Inference and sample size calculation in the fit assessment of filtering facepiece respirators

Filtering facepiece respirators have recently been cleared by the U.S. Food and Drug Administration (FDA) for use by the general public in public health medical emergencies such as pandemic influenza. In the fit assessment of these devices it is important to distinguish between the two sources of variability: population heterogeneity and random fluctuations over repeated donnings. The FDA Special Controls Guidance Document (SCGD) which describes these devices and their evaluation, recommends that the fit performance of a filtering facepiece respirator be evaluated in terms of the proportion of users who will receive a specified level of protection 95% of the time. A point estimator of this proportion is easily obtained under an analysis of variance model, and the SCGD suggests bootstrap as one possible approach to interval estimation. This paper describes a closed-form procedure to obtain confidence intervals and provides sample size formulas. Simulation results suggest that the proposed procedure performs well in realistic settings and compares favorably to two simple bootstrap procedures.