Determining sample size and a passing criterion for respirator fit-test panels

Few studies have proposed methods for sample size determination and specification of passing criterion (e.g., number needed to pass from a given size panel) for respirator fit-tests. One approach is to account for between- and within- subject variability, and thus take full advantage of the multiple donning measurements within subject, using a random effects model. The corresponding sample size calculation, however, may be difficult to implement in practice, as it depends on the model-specific and test panel-specific variance estimates, and thus does not yield a single sample size or specific cutoff for number needed to pass. A simple binomial approach is therefore proposed to simultaneously determine both the required sample size and the optimal cutoff for the number of subjects needed to achieve a passing result. The method essentially conducts a global search of the type I and type II errors under different null and alternative hypotheses, across the range of possible sample sizes, to find the lowest sample size which yields at least one cutoff satisfying, or approximately satisfying all pre-determined limits for the different error rates. Benchmark testing of 98 respirators (conducted by the National Institute for Occupational Safety and Health) is used to illustrate the binomial approach and show how sample size estimates from the random effects model can vary substantially depending on estimated variance components. For the binomial approach, probability calculations show that a sample size of 35 to 40 yields acceptable error rates under different null and alternative hypotheses. For the random effects model, the required sample sizes are generally smaller, but can vary substantially based on the estimate variance components. Overall, despite some limitations, the binomial approach represents a highly practical approach with reasonable statistical properties.