A generalized modified-chi2 analysis of categorical bacteria survival data from a complex dilution experiment

A well-known method of estimation for the density of bacteria in a sample solution is the most probable number (MPN) procedure. This paper considers the change in density through time of bacteria populations which are undergoing extinction. The MPN with its estimated variance for a fixed time point is a basic module of these investigations and is treated as a general implicit function of the cell proportions in linear categorical data analysis. These quantities are then used to fit exponential decay models over time by weighted least squares. When such models are supported by the data, comparisons of decay rates between populations under possibly different experimental conditions can be undertaken. This methodology is illustrated with an example pertaining to the survival experience of Leptospira autumnalis.