Estimating the antimicrobial log reduction: part 1. quantitative assays

Abstract

In quantitative antimicrobial assays, the responses are counts of viable microbes in two treatment groups. One group is treated with a chemical germicide and the other group is control, treated with an inactive chemical. This is part 1 of a pair of papers that pertain to assays that estimate the log reduction (LR), in the density of viable microbes, attributable to the germicide treatment (part 2 is concerned with presence=absence responses). Such assays are used by producers, consumers, and regulatory agencies to assess the ef®cacy of liquid germicides. We de®ne and compare the two different mathematical formulations for LR that are commonly used in practice when there are replicate density measurements. One LR parameter is based on the mean of the log-transformed densities; the other is based on the logarithm of the mean of densities. We build a statistical model relating microbial count data to the LR parameters, derive maximum likelihood and method of moments estimators for each LR parameter, and compare the estimators according to both their asymptotic characteristics and the results of a simulation study utilizing realistic sample sizes. Standard error formulas for the estimators are derived, and they are evaluated via simulation studies. The results of this investigation lead us to recommend the method of moments estimator, regardless of which de®nition of LR is chosen.