Quantitative Microbiology 1 (1999): 29±45
# 1999 Kluwer Academic Publishers, Manufactured in The Netherlands
Estimating the Antimicrobial Log Reduction:
Part 1. Quantitative Assays
TODD A. DeVRIES
Dept. of Statistical & Mathematical Sciences, Eli Lilly & Company, Indianapolis, IN 46285, U.S.A.
MARTIN A. HAMILTON
Center for Bio®lm Engineering & Dept. of Mathematical Sciences, Montana State University, Bozeman, MT
Received July 13, 1998; Accepted February 24, 1999
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 presenceaabsence 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.
Key words: antimicrobial, bioassay, count data, disinfectant, log reduction, statistical models
Laboratory assays are used to assess the ability of liquid chemicals to kill pathogenic
microorganisms, such as bacteria, spores, fungi, and viruses, that contaminate hard,
nonporous surfaces in hospitals, restaurants, the home, etc. Each standard assay is
conducted according to a protocol that clearly speci®es the microbial species and strain,
inoculum sizes, culture conditions, testing materials, and the carriers. The carriers are
small objects constructed of glass, stainless steel, or other nonporous material, designed
for ease of handling in the laboratory. They are inoculated with microorganisms to create
laboratory surrogates for contaminated surfaces. The standardized carrier assays are
designed to provide an inexpensive and reproducible laboratory assessment of each
disinfectant's activity under conditions similar to real world applications.
Governmental regulatory agencies review data from antimicrobial assays when deciding
whether a chemical formulation is suf®ciently effective to be registered as a germicide.