Calculating the limit of detection for a dilution series

Microbial samples are often serially diluted to estimate the number of microbes in a sample, whether as colony-forming units of bacteria or algae, plaque forming units of viruses, or cells under a microscope. There are at least three possible definitions for the limit of detection (LOD) for dilution series counts in microbiology. The statistical definition that we explore is that the LOD is the number of microbes in a sample that can be detected with high probability (commonly 0.95). Our approach extends results from the field of chemistry using the negative binomial distribution that overcomes the simplistic assumption that counts are Poisson. The LOD is a function of statistical power (one minus the rate of false negatives), the amount of overdispersion compared to Poisson counts, the lowest countable dilution, the volume plated, and the number of independent samples. We illustrate our methods using a data set from Pseudomonas aeruginosa biofilms. The techniques presented here can be applied to determine the LOD for any counting process in any field of science whenever only zero counts are observed. We define the LOD when counting microbes from dilution experiments. The practical and accessible calculation of the LOD will allow for a more confident accounting of how many microbes can be detected in a sample.