NIOSH's Reconsideration ofthe Application ofthe OPOS Methodology: 


Allowance for Time-Weighted Averaging 


June 16,2014 


James W. Neton, Ph.D., CHP 


Daniel Stancescu, Ph.D. 


In their review ofNIOSH's proposed one person-one statistic (OPOS) approach to the analysis of 

coworker bioassay data, SC&A raised an objection to the general use ofthe mean value of a worker's 

bioassay result in the development of coworker models. In SC&A' s opinion, the coworker dataset 

should contain all measured bioassay results during the modeled period without regard to how many 

samples a person contributed to that data set. SC&A did, however, acknowledge that in "clear cases of 

data dominance," the use ofOPOS may be warranted, but this should be the exception rather than the 

norm. 

After the recent SEC Issues Work Group discussions on this subject, NIOSH has reconsidered the use of 

the mean value of a worker's bioassay result. Although the OPOS method provides, in our opinion, a 

closer approximation ofthe urinary excretion patterns ofworkers than the previous method, it does 

suffer from several shortcomings that can be improved upon. As SC&A has suggested, OPOS fails to 

consider the temporal nature of the exposures and does not distinguish samples collected following an 

incident. 

The original proposed OPOS method is the arithmetic average of the face values of all the exposures for 

one individual in one year (or other specified time period). After reconsidering this approach, NIOSH is 

proposing a version ofthe OPOS method that makes allowance for varying potential exposure patterns. 

The revised approach, designated as Time-weighted OPOS, is the weighted average of the same results 

that are used in the computation ofthe original OPOS method, with the only difference being that the 

days between the measurements are used as weights. NIOSH believes that this statistic provides a more 

accurate method to compute the yearly average exposure for an individual. In cases of incident samples, 

the values are weighted depending on the time of the incident during the modeled period. The weighting 

also accounts for the duration of the elevated sample if subsequent follow-up samples are collected. It 

should be noted that, for samples collected on a routine frequency, the time-weighted OPOS statistic is 

the same as the originally proposed OPOS that used the arithmetic mean. 

While the computation of the Time-weighted OPOS is straightforward (a weighted average, instead of 

the simple average), three rules have been adopted to account for special circumstances. These are: 

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. 

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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 ofthe 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 ofthe current year until the first exposure 

observed in the current year. 

Once all the average daily excretion and days between samples are computed for an individual during a 

year (or other specified time period), a weighted average is used to compute the Time-weighted OPOS 

statistic, where the days between samples are used as weights. Note here, that the sum of all the days 

between samples should be either 365 or 366 (for leap years), which means that we assume a continuous 

exposure during the year, even though some individuals might had started working sometime in the 

middle of the year. 

The mathematical details of the computation of the Time-weighted OPOS are shown in Attachment A. 

To test this new approach, NIOSH applied this methodology to the all the [redacted) bioassay data 

collected at [redacted). Attachment B provides seven examples of the computation of the OPOS and 

Time-weighted OPOS values for workers that were monitored for exposure to [redacted) at the 

[redacted) site (the file that was used is [redacted)). These were chosen to demonstrate the calculation 

methodology that was used for the special circumstances described above. 

A comparison of all the results of the original OPOS to the Time-weighted OPOS approach shows that, 

in about 83% ofthe cases, the two statistics are the same. In about 15% ofthe cases, the difference 

between the two statistics is less than 1 dpm/day in absolute value, and only 2% ofthe 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. For the total [redacted) data set, the average of all the 

Time-weighted OPOS values is about the same as the average of all the OPOS values in the data set, so 

it doesn't appear that one ofthe two methods is overall more claimant favorable than the other. 

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ATTACHMENT A 


Mathematical Details of the Computation of Time-Weighted OPOS 


The OPOS method was defined as the maximum possible mean (MPM) ofthe face values for all 

the censored and uncensored excretion results for one person in a year. The formula for the statistic 

computed using the OPOS method is the following: n 

OPOS = ~L xi 

i=1 

where: 

n = number of all excretion results for a person in a year, 

xi = individual excretion result (can be either uncensored or censored). 

Note that in the case in which there are censored excretion results, the face values of these excretion 

results are used in the formula above. 

The Time-weighted OPOS method is defined as the maximum possible weighted mean ofthe 

face values for all the censored and uncensored excretion results for one person in a year, where the 

results are weighted by the numbers of days that the person was assumed to have excreted the measured 

value. The formula for the statistic computed using the T~e-weig/hte~OPOS method is the following: 

Time-weighted OPOS = ~ y1 d1 d1 

where: 

m = number of days when the person had excretion results in the year, 

y = average daily excretion results (can be either uncensored or censored), 1 

d = number of days that the person was exposed at result YJ. 1 

The average daily excretion result y , is computed as the arithmetic mean of all the excretion results that 1

a person had in one day: 

where: 

n = number of all excretion results for a person in a day. 1 

The average daily excretion result Yo that is used in the formula for the Time-weighted OPOS, 

represents the excretion result from the beginning of the current year until the first day when an 

excretion occurs during the current year, and is defined as follows: 

- {yp, if the individual had a sample in the previous year 

Yo- Yv if the individual had no sample in the previous year 

where: 

Yp = the last average daily excretion result in the previous year. 

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Note that the denominator in the formula for the Time-weighted OPOS is L:~o dj = 365 (for non-leap 

years), or 366 (for leap years). 

Similarly as in the OPOS method, the statistic computed using the Time-weighted OPOS will be used as 

an uncensored value, if the individual has at least one uncensored excretion result in the current year, or 

will be used a censored value, if all the excretion results in the current year are censored. 

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ATTACHMENT B 


Example of Calculations of the Time-Weighted OPOS 


([redacted] bioassay data) 


Example 1 


This example shows how the OPOS, and Time-weighted OPOS statistics are computed for a typical 

person in a year, when there are also samples for that person in the previous year. 

loPOS Samples for ID= AAA, Year=[redacted) 

Obs 10 Date Sample Type Result 


1 AAA [redacted] Detect 4 


2 AAA [redacted] Detect 6 


3 AAA [redacted] Non-detect 2 


4 AAA [redacted] Non-detect 3 


5 AAA [redacted] Non-detect 2 


6 AAA [redacted] Non-detect 2 


7 AAA [redacted] Non-detect 3 


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6 

5 

4 
 T4 I 

I 

>; 

ro 

~ 

"E 

:s 3 ~ 

= 

2 

0 

Te 

I 


I 


I 


I 


I 


I I 


-+ -+-----­

I I 


"' 

~ 

0::•• 
 I I 


I 0 I 


I I 


I I 


I I 


I I 


I I 


l l 

Original excretions for ID=AAA, Year= 

foPOS- 3141 

------------------------------~--------- ---·---------­

0 ,; 

1--w----- !\Jon-Detects - -e- Detects I 


ILast OPOS Sample for ID= AAA, Year=[redactedj 

Obs ID Date Sample Type Result 

15 AAA [redacted] Detect 3.0 

Time-weighted OPOS Samples for ID= AAA, Year=[redacted) 

Obs ID Date Sample Type Daily Excretion Days Between Samples 

1 AAA [redacted] Non-censored 3 [redacted] 

2 AAA [redacted] Non-censored 4 [redacted] 

3 AAA [redacted] Non-censored 6 [redacted] 

4 AAA [redacted) Censored 2 [redacted] 

5 AAA [redacted] Censored 3 [redacted] 

6AAA [redacted] Censored 2 [redacted) 

7 AAA [redacted] Censored 2 [redacted) 

8 AAA [redacted] Censored 3 [redacted] 

Page 6 


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--- --------------------- -----------------------

Average daily excretions for ID=AAA, Year= 

6 ITime·INeighted OPOS- 2.821 IOPOS- 3.141 

5 

-;;:; 

4 ~ 

"' 

-

"'E 

0.. ---~

~ 3 ~ 

""=> 

"' 

0::"' 

2­

0~~-L___L_L~--~----------------~----------------~ 

Censored values . Uncensored values I 

-~----

The last sample result from the previous year (a detect with a value of 3, from [redacted]) is assumed 

to be excreted from the beginning of the current year until the first sample in the current year 

([redacted)). For this example, OPOS =3.14, and Time-weighted OPOS =2.82. 

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Original excretions for 10=888, Year= 

3.0 3 

2.5­

2.0 

-;;:; 

~ "' 

E 

:2= 1.5 \OPOS= 167\ 

.1 1.0 

0.5 

004---------~L-------------------------L---------------~--~ 

" Non-Detects I 

Example 2 

This example shows how the OPOS, and Time-weighted OPOS statistics are computed for a typical 

person in a year, when there are no exposures for that person in the previous year. 

\oPOS Samples for ID=BBB, Year=[redacted) 

Obs ID Date Sample Type Result 

1 BBB [redacted] Non-detect 3 

2 BBB [redacted] Non-detect 1 

3 BBB [redacted] Non-detect 1 

There are no OPOS Samples for ID=BBB, Year=(redacted] 

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2.261 

2.5 

2.0­ ~ 

"' 

-o"'

-E 

o_ 

::s­ 1.5 ~ 

::> 

"' 

0:: ~· 

1.0 

0.5 

0.0~---------l-------------------------L---------------l--~ 

3.0 3 3 iTilne-Weighted OPOS

Average daily excretions for ID=BBB, Year= 

" Censored values I 

!rime-weighted OPOS Samples for ID=BBB, Year=[redacted) J 

Obs ID Date Sample Type Daily Excretion Days Between Samples 

1 BBB [redacted) Censored 3 [redacted) 

2 BBB [redacted] Censored 3 [redacted) 

3 BBB [redacted) Censored 1 [redacted) 

4 BBB [redacted] Censored 1 [redacted) 

Since there are no exposures in the previous year ([redacted)), it is assumed that the first 

measurement in the current year (a non-detect with a value of 3, from [redacted)) is representative of 

excretion from the beginning of the current year. For this example, OPOS = 1.67, and Time-weighted 

OPOS = 2.26. 

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Act 5 USC §SS2a and has been cleared for distribution. 
Example3 

This example shows how the OPOS, and Time-weighted OPOS statistics are computed for a person in a 

year, when there is more than one detectable measurement in the same day. 

joPOS Samples for ID=CCC, Year=[redacted] 

Obs ID Date Sample Type Result 

1 CCC [redacted] Detect 0.4 

2 CCC [redacted] Non-detect 0.3 

3 CCC [redacted] Detect 10.0 

4 ccc [redacted] Detect 14.0 

5 CCC [redacted] Detect 4.9 

6 CCC [redacted] Detect 4.4 

7 CCC [redacted] Detect 3.5 

8 CCC [redacted] Detect 2.0 

9 CCC [redacted] Detect 2.4 

10 CCC [redacted] Detect 0.6 

11 CCC [redacted] Detect 0.4 

12 CCC [redacted] Non-detect 0.3 

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"' 0 

'il 

~ 

'§ 

w

o; •

11.5 

10.0 

7.5 

5.0 

1.5 

0.0 

Original excretions for ID=CCC, Year= 

f,. 

I 

I 

I 

I 

t" 

I 

I 

I 

I \OPOS­ 3.6j 

I 

I

1.4.9 

I 1f4.4 

------------------------------------llho--------------------------­

1111 35 

Ill!.f' 4 

IHI 

, 04 ,I'' iii i i T'' f 04 .,, 

1--..-- Non-Detects - ...- Detects I 

ILast OPOS Sample for ID=CCC, Year=[redacted) 

Obs 10 Date Sample Type Result 

2 CCC [redacted] Non-detect 0.3 

!rime-weighted OPOS Samples for ID=CCC, Year=[redacted] 

Obs ID Date Sample Type Daily Excretion Days Between Samples 

1 ccc [redacted] Censored 0.3 [redacted] 

2 CCC [redacted] Non-censored 0.4 [redacted) 

3 CCC [redacted) Censored 0.3 [redacted) 

4 CCC [redacted) Non-censored 12.0 [redacted) 

s ccc (redacted) Non-censored 4.9 [redacted) 

6 CCC [redacted) Non-censored 4.4 [redacted) 

7 CCC [redacted) Non-censored 3.5 [redacted) 

8 ccc (redacted) Non-censored 2.0 [redacted) 

9 CCC [redacted) Non-censored 2.4 [redacted) 

10 CCC [redacted) Non-censored 0.6 [redacted) 

11 CCC [redacted) Non-censored 0.4 [redacted) 

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Average daily excretions for ID=CCC, Year= 

12.5 12 [Time·Weigl1ted OPOS- 0.95[ 

10.0 

7.5­

5.0 

2.5 ­

[OPOS= 3.6[ 

4.9 

4.4 

iJ.P..---------------------·-­

2.4 

-- ·- --· -- a.e-·---·-- ---·------·­

oo-i G.D~..3~======!o~-~4:=:=:=:=:=:=~o~.3============iJllJL_______j~~========~~o=.4~~o~.3~

.. Censored values • Uncensorecl values I 

Obs ID Date Sample Type Daily Excretion Days Between Samples 

12 CCC [redacted) Censored 0.3 [redacted) 

In this example, since there are two samples in the same day (two detects with values of 10 and 14, on 

[redacted)), the average of the two (12) is used as the excretion for that day in the computation ofthe 

Time-weighted OPOS statistic. For this example, OPOS =3.6, and Time-weighted OPOS = 0.95. 

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Original excretions for ID=DDD, Year= 

1.0 

0.8 

0.6 

0.4 

0.3 

0.2 

oo+---------~---------------------------L---------------4 

1--- Non-Detects! 

Example4 

This example shows how the OPOS, and Time-weighted OPOS statistics are computed for a person in a 

year, when there is more one non-detect in the same day. 

[?Pas Samples for ID=DDD, Year=[ redacted] 

Obs ID Date Exposure Type Exposure 

1 DDD [redacted] Non-detect 0.3 

2 DDD [redacted] Non-detect 0.3 

3 DDD [redacted] Non-detect 1.0 

!There are no OPOS Samples for ID=DDD, Year=[ redacted] 

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----------------------------------------------- --------------------

----------------------------------------------- ------ -------------

Average daily excretions for ID=DDD, Year= 

IOPOS 0.531 ITime-Weighted OPOS 0.65 

0.6 

>; 0.4 "0"' 

~ 

E 

CL 

:3­ 0.3 0.3 

"" " "' ...

IX 

0.2 

0.0 f-1-----_L_______________l_______-1 

'" Censored values I 

Time-weighted OPOS Samples for ID=DDD, Year=[redacted] 

Obs ID Date Sample Type Daily Excretion Days Between Samples 

1 DDD [redacted] Censored 0.30 [redacted] 

2 DDD [redacted] Censored 0.30 [redacted] 

3 DDD [redacted] Censored 0.65 [redacted] 

In this example, since there are two samples in the same day (two non-detects with values of 0.3 and 

1.0, on[redacted] ), the average of the two samples (0.65) is used as the excretion value for that day in 

the computation of the Time-weighted OPOS statistic. For this example, OPOS = 0.53, and Timeweighted OPOS = 0.4. 

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

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Original excretions for ID=EEE, Year=· 

0.6­

>; 

"0 "' - 0.4 E 

CL 

:s 

'5 

00 

"' "' 

0.2 ­

To.? 

I 


I 


I 


I 


I 


I 


I 


---- TQ-:4---- - _!_ --- .. ------ -- ----- - -- -- - --- - ---- -- -- -- - - - ---- ----- -- ---- I . I I IOPOS- 04J 

I .lo.3 _o.3 ,p.3 

I 

I 

I 

I 

I 

I 

I 

I 0.0 +---'-----'-------'----'-------------------1 

" Non-Detects - -e- Detects \ 

Example 5 

This example shows how the OPOS, and Time-weighted OPOS statistics are computed for a person in a 

year, when there are both detects and non-detects in the same day. 

[oPOS Samples for ID=EEE, Year=[redacted] 

Obs ID Date 

1 EEE [redacted) 

2 EEE [redacted] 

3 EEE [redacted] 

4 EEE [redacted) 

5 EEE [redacted] 

Sample Type Result 

Detect 0.4 

Non-detect 0.3 

Detect 0.7 

Non-detect 0.3 

Non-detect 0.3 

­ ­

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!Last OPOS Sample for ID=EEE, Year=[redacted] 

Obs ID Date Sample Type Result 

1 EEE [redacted] Detect 11 

!rime-weighted OPOS Samples for ID=EEE, Year=[redacted] 

Obs ID Date Sample Type Daily Excretion Days Between Samples 

1 EEE [redacted) Non-censored 11.0 (redacted) 

2 EEE [redacted] Non-censored 0.4 [redacted] 

3 EEE [redacted) Non-censored 0.5 [redacted] 

4 EEE [redacted) Censored 0.3 [redacted) 

5 EEE [redacted] Censored 0.3 [redacted) 

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10 

8 

--;;:; 

"' 

-

"'E 6 0­

:::<­

" (I) 

~ 

"' 

a: 4 ­

2 

Average daily excretions for ID=EEE, Year=· 

jTime-Weighted OPOS- 0.89j jOPOS= 0.4j 

1-- Censored values Uncensored values j "' 

In this example, since there are two samples in the same day (a detect value of 0. 7, and a non-detect 

value of 0.3, on [redacted]), the average of the two samples (0.5) is used as the excretion for that day 

in the computation of the Time-weighted OPOS statistic. For this example, OPOS =0.4, and Timeweighted OPOS = 0.89. 

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Original excretions for ID=FFF. Year= 

15oo T1540 IOPOS = 58731 

I 

I 

I 

I 

I 

I 

-;;; 1000 I '0"' - I 

E I Q. 

:3­ I 

"" => 

V> 

"' 

I 

I 

0:: 

500 I 

I 

1 34 

1~ 73 79 14 35 8.4 14 1.5 0 8 

M 

I 

28 82 

15 

31 

"" ""'-' 

20 

17 

1.8 12 

31 3.3 

. 1.5 0.6 

120 55 19 11 30 1.9 2.2 

3(L:m-3a _ 

0 

" Non-Detects - ..... ­ Detects I 

Example 6 

This example shows a scenario when the OPOS statistic produces a much higher value than the Timeweighted OPOS statistic. 

This individual had 52 samples during the year (not listed here), of which 44 were detects. 

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Act 5 USC §552a and has been cleared for distribution. 
Average daily excretions for ID=FFF, Year= 

/Time-Weigl1led OPOS = 13.94/ I

13.033 

1-- . Censored values Uncensored values / 

1500 OPOS = 58.73/

1000 ;;;; 

-a"' -E 

:s

D. 

:0 

"' 

0:: "' 

500 

10.2 14 

0.6 

25.867 0.7 0.8 

0 

There are 34 daily samples for the individual, that were used in the computation of the Time-weighted 

OPOS statistic {the first exposure of the current year is assigned on the first day of the year, based on 

the last exposure from the previous year). For this example, which is typical for an individual that had 

an incident during the year, OPOS = 58.73, and Time-weighted OPOS = 13.94, so the OPOS statistic is 

much higher than the Time-weighted OPOS statistic, due to the fact that the high exposures lasted for 

only a few days, so the samples received very small weights in the computation ofthe Time-weighted 

OPOS statistic. 

Page 19 

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. 
Original excretions for ID=GGG, Year= 

1000-,-------------~,.1-oo-o--------------------------~~~O~P~0 S===729~.7~7~j 

I 

__ 22---2oL~ 7 -~-0.3 

I 

I 

800 I 

I 

I 

I 

600 I 

I 

I 

I 

400 I 

I 

I 

I 

200 I 

123 12.8 4 0.4 0~34 0.3 

37 60 5 9 · 6.7 0.4 0 ~ 0.5 

34 7 73 ~ 9.e e.o o ~ 0.3 0.3 0.3 0.3 0.3 

.---- ---- '3::.- n::r .o.3.oA­ _____ -o.J :r:.-o.3-0.3 ______ _ 

0 

1---- Non-Detects --4>- Detects I 

Example 7 

This example shows a scenario when the Time-weighted OPOS statistic is much higher than the OPOS 

statistic. 

This individual had 52 samples during the year (not listed here), of which 38 were detects. 

Page 20 

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 §S52a and has been cleared for distribution. 
500 

Average daily excretions for ID=GGG, Year= 

517 5171Time-Weighted OPOS 146.231 IOPOS 29.771 

400­

-;;:; 

-o "' 300­ 'E 

CL 

:8­

"=' 

" "' Q,_l 200

0:: 

1-- Censored values e Uncensored values I 

There are 44 daily samples for the individual, that were used in the computation of the Time-weighted 

OPOS statistic (the first sample ofthe current year is assigned on the first day of the year, based on the 

first observed sample in the current year, since there is no measurement for this individual in the 

previous year). For this example OPOS = 29.77, and Time-weighted OPOS =146.23, so the Timeweighted OPOS statistic is much higher than the OPOS statistic, due to the fact that the high exposure 

of 517 was assumed to occur from [redacted) until [redacted), in the absence of any other exposure 

before the incident. 

Page 21 

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 N!OSH or its contractor. NOTICE: This report has been reviewed to identify and redact any information that is protected by the Privacy 

Act 5 USC §S52a and has been cleared for distribution.