Sample Size Formulae for Estimating the True Arithmetic or Geometric Mean of Lognormal Exposure Distributions

Formulae are presented for calculating the approximate sample size needed to estimate the true arithmetic mean or true geometric mean exposure for an exposure group to within a specified accuracy (±x% of the true arithmetic or geometric mean) with a specified level of confidence. These formulae are intended for use in prospective or cross-sectional occupational health studies, or when building an exposure database for use in assessing long-term changes in worker health status. They are applicable where the investigator is satisfied that the distribution of exposures within a group can be approximated by a lognormal distribution. The formulae were validated by computer simulation and show that large sample sizes are required when the existing parameter estimates were derived from a limited number of prior measurements and/or the true exposure distribution has a large geometric standard deviation. When summed across all exposure groups, an unreasonable total sample size may result. The total sample burden can be reduced in several ways: (1) A pilot study should be used to provide reasonably precise initial estimates of the distribution parameters for each exposure group. This may require 20 or more measurements per group. (2) Workers should be grouped into exposure groups where the group geometric standard deviation is two or less. (3) The desired accuracy should be kept at a reasonable level, perhaps between 20 and 30% of the true parameter. Accuracy levels less than 20% can result in large total sample size requirements.