COWORKER DOSE MODELING

Arjun Makhijani, SC&A

Advisory Board on Radiation and Worker Health

Idaho Falls, Idaho

July 16–17, 2013
I. BACKGROUND

• ORAUT-RPRT-0053 discusses methods for developing coworker models. Statistical tests 

are recommended to decide if a single coworker model is appropriate for all workers at 

a site, or if separate coworker models are necessary for different sub-groups of workers 

(strata).

•

• Several ORAUT documents are based on the analytical methods proposed in RPRT- 0053. These documents compare coworker models for construction trades workers 

(CTWs) and non-construction trades workers (NCWs) at the Savannah River Site (SRS).

•

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

Models at the Savannah River Site, July 2012

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

River Site, August 2012

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

Coworker Models at the Savannah River Site, September 2012.

•

• This presentation includes examples drawn from our review of these documents. •

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II. DATA ISSUES

A. SAMPLING PROTOCOL ISSUE (Finding 4)

• Strata comparisons are valid only when the sampling protocols were the 

same.

• Issue applies to datasets reduced using the One Person-One Sample 

(OPOS) procedure and to raw datasets of samples.

• If sampling protocols differ, valid statistical comparisons cannot be made.

• Example: If monitoring is incident-driven for one group of workers and not 

for the other, the hypothesis tests do not provide a valid comparison.

• NIOSH states in RPRT-0056 and RPRT-0058: 

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. 

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B. REPRESENTATIVENESS AND COMPLETENESS 

(Finding 2)

• The completeness and representativeness of the data available for coworker model is not 

addressed in ORAUT-RPRT-0053. If the unmonitored workers are from a different 

population, the applicability of a coworker model derived from monitored coworkers would 

be in question. 

• Characteristics of monitored and unmonitored populations should be the same. The relative 

exposure potential of the monitored versus unmonitored workers needs to be 

demonstrated rather than assumed.

• The methods proposed in ORAUT-RPRT-0053 for analyzing the coworker datasets require 

verification that: 

– The available coworker data are representative of all groups of workers 

– 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.

• To this end, it is necessary to examine subgroups of CTWs. Data for the coworker model 

must be representative of these groups, and there must be sufficient data for pairwise 

comparisons with other monitored workers.

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C. NUMBER OF STRATA (Recommendation 3)

• NIOSH has not made comparisons of CTW subgroups.

• Analysis of SRS CTWs by job type and by area of work 

(SC&A 2010a, 2010b) indicates that subgroups of CTWs 

have unique distributions of exposure and are not from the 

same distribution as NCWs or other CTW subgroups.

• Multiple pairwise comparisons would be required for the 

CTW analysis. Sufficient data (at least 30 samples for each 

category) would be required in each job/area category for 

which a coworker model is to be constructed. The hurdle is 

sufficient data for such comparisons.

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D. WORKERS CHANGING JOBS (Finding 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 period, the OPOS values are correlated for this worker. (Note 

that OPOS aggregation periods can be as long as 3 years.)

• 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. If CTW and NCW are being compared, it is essential that the job 

designation has not changed during the period of OPOS aggregation. 

• NIOSH has not investigated whether changes of workers from one stratum 

to another occurred during the period of OPOS aggregation and, if so, how 

such data are to be handled.

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III. METHODOLOGICAL ISSUES

A. POWER CONCERNS (Finding 8)

• NIOSH has not provided any measure of the power of the hypothesis test 

procedures to detect differences within the worker population. This 

deficiency should be corrected before the tests are adopted as an 

appropriate procedure for coworker models. 

• Accepting the null hypothesis could often be very claimant unfavorable if 

the available data do not provide adequate power for the test. 

• NIOSH has stated that 30 samples in each strata is sufficient for a valid 

comparison. We investigated this issue further during our review of the 

SRS application documents noted above. The following very general 

results are reported in our review of the neptunium coworker model.

• Table 1 and Figure 1 show results of simulations performed to show the 

power of the WRS test when using 30 samples to compare lognormal 

distributions which differ by a factor of 2.73. The samples include 24% 

nondetects. The GSDs are assumed the same for the two distributions. 

Simulation was conducted using Crystal Ball.

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A. POWER CONCERNS (Finding 8 - continued)

• Results: Type 2 error rates can be very high (15–35%) when using the 95% confidence level 

(α=0.05) if the GSDs exceed 4. If the confidence level is reduced to 90% (α=0.10), the Type 2 

error rate is maintained below 20% up to a GSD of 6. If the confidence level is 80% (α=0.20), 

the Type 2 error rate maintained is below 10%.

• Overall, SC&A concludes that the NIOSH method of determining that there are no 

significant differences based on the available data would often lead to very claimantunfavorable results.

SIMULATION RESULTS

Table 1. Type 2 Error Rate of WRS Test using 30 Samples from Two Lognormal Distributions: LN(0,1) and 

LN(1,1)

GSD

α 6 5 4 3 2

0.05 0.35 0.27 0.16 0.04 <0.001

0.10 0.22 0.16 0.09 0.02 <0.001

0.20 0.11 0.07 0.04 0.006 <0.001

0.25 0.09 0.05 0.02 0.003 <0.001

n1=n2=30, 24% nondetects, and GM2/GM1 = 2.73

Shaded region of table has Type 2 Error rate ≤10%

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Figure 1. Type 2 Error Rate of WRS Test using 30 Samples from 

Two Lognormal Distributions: LN(0,1) and LN(1,1)

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B. SMALL SAMPLE SIZES (Finding 6)

• Power of the statistical tests to detect differences given the limited quantity of 

data with high proportion of nondetects has not been established. The size of 

difference that can be detected reliably by the statistical tests was not examined. 

This deficiency should be corrected before RPRT-0053 is adopted as an appropriate 

procedure for evaluating coworker models.

• If the quantity of data is insufficient to provide adequate power of resolution for 

the test, differences may go undetected. Accepting the null hypothesis in this case 

could often be very claimant unfavorable.

• The Data Quality Objectives (DQO) process should be used to define the Gray 

Region for the test, and to balance Type 1 and Type 2 decision errors. The 

MARSSIM procedure for conducting hypothesis tests is depicted in Figure 2.

• In our review, we examined SRS Logbook Np OPOS data for 1961–1989 (Table 2). 

The WRS test shows slightly less power than the t-test for these datasets. We 

found there are sufficient data in 1961–1963 to detect differences as small as a 

factor of 2. The year 1985 produced anomalous results in this analysis. In many 

years, the WRS test cannot reliably detect differences smaller than a factor of 4 

to 10 in the CTW/NCW ratio of GMs.

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

cannot be detected reliably with the available data.

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Figure 2. The DQO Process is Used to Define the Gray Region for the Test.

Power is Low and Type 2 Error Rates are High Below the Upper Bound of 

the Gray Region (UBGR)

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Number of Samples Upper Bound of Gray Region 

(UBGR)

Year NCW CTW t-Test WRS Test

1961 252 57 1.5 1.5

1962 734 175 1.5 1.5

1963 362 82 2.0 2.1

1974 58 10 3.5 3.8

1975 64 21 3.4 3.8

1977 43 11 8.4 10.2

1978 73 19 3.9 4.6

1979 55 12 4.9 4.6

1980 87 19 3.8 4.3

1981 99 23 4.4 4.5

1983 82 24 3.2 3.4

1984 92 25 3.8 4.1

1985 62 13 29.0 57.4

1986 65 13 5.5 5.6

1987 81 15 6.4 8.6

1988 77 13 5.0 5.0

1989 69 17 7.9 11.0

Table 2. Sample Sizes and Upper Bound of the Gray Region (UBGR) for Test 

of “No Difference” Hypothesis with SRS Logbook Np OPOS Data 1961–1989

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C. LEVEL OF CONFIDENCE (Finding 5)

• The test procedures recommended in RPRT-0053 require a 

high level of confidence before deciding that two worker 

groups are significantly different. 

• This is not claimant favorable, since there is a trade-off 

between high confidence and power to detect differences 

given a fixed sample size. A high level of confidence 

reduces the power of the test to detect differences.

• Conducting the 2-sided test of the “No Difference” 

hypothesis at a 90% level of confidence would result in 

lower Type 2 error rates and be more claimant favorable.

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D. 1-SIDED VERSUS 2-SIDED TESTS (Recommendation 1)

• RPRT-0053 recommends using 2-sided tests to determine if there is 

a significant difference between groups of workers. The null 

hypothesis for these tests states there is “No Difference” between 

the two groups. This form of test is not claimant favorable at SRS, 

as it places the burden of proof on the CTW claimants to prove 

that a significant difference exists.

• In the specific case of the SRS SEC for CTWs, a 1-sided test is more 

appropriate, as it addresses directly the question at hand: Are the 

CTW samples higher than the NCWs, or not? There are two 

possible forms of null hypothesis for a 1-sided test:

(1) H0: FNCW > FCTW

 or

(2) H0: FNCW < FCTW

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D. 1-SIDED VS. 2-SIDED TESTS (Recommendation 1 - continued)

• With either selection, the null hypothesis may not be rejected simply because there are 

insufficient data. In English, the two options are as follows.

(1) Assume that NCW exceed CTW, and look for evidence in the data that this assumption is 

false (i.e., CTW are lower, until proven higher)

This option is not claimant favorable in the SRS applications, as it places the burden of proof on 

the CTW claimants to provide sufficient data to prove their exposures were higher. 

(2) Assume that CTW exceed NCW, and look for evidence in the data that this assumption is 

false (CTW are higher, until proven lower)

It is more claimant favorable to choose the second form of null hypothesis for a 1-sided test, as 

it places the burden of proof on NIOSH to provide evidence that the NCW distribution bounds 

the CTW distribution. Groups of workers with suspected high exposures should be considered 

different in the absence of strong evidence that they are not.

• NIOSH might consider using the second form of the 1-sided hypothesis test instead of the 2-sided 

test now used. The non-parametric Peto-Prentice test is more generally applicable than the 

parametric MCPT, and may be applied using the more claimant-favorable 1-sided null hypothesis 

number (2) above. This is more likely to result in a claimant-favorable coworker model.

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REFERENCES

ORAUT-RPRT-0055: A Comparison of Exotic Trivalent Radionuclide Coworker 

Models at the Savannah River Site, July 2012

ORAUT-RPRT-0056: A Comparison of Neptunium Coworker Models at the 

Savannah River Site, August 2012.

ORAUT-RPRT-0058: A Comparison of Mixed Fission and Activation Product 

Coworker Models at the Savannah River Site, September 2012.

SC&A 2010a. Review of ORAUT-0075: Use of Claimant Datasets for Coworker 

Modeling for Construction Workers at Savannah River Site, S. Cohen & 

Associates, January 2010.

SC&A 2010b. Comparison of Claimant Tritium Samples from Construction 

Trade Workers and Non-Construction Workers at Savannah River Site. S. 

Cohen & Associates, November 2010.

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