Use of Bioassay Sample Data in 

Co-Worker Models

Summary for SEG WG Meeting

James W. Neton, PhD, CHP

Associate Director for Science

Division of Compensation Analysis and Support

National Institute for Occupational Safety and Health

September 26, 2013
Summary of Internal 

Co-worker Model Calculations

(1) Urine Data

(2) OPOS Urine Data

(3) 50th and 84th 

Percentile Urine Data

(4) 50th and 84th 

Percentile Intake Rates

(GM and GSD of intake rates)

(5) Person-specific Intakes and Doses

(6) Probability of Causation
Example Bioassay Distribution for a Single Year

GM

84th percentile
Example Fit of Bioassay Data to Chronic 

Intake Scenario Over Multiple Years

Regression of median excretion rate on chronic Intake Retention Function
Co-worker Application

 Based on potential for exposure an unmonitored 

worker would receive either:

• The full intake distribution (i.e., the 50th percentile and 

the Geometric Standard Deviation (GSD) as input 

parameters or;

• The 95th percentile of the distribution input as a 

constant

 Each situation is evaluated on a site and case-specific 

basis

 Approach to evaluation of data stratification 

described in ORAUT-RPRT-0053

• Introduces concept of one person one sample (OPOS)
One Person One Sample 

 Minimizes issues related to correlated data

 Uses the Maximum Possible Mean (MPM) approach

• Using MPM, censored data are taken to be a positive 

measurement, i.e., <0.05 dpm = 0.05 dpm

Example A: 10, 3, 5, 6

Mean = 24/4 = 6 (report as 6)

Example B: 10, <3, <5, 6

Maximum Mean = 24/4 = 6 (report as 6)

Example C: <10, <3, <5, <6

Maximum Mean = 24/4 = 6 (report as <6)
Data Stratification

 Monitored population is really a conglomerate 

of a number of subgroups

 Single distribution can be applied to 

unmonitored workers if:

• Highest exposed workers were monitored or

• Representative sampling of the exposed workers was 

conducted

 If stratification suspected, can be statistically 

evaluated

• Monte Carlo Permutation Test

• Peto-Prentice Test

• Must consider the effect of multiple comparisons
Monte Carlo Permutation Test

 Assumptions:

• Data can be described by a lognormal distribution

• Data is not heavily censored

 Stratify data using an a priori criterion

• Construction workers vs. non-Construction workers

• Area 100 workers vs. Area 200 workers

 For each strata calculate the Geometric mean 

(GM) and Geometric Standard Deviation (GSD)
Monte Carlo Permutation Test—cont.

 Calculate the difference in the GM and GSD 

between strata

• These differences comprise one data point with (x,y) 

coordinates

 Random Sample

• Combine all data and randomly pull samples without 

replacement equal to the size of one strata

• Calculate GM and GSD of each random strata

• Calculate and plot the difference in GM and GSD

• Repeat 10,000 times
Monte Carlo Permutation Test—cont.

Not significantly different

Significantly different
Monte Carlo Permutation Test—cont.

 Benefits

 Can easily compare whether different size strata are 

significantly different

 Limitations

• Requires some a priori decision on distribution

• Doesn’t work if data set is heavily censored

‒ Too many random pulls of zero 

‒ Peto-Prentice Test is more appropriate
Peto-Prentice Test

 Advantages

• Non-parametric – i.e. no a priori distribution 

assumption

• Can handle censored data sets

• Can compare whether different size strata are 

significantly different (p-value)

 For cases where both the Monte Carlo and PetoPrentice are applicable, they typically lead to the 

same conclusion
Peto-Prentice Test—cont.

Not significantly different

Significantly different
Summary

 Co-worker models can be used to reconstruct 

doses to unmonitored workers if:

• Highest exposed workers were monitored or;

• Representative sampling of the exposed workers was 

conducted

 Data must be carefully reviewed for applicability

• Data quality and representativeness

• Potential for stratification

 One person one sample approach is useful in 

normalizing data

 Stratification can be evaluated using standard 

statistical tests