Hierarchical Bayesian linear mixed model to estimate variability in the thermal inactivation parameters for Listeria species

Abstract

A total of 476 D-values associated with 76 strains of Listeria spp. in liquid media were obtained from 27 scientific articles. Meta-analysis was carried out using hierarchical Bayesian models to assess variability, predict the D-, and estimate the $z_T$-, and $z_{pH}$-values for Listeria spp. across a range of temperatures (55–70 °C) and pH values (3–8 units). Different hypotheses regarding variability between strains or studies in each model correspond to different hierarchical assumptions about the inactivation parameters. The models produced were compared based on their predictive ability, Bayes-R² and widely applicable information criterion (WAIC) values. A hierarchical model that considered random effects due to both strain and study effects on the thermal inactivation parameters was determined to be the “best” model and was subsequently used to estimate the posterior distributions for the D-, $z_T$-, and $z_{pH}$-values. The variability introduced in the parameters due to differences between studies was higher than that of variability between strains. The parameters estimated using the model for different strains of Listeria species may be applicable for processing aqueous foods such as milk and liquid products such as sauces and gravies across a temperature range of 55–70 °C and pH values of 3–8 units.