title: Confidence Intervals for Asbestos Fiber Counts: Approximate Negative Binomial Distribution.
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.
authors.affiliation: Consultant, 3904 Pocahontas Avenue, Cincinnati, OH 45227, USA.
authors.forename: David
authors.initials: D
authors.lastname: Bartley
authors.affiliation: Department of Biostatistics, Indiana University School of Medicine, 340 W 10th St #6200, Indianapolis, IN 46202, USA.
authors.forename: James
authors.initials: J
authors.lastname: Slaven
authors.affiliation: Health Effects Laboratory Division, Exposure Assessment Branch, National Institute for Occupational Safety and Health, 1095 Willowdale Rd MS-3030, Morgantown, WV 26505, USA.
authors.forename: Martin
authors.initials: M
authors.lastname: Harper
mesh_terms: D017632:Asbestos, Serpentine / Q000032:analysis*; D016010:Binomial Distribution; D016001:Confidence Intervals; D006801:Humans; D057230:Limit of Detection
chemical_list: D017632:Asbestos, Serpentine
keywords: asbestos; fiber counting quality control; negative binomial confidence