To pool or not to pool: That is the question in microbial kinetics

Abstract

Variation observed in heat inactivation of Salmonella strains (data from Combase) was characterized using multilevel modeling with two case studies. One study concerned repetitions at one temperature, the other concerned isothermal experiments at various temperatures. Multilevel models characterize variation at various levels and handle dependencies in the data. The Weibull model was applied using Bayesian regression. The research question was how parameters varied with experimental conditions and how data can best be analyzed: no pooling (each experiment analyzed separately), complete pooling (all data analyzed together) or partial pooling (connecting the experiments while allowing for variation between experiments).In the first case study, level 1 consisted of the measurements, level 2 of the group of repetitions. While variation in the initial number parameter was low (set by the researchers), the Weibull shape factor varied for each repetition from 0.58–1.44, and the rate parameter from 0.006–0.074 h. With partial pooling variation was much less, with complete pooling variation was strongly underestimated.In the second case study, level 1 consisted of the measurements, level 2 of the group of repetitions per temperature experiment, level 3 of the cluster of various temperature experiments. The research question was how temperature affected the Weibull parameters. Variation in initial numbers was low (set by the researchers), the rate parameter was obviously affected by temperature, the estimate of the shape parameter depended on how the data were analyzed. With partial pooling, and one-step global modeling with a Bigelow-type model for the rate parameter, shape parameter variation was minimal. Model comparison based on prediction capacity of the various models was explored.The probability distribution of calculated decimal reduction times was much narrower using multilevel global modeling compared to the usual single level two-step approach. Multilevel modeling of microbial heat inactivation appears to be a suitable and powerful method to characterize and quantify variation at various levels. It handles possible dependencies in the data, and yields unbiased parameter estimates. The answer on the question “to pool or not to pool” depends on the goal of modeling, but if the goal is prediction, then partial pooling using multilevel modeling is the answer, provided that the experimental data allow that.