Estimating the antimicrobial log reduction: part 2. presence/absence assays

Abstract

This is part 2 of a pair of papers on antimicrobial assays conducted to estimate the log reduction (LR), in the density of viable microbes, attributable to the germicide. Two alternative de®nitions of LR were de®ned in part 1, one based on the mean of the log-transformed densities; the other is based on the logarithm of the mean of densities. In this paper, we evaluate statistical methods for estimating LR from an antimicrobial assay in which the responses are presence=absence observations at each dilution in a series of dilutions. We provide a model for the presence=absence data, and, for each de®nition of LR, we derive the maximum likelihood estimator (mle). Using computer simulation methods, we compare the mle to several alternative estimators, including an estimator based on averaging the log-transformed most probable number (mpn) values. Standard error formulas for the estimators are also derived and evaluated using computer simulations. This investigation results in the following recommendations. If the parameter of interest is based on the mean of log-transformed densities, then the results favor use of the log-transformed mpn method. If, however, the parameter of interest is based on the logarithm of the mean of densities, then the results show that the mle should be used.