, depending solely on whether an (unrelated) excretion result was or was not 

collected in the previous year. SC&A suggests that this arbitrary weighting outcome be avoided 

by using the “pre-weighted” approach.

Figure 1. Alternatives A and B at Start of Year for Post-Weighted OPOS 
Memo to SEC Work Group 20 SC&A – July 25, 2014 

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution. 

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.

Figure 2. Alternatives A and B at End of Year for Post-Weighted OPOS
Memo to SEC Work Group 21 SC&A – July 25, 2014

NOTICE: This report has been reviewed for Privacy Act information and has been cleared for distribution.

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.

REFERENCES

ABRWH 2013. Transcript of the SEC Issues Work Group Meeting held September 26, 2013.

Advisory Board on Radiation Worker Health. U.S. Department of Health and Human Services –

Centers for Disease Control – National Institute for Occupational Safety and Health. September 

26, 2013.

ORAUT 2012a. Analysis of Stratified Coworker Datasets, ORAUT-RPRT-0053, Rev. 01, Oak 

Ridge Associated Universities Team, Cincinnati, Ohio. July 16, 2012.

ORAUT 2012b. A Comparison of Exotic Trivalent Radionuclide Coworker Models at the 

Savannah River Site. ORAUT-RPRT-0055 Rev. 00. Oak Ridge Associated Universities Team. 

July 20, 2012.

NIOSH 2013. Response to SC&A Comments on ORAUT-RPRT-0053, Rev. 0. National Institute 

for Occupational Safety and Health. August 2013.

NIOSH 2014a. Draft Criteria for the Evaluation and Use of Internal Exposure Coworker 

Datasets. National Institute for Occupational Safety and Health. June 17, 2014.

NIOSH 2014b. Evaluation of Differences between Strata Coworker Models. National Institute 

for Occupational Safety and Health. Neton, J.W. and Stancescu, D. July 11, 2014

NIOSH 2014c. NIOSH’s Reconsideration of the Application of the OPOS Methodology: 

Allowance for Time-Weighted Averaging. National Institute for Occupational Safety and Health.

June 16, 2014.

SC&A 2013. Draft Review of ORAUT-RPRT-0053: Analysis of Stratified Coworker Datasets

Rev. 1. SC&A, Inc., Vienna, Virginia. April 2013.

SC&A 2014. Draft Review of Proposed One Person-One Sample (OPOS) Approach to 

Coworker Modeling, SCA-SEC-PR2014-0053, Rev. 0. SC&A, Inc., Vienna, Virginia. February 

21, 2014.