Critical comparison of statistical methods for quantifying variability and uncertainty of microbial responses from experimental data

Variability and uncertainty are important factors for quantitative microbiological risk assessment (QMRA). In this context, variability refers to inherent sources of variation, whereas uncertainty refers to imprecise knowledge or lack of it. In this work we compare three statistical methods to estimate variability in the kinetic parameters of microbial populations: mixed-effect models, multilevel Bayesian models, and a simplified algebraic method previously suggested. We use two case studies that analyse the influence of three levels of variability: (1) between-strain variability (different strains of the same species), (2) within-strain variability (biologically independent reproductions of the same strain) and, at the most nested level, (3) experimental variability (species independent technical lab variability resulting in uncertainty about the population characteristic of interest) on the growth and inactivation of Listeria monocytogenes. We demonstrate that the algebraic method, although relatively easy to use, overestimates the contribution of between-strain and within-strain variability due to the propagation of experimental variability in the nested experimental design. The magnitude of the bias is proportional to the variance of the lower levels and inversely proportional to the number of repetitions. This bias was very relevant in the case study related to growth, whereas for the case study on inactivation the resulting insights in variability were practically independent of the method used. The mixed-effects model and the multilevel Bayesian models calculate unbiased estimates for all levels of variability in all the cases tested. Consequently, we recommend using the algebraic method for initial screenings due to its simplicity. However, to obtain parameter estimates for QMRA, the more complex methods should generally be used to obtain unbiased estimates