title: Counting rules for estimating concentrations of long asbestos fibers.
abstract: Mounting evidence that long asbestos fibers (e.g. >20 or even 40 μm) pose the greatest cancer risk underscores the need for accurate measurement of concentrations of such fibers. These fiber lengths are of the same order of magnitude as the size of openings in the grids (typically ≈90 μm per side) used to analyze asbestos samples by transmission electron microscopy. This means that a substantial proportion of long fibers will cross the edge of a grid opening (GO) and therefore not be completely visible. Counting rules generally deal with such fibers by assigning a length equal to twice the visible length. Using both theoretical and simulation methods, we show that this doubling rule introduces bias into estimates of fiber concentrations and the amount of bias increases with fiber length. We investigate an alternative counting rule that counts only fibers that lie completely within a GO and weights those fibers by the reciprocal of the probability that a fiber of that length lies totally within a GO. This approach does not have the bias inherent in the doubling rule and is essentially unbiased if the stopping rule specifies a fixed number of GOs to be scanned. However, a stopping rule based on successively scanning GOs until a fixed number of fibers have been counted will introduce bias into any counting method, although this bias may typically not be large enough to be of practical concern. We recommend use of the weighted approach as a supplement to use of the doubling rule when estimating concentrations of long fibers, irrespective of the stopping rule employed.
authors.affiliation: Department of Mathematics and Statistics, Louisiana Tech University, Ruston, 71273, USA. kennycrump@email.com
authors.forename: Kenny S
authors.initials: KS
authors.lastname: Crump
authors.forename: D Wayne
authors.initials: DW
authors.lastname: Berman
mesh_terms: D000393:Air Pollutants / Q000032:analysis* / Q000737:chemistry; D001194:Asbestos / Q000032:analysis* / Q000737:chemistry; D015982:Bias; D004781:Environmental Exposure / Q000032:analysis; D004784:Environmental Monitoring / Q000295:instrumentation / Q000379:methods*; D005374:Filtration / Q000295:instrumentation / Q000379:methods; D006801:Humans; D046529:Microscopy, Electron, Transmission; D019016:Mineral Fibers; D008962:Models, Theoretical; D010316:Particle Size
chemical_list: D000393:Air Pollutants; D019016:Mineral Fibers; D001194:Asbestos