Confidence Intervals for Asbestos Fiber Counts: Approximate Negative Binomial Distribution

Our plain-English summary of Confidence Intervals for Asbestos Fiber Counts: Approximate Negative Binomial Distribution, by D. Bartley, J. Slaven, M. Harper (Annals of Work Exposures and Health, 2017).

The study

• Authors: D. Bartley, J. Slaven, M. Harper
• Journal: Annals of Work Exposures and Health
• Published: 2017;61(2):237-247
• Cited by: 2 articles, as counted by NIH iCite
• Read it: PubMed · Publisher · Free full text

Abstract

The negative binomial distribution is adopted for analyzing asbestos fiber counts so as to account for both the sampling errors in capturing only a finite number of fibers and the inevitable human variation in identifying and counting sampled fibers. A simple approximation to this distribution is developed for the derivation of quantiles and approximate confidence limits. The success of the approximation depends critically on the use of Stirling's expansion to sufficient order, on exact normalization of the approximating distribution, on reasonable perturbation of quantities from the normal distribution, and on accurately approximating sums by inverse-trapezoidal integration. Accuracy of the approximation developed is checked through simulation and also by comparison to traditional approximate confidence intervals in the specific case that the negative binomial distribution approaches the Poisson distribution. The resulting statistics are shown to relate directly to early research into the accuracy of asbestos sampling and analysis. Uncertainty in estimating mean asbestos fiber concentrations given only a single count is derived. Decision limits (limits of detection) and detection limits are considered for controlling false-positive and false-negative detection assertions and are compared to traditional limits computed assuming normal distributions.

Published by Oxford University Press on behalf of the British Occupational Hygiene Society 2017.

In plain English

This was a statistics methods paper, not a study of people or disease. The authors aimed to improve error bounds on asbestos fiber counts made under a microscope, which vary both because only a limited number of fibers are captured and because human counters differ. They developed a simple approximation to a statistical model called the negative binomial distribution and checked it with computer simulations. The simulations showed limited scatter and no evident bias in the confidence levels. The method gave limits consistent with a 1982 experiment by Ogden. They tabulated 95% confidence limits for single counts, assuming counting variability approaching 20% at large counts. A count of 10 gave limits of 5 to 21, and the authors called values below a count of 5 only suggestive. The authors also applied the method to the NIOSH Method 7400 blank-filter background of 2.5 fibers per square millimeter, assuming 20% counter variability and 100 fields (0.785 square millimeters). This gave a limit of detection of 7.7 per square millimeter for a signal with that background subtracted. The authors concluded this was almost twice the normal-distribution result.

We wrote this plain-English summary from the full article with the help of AI, and a second AI model checked each sentence against the article. It is not the authors' wording; the abstract and the article are their own account.

What the study did and found

• Design: Statistical methods study: development of an approximation to the negative binomial distribution, checked by computer simulation and compared with earlier published data
• Who was studied: No human subjects. Computer-simulated fiber counts (10,000 simulated values at each of a range of mean counts up to 30), plus previously published data: the Ogden (1982) Cricklewood counting experiment and blank-filter background counts from the development of NIOSH Method 7400
• Exposure: Airborne asbestos fiber counts made manually under a microscope, typically over 100 fields with a total area of 0.785 square millimeters; no specific fiber type analyzed in this study
• Main results:
  • In simulations, scatter around the intended confidence levels was strictly limited; at a counter variability of 20% and a mean count of 10, the upper confidence limit shifted by only about plus or minus 5%
  • At a counter variability of 20%, the method gave normalized limits of -1.5 and 1.8, which the authors found consistent with Ogden's published values of -1.5 and 2.0
  • Two-sided 95% confidence limits for a single count, assuming a relative standard deviation approaching 20% at large counts: a count of 10 gave limits of 5 to 21; a count of 100 gave 67 to 163
  • The limit of detection was 7.7 fibers per square millimeter for a background-subtracted signal from a single filter. The calculation used the NIOSH 7400 mean background of 2.5 per square millimeter, an assumed 20% large-count counter variability and 100 fields of 0.785 square millimeters. Used as the threshold, it gives a false-positive rate below 0.001
  • The limit of detection from the negative binomial distribution was almost twice the 4.5 per square millimeter obtained under normal-distribution assumptions
  • The detection limit (controlling false negatives) was calculated as 12 per square millimeter (about 10 counts in 0.785 square millimeters) at 80% confidence
• The authors' conclusion: The authors concluded that agreement with the earlier experiment supported the usefulness of the negative binomial distribution for fiber counts. They also concluded that limit-of-detection calculations based on the normal distribution differ significantly from those that account for the discrete nature of counting.
• Limitations the authors state:
  • The approximation is less accurate at higher counter variability
  • Confidence limits for counts below 5 are only suggestive
  • The 0.999 confidence level for the limit of detection may be misleading because the distribution of interfering non-asbestos fibers on filters is uncertain
  • The design of the experiment behind the NIOSH 7400 background variance is no longer documented, so the authors used an assumed 20% counter variability instead of that variance
  • When interfering fibers are present, the confidence limits apply to total fibers, not specifically asbestos fibers
  • It is unknown how the counter-variability figures used would differ by asbestos type

Topics

The National Library of Medicine indexes this study under subjects our site covers: Chrysotile.

Medical terms in this study, explained in our Lexicon: confidence interval.

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