The Effect of Uncertainty in Exposure Estimation on the ExposureResponse Relation between 1,3Butadiene and Leukemia
Abstract
:1. Introduction
2. Methods
2.1. Overview of Exposure Estimation
2.2. TaskSpecific Exposure Estimates
2.3. Work Area/Job Group Exposure Estimates
2.4. SubjectSpecific Cumulative Exposure Estimates
2.5. Vital Status and Cause of Death Information
2.6. Association of Butadiene Exposure to Leukemia Mortality in the Main Analysis
2.7. Uncertainty Analyses
2.8. ExposureResponse Simulation
3. Results
4. Discussion
Appendix
Illustration of Exposure Estimation
Introduction
I. Overview of One Subject’s Work History and Butadiene Cumulative Exposure Estimates
Segment  Work area/job group  Start date  End date  Days  BD ppm 8hour TWA  BD ppmyears 

1  812  08/27/1943  09/24/1943  28  36.0066  2.76 
2  812  09/24/1943  12/31/1943  98  36.0066  12.42 
3  812  12/31/1943  01/23/1944  23  36.2725  14.71 
4  812  01/23/1944  10/01/1944  252  36.2725  39.73 
5  817  10/01/1944  12/31/1944  91  43.1242  50.48 
6  816  12/31/1944  12/12/1945  346  42.9674  91.18 
7  816  12/12/1945  12/31/1945  19  42.9674  93.41 
8  816  12/31/1945  01/06/1946  6  42.5815  94.11 
9  816  01/06/1946  12/31/1946  359  42.5815  135.97 
10  816  12/31/1946  12/31/1947  365  42.7788  178.72 
11  816  12/31/1947  10/31/1948  305  37.3081  209.87 
12  817  10/31/1948  12/31/1948  61  43.1242  217.07 
13  817  12/31/1948  12/31/1949  365  43.1242  260.17 
14  817  12/31/1949  10/22/1950  295  43.1242  295.00 
15  817  10/22/1950  12/31/1950  70  43.1242  303.26 
16  817  12/31/1950  12/31/1951  365  43.1242  346.36 
17  817  12/31/1951  12/31/1952  366  43.1242  389.57 
18  817  12/31/1952  12/31/1953  365  43.1242  432.66 
19  817  12/31/1953  12/31/1954  365  43.1242  475.76 
20  817  12/31/1954  12/31/1955  365  43.1242  518.85 
21  817  12/31/1955  12/31/1956  366  43.1242  562.06 
22  817  12/31/1956  12/31/1957  365  43.1242  605.16 
23  817  12/31/1957  12/31/1958  365  43.1242  648.25 
24  817  12/31/1958  12/31/1959  365  43.1242  691.35 
25  817  12/31/1959  12/31/1960  366  40.4189  731.85 
26  817  12/31/1960  12/31/1961  365  40.4189  772.24 
27  817  12/31/1961  12/31/1962  365  40.4189  812.63 
28  817  12/31/1962  03/14/1963  74  40.4189  820.82 
29  817  04/30/1963  12/31/1963  245  40.4189  847.93 
30  817  12/31/1963  12/31/1964  366  40.4189  888.44 
31  817  12/31/1964  12/31/1965  365  40.4189  928.83 
32  817  12/31/1965  12/31/1966  365  40.4189  969.22 
33  817  12/31/1966  12/31/1967  365  40.4189  1009.61 
34  817  12/31/1967  12/31/1968  366  40.4189  1050.11 
35  817  12/31/1968  10/31/1969  304  40.4189  1083.75 
36  817  10/31/1969  12/31/1969  61  40.4189  1090.50 
37  817  12/31/1969  12/31/1970  365  40.4189  1130.89 
38  817  12/31/1970  04/29/1971  120  40.4189  1144.17 
II. Derivation of Butadiene Estimate for One of the Tasks Comprising One Work Area/Job Group
Task number  Task name 

301  Recovery area background 
303  Water drawoff from vacuum pumps 
305  Minor maintenance of recovery compressor house 
312  Drain water from butadiene decanter (recycle tanks) 
315  Minor maintenance of butadiene pumps 
Description The inspection and maintenance of the recovery compressors involved inspecting the area for compressor leaks and preparing the compressor for repair by a mechanic or pipefitter. Exposure is a function of the compressor leak rate. The leak rate for compressors was determined to be 20–30 lbs per day. The compressors leaked liquid that was approximately 90% butadiene. The average wind speed values (lower and upper limit) for this task across all plants was used. We assumed that, during the inspection, the operator maintained an average distance of 1 meter from any one of the four compressor seals. The upper and lower limits were calculated based on the theory that the probability that the operator stood directly in the plume was 0.125 (lower limit) to 0.25 (upper limit) of standing directly in the plume. Exposure scenario Point source emission of butadiene. During the time period 1943–1983, compressors leaked a water/butadiene mixture at a rate of 20–30 lbs/day; 90% of this mixture was butadiene; thus 18–27 lbs of butadiene were lost from each seal per compressor per day.  
Parameters  
• Butadiene emission rate, Q  
• Duration of task (minutes)  
 
• Duration of exposure  
 
• Frequency of task = 4 times/shift  
• Distance of the operator = 1 meter  
• Wind speed (meters/second)*  
 
• Probability of operator standing directly in the plume  

Description Intensity of exposure originating from a point source was calculated using a nearfield air dispersion model that estimates worker exposure to gases and vapors leaking from pumps and valves:
$${\text{E}}_{\text{ppm}}\hspace{0.17em}=\hspace{0.17em}1000\hspace{0.17em}*\hspace{0.17em}24.45\hspace{0.17em}*\hspace{0.17em}\text{Q}/(\text{MW}\hspace{0.17em}*\hspace{0.17em}0.136\hspace{0.17em}*\hspace{0.17em}{\text{D}}^{1.84}\hspace{0.17em}*\hspace{0.17em}\text{u})$$
Information from interviews indicated that duration of task 305 ranged from a lower limit of 10 minutes to an upper limit of 20 minutes, with an exposure frequency of four times per shift. The partial eighthour time weighted average was calculated as the point source exposure (E_{ppm}) multiplied by the duration and frequency of the task, divided by 480 (the number of minutes in an eighthour shift). The probability of an operator standing directly in the plume and having an exposure greater than zero ranged from a lower limit of 0.125 to an upper limit of 0.25. If the operator was not directly in the plume, exposure would have been equal to zero. Therefore, the majority of exposure estimates for task 305 had a value of zero (see Figure B1).  
Calculation of nonzero exposure values  
Lower limit (LL):  
Point source exposure, if operator was in the emission plume:  E_{ppm} = [1000 * 24.45 * 0.09458/(54.1 * 0.136 * 1^{1.84} * 1.44)] = 218.2627 
Partial timeweighted average (ppm) if in the plume:  TWA (task 305) = [E_{ppm}(LL) * duration (LL) * frequency (LL)]/480 = [218.2627 * 10 * 4]/480 = 18.1886 ppm 
Upper limit (UL):  
Point source exposure if operator was in the emission plume:  E_{ppm} = [1000 * 24.45 * 0.141875 /(54.1 * 0.136 * 1^{1.84} * 0.42)] = 1122.5334 
Partial timeweighted average (ppm) if in the plume:  TWA (task 305) = [E_{ppm}(UL) * duration (UL) * frequency (UL)]/480 = [1122.5334 * 20 * 4]/480 = 187.0889 ppm 
Description We computed an approximate probability distribution of the butadiene exposure intensity for task 305 by assuming that each parameter in the exposure model followed a triangular distribution with a mode at the midpoint between the lower and upper boundaries, by identifying the 1^{st}, 2^{nd}, …, 99^{th} percentile of this distribution, and by computing the exposure intensity for all possible combinations of parameter quantiles (i.e., for the approximate joint distribution of the exposure parameters). We evaluated the resulting empirical distribution of exposure estimates to find the approximate 1^{st}, 2^{nd}, …, 99^{th} percentile of each taskand time periodspecific exposure intensity estimate.  
Results  
Percentile of probability distribution  BD ppmminutes  Percentile of probability distribution  BD ppmminutes  Percentile of probability distribution  BD ppmminutes 
1–80  0  87  21850.47  94  28984.96 
81  5866.33  88  22790.27  95  30450.26 
82  12203.21  89  23681.70  96  32126.42 
83  17268.85  90  24669.88  97  34454.32 
84  18717.13  91  25609.69  98  37932.57 
85  19896.17  92  26594.45  99  45111.79 
86  20910.66  93  27721.00 
III. Derivation of Butadiene PPM Estimates for Work Area/Job Group 817 from Component Tasks
Procedure Using the five component tasks for work area/job group 817 that entailed butadiene exposure, we computed the approximate probability distribution of the eighthour time weighted average exposure intensity. We selected 100 points from each of the approximate probability distributions of exposure intensity of the first two component tasks, and created a new distribution of every possible combination of these exposure intensities (100 * 100 = 10,000 possible combinations). From that distribution we selected 100 new points of the approximate probability distribution of exposure intensity attributable to the first two component tasks. We then combined those values with 100 selected points of the approximate probability distribution of exposure intensity of the third component task, created a distribution of all possible combinations of exposure intensities, and selected 100 new percentile points of the exposure intensity attributed to the first three tasks. We repeated this process for each of the other two component tasks of work area/job group 817. Distribution of estimates for work area/job group 817 Below are selected values of the approximate probability distribution of BD ppmminutes for work area/job group 817 in plant four in 1950.  
Percentile of probability distribution  BD ppmminutes  Percentile of probability distribution  BD ppmminutes  Percentile of probability distribution  BD ppmminutes 
5  9213.70  45  14415.39  85  33112.75 
10  10208.70  50  15007.26  90  38563.94 
15  10920.08  55  15666.86  95  45231.64 
20  11557.11  60  16382.51  
25  12149.74  65  17295.72  min  5435.93 
30  12718.85  70  18323.38  mean  20699.60 
35  13283.74  75  19912.71  max  130474.33 
40  13788.17  80  23472.45  
Calculation of BD ppm 8hour TWA for work area/job group 817, plant four, 1950 (main analysis) BD ppm 8hour TWA = mean of approximate probability distribution/ 480 minutes = 20699.60/480 = 43.1242  
Calculation of BD ppm 8hour TWA for work area/job group 817, plant four, 1950 (dataset 70 of uncertainty analysis) In the 70^{th} of the 1,000 datasets created for the uncertainty analysis, we randomly selected the 25^{th} percentile of approximate probability distribution of butadiene exposure intensity for work area/job group 817 in plant four. BD ppm 8hour TWA = 25^{th} percentile value of approximate probability distribution/ 480 minutes = 12149.74/480 = 25.3120 
Segment  Work area/job group  Start date  End date  Days  BD ppm 8hour TWA  BD ppmyears 

1  812  08/27/1943  09/24/1943  28  18.5570  1.42 
2  812  09/24/1943  12/31/1943  98  18.5570  6.40 
3  812  12/31/1943  01/23/1944  23  18.5622  7.57 
4  812  01/23/1944  10/01/1944  252  18.5622  20.38 
5  817  10/01/1944  12/31/1944  91  25.3114  26.68 
6  816  12/31/1944  12/12/1945  346  16.4205  42.24 
7  816  12/12/1945  12/31/1945  19  16.4205  43.09 
8  816  12/31/1945  01/06/1946  6  16.4347  43.36 
9  816  01/06/1946  12/31/1946  359  16.4347  59.52 
10  816  12/31/1946  12/31/1947  365  16.4499  75.96 
11  816  12/31/1947  10/31/1948  305  16.6307  89.84 
12  817  10/31/1948  12/31/1948  61  25.3126  94.07 
13  817  12/31/1948  12/31/1949  365  25.3045  119.36 
14  817  12/31/1949  10/22/1950  295  25.3120  139.80 
15  817  10/22/1950  12/31/1950  70  25.3120  144.65 
16  817  12/31/1950  12/31/1951  365  25.3614  169.20 
17  817  12/31/1951  12/31/1952  366  25.3120  195.36 
18  817  12/31/1952  12/31/1953  365  25.3366  220.68 
19  817  12/31/1953  12/31/1954  365  25.3100  245.97 
20  817  12/31/1954  12/31/1955  365  25.3139  271.27 
21  817  12/31/1955  12/31/1956  366  25.3084  296.63 
22  817  12/31/1956  12/31/1957  365  25.3092  321.92 
23  817  12/31/1957  12/31/1958  365  25.3137  347.22 
24  817  12/31/1958  12/31/1959  365  25.3126  372.51 
25  817  12/31/1959  12/31/1960  366  23.7432  396.30 
26  817  12/31/1960  12/31/1961  365  23.7102  415.00 
27  817  12/31/1961  12/31/1962  365  23.7005  443.68 
28  817  12/31/1962  03/14/1963  74  23.6767  448.41 
29  817  04/30/1963  12/31/1963  245  23.6767  464.30 
30  817  12/31/1963  12/31/1964  366  23.7113  488.06 
31  817  12/31/1964  12/31/1965  365  23.6885  511.73 
32  817  12/31/1965  12/31/1966  365  23.6767  535.39 
33  817  12/31/1966  12/31/1967  365  23.6888  559.06 
34  817  12/31/1967  12/31/1968  366  23.6718  582.78 
35  817  12/31/1968  10/31/1969  304  23.7432  602.54 
36  817  10/31/1969  12/31/1969  61  23.7432  606.51 
37  817  12/31/1969  12/31/1970  365  23.6718  630.16 
38  817  12/31/1970  04/29/1971  120  23.7115  637.89 
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Butadiene ppmyears*  Relative rate  

Minimum  Maximum  Mean  Median  
0  1.0  1.0  1.0  1.0 
>0–<33.7  1.2  1.8  1.5  1.5 
33.7–<184.7  1.1  2.2  1.6  1.6 
184.7–<425.0  1.2  3.8  2.6  2.6 
425.0+  2.4  4.3  3.3  3.3 
Nonmonotonic pattern*  N 

RR_{2} = RR_{1}  116 
RR_{3} = RR_{2}  19 
RR_{3} = RR_{2} = RR_{1}  1 
RR_{4} = RR_{3}  20 
RR_{4} = RR_{3} & RR_{2} = RR_{1}  10 
RR_{4} < RR_{3}  59 
RR_{4} < RR_{3} & RR_{2} = RR_{1}  20 
RR_{3} < RR_{2}  43 
RR_{3} < RR_{2} = RR_{1}  1 
RR_{2} < RR_{1}  182 
RR_{4} = RR_{3} & RR_{2} < RR_{1}  17 
RR_{4} < RR_{3} & RR_{2} < RR_{1}  38 
RR_{3} < RR_{2} < RR_{1}  1 
© 2009 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an openaccess article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).
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Graff, J.J.; Sathiakumar, N.; Macaluso, M.; Maldonado, G.; Matthews, R.; Delzell, E. The Effect of Uncertainty in Exposure Estimation on the ExposureResponse Relation between 1,3Butadiene and Leukemia. Int. J. Environ. Res. Public Health 2009, 6, 24362455. https://doi.org/10.3390/ijerph6092436
Graff JJ, Sathiakumar N, Macaluso M, Maldonado G, Matthews R, Delzell E. The Effect of Uncertainty in Exposure Estimation on the ExposureResponse Relation between 1,3Butadiene and Leukemia. International Journal of Environmental Research and Public Health. 2009; 6(9):24362455. https://doi.org/10.3390/ijerph6092436
Chicago/Turabian StyleGraff, John J., Nalini Sathiakumar, Maurizio Macaluso, George Maldonado, Robert Matthews, and Elizabeth Delzell. 2009. "The Effect of Uncertainty in Exposure Estimation on the ExposureResponse Relation between 1,3Butadiene and Leukemia" International Journal of Environmental Research and Public Health 6, no. 9: 24362455. https://doi.org/10.3390/ijerph6092436