A Review of the NIOSH Roadmap for Research on Asbestos Fibers and Other Elongate Mineral Particles (2009) / Chapter Skim
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Appendix B: Counting Strategies
Appendix B: Counting Strategies
Pages 93-108
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From page 93... ...
to the case of a Poisson random variable, which is the appropriate distribution for rare-event count data. This appendix provides a brief sketch of a potential methodology for addressing the variability and includes an illustration of this methodology using data from the New York state inter-laboratory asbestos testing program.
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From page 94... ...
We do not know the value of the corresponding true observation xil . Our goal is to estimate xil and construct a confidence region for xil using the previous esti ˆˆ ˆ mates ∑ , β , and β of ∑ , β , and β , respectively.
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From page 95... ...
If it is, then we can have 95 percent confidence that the true number of asbestos fibers in the sample is greater than 0. Third, we can determine the detection limit, which is the smallest observed count for which the true count is greater than zero.
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From page 96... ...
In order to apply the previously described methodology based on a mixed-effects Poisson regression model, we must obtain an estimate of true count for each sample. To this end, we used the overall mean count over all of the laboratories that analyzed each sample.
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From page 97... ...
of the calibration curve over all of the 45 laboratories. This is an enormous relative standard deviation, indicating that the laboratories exhibit considerable variability in their individual calibration curves (i.e., differential sensitivity to changing numbers of particles from lab to lab)
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From page 98... ...
counts analyzed by TEM. TABLE B-1 Marginal Maximum Likelihood Estimates of the Mixedeffects -- Poisson Regression Model for TEM Data Parameters Estimates SE z-value p-value γ0 5.8000 0.0718 80.73 < .0001 γ1 1.0128 0.0965 10.50 < .0001 Σ(1,1)
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FIGURE B-2 Individual laboratory estimated calibration functions. NOTE: The y-axis is in a log scale with base = 10.
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100 REVIEW OF THE NIOSH ROADMAP FIGURE B-3 Alternative minimum level model with 99 percent interval for asbestos TEM samples in mm2. FIGURE B-4 Standard deviation vs.
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From page 101... ...
of the calibration curve over all of the laboratories. This is an even larger relative standard deviation than obtained for TEM, indicating also that the laboratories exhibit considerable variability in their individual calibration curves (i.e., differential sensitivity to changing numbers of particles from lab to lab)
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From page 102... ...
TABLE B-2 Marginal Maximum Likelihood Estimates of the Mixedeffects -- Poisson Regression Model for PCM Data Parameters Estimates SE z-value p-value γ0 3.8559 0.0864 44.63 < .0001 γ1 0.6006 0.0498 12.07 < .0001 Σ(1,1)
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From page 103... ...
FIGURE B-8 Individual laboratory estimated calibration functions for PCM. NOTE: The y-axis is in a log scale with base = 10.
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Finally, Figure B-11 displays a plot of the relationship between average counts and the relative standard deviation. The figure shows that considerable uncertainty exists in PCM asbestos counts throughout all of the samples investigated, regardless of the number of fibers.
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FIGURE B-11 Percent relative standard deviation vs. concentration for asbestos PCM samples in mm2.
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. The relevant theory would need to be developed for the mixed effects Poisson regression model proposed here and is likely to be quite valuable in the context of the RockeLorenzato model as well.
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From page 107... ...
It is critically important for the analytic community to address the issue of TEM variability so that more reliable exposure concentrations can be determined. THE PROBLEM OF NON-DETECTS A complication in the statistical analysis of environmental data in general and asbestos in particular is the presence of non-detects.
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From page 108... ...
1997. An alterna tive minimum level definition for analytical quantification.
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