The impact of experiment design on the parameter estimation of cardinal parameter models in predictive microbiology

In predictive food microbiology, cardinal parameter models are often applied to describe the effect of temperature, pH and/or water activity on the microbial growth rate. To identify the model parameters, full factorial designs are often used, in spite of the high experimental burden and cost related to this method.In this work, the impact of the selected experimental scheme on the estimation of the parameters of the cardinal model describing the effect of temperature, pH and/or water activity has been evaluated. In a first step, identification of a simple model describing only the effect of temperature, pH or water activity was considered. The comparison of an equidistant design and a D-optimal (based) design showed that the latter, which is based on the model's sensitivity functions, yields more realistic parameter estimates than the typical equidistant design. By selecting the experimental levels based on the sensitivity functions, a more realistic description of the behavior around optimal conditions can be obtained.In the second step, focus was on the efficient and accurate estimation of the ten parameters of the extended cardinal model that describes the combined effect of temperature, pH and water activity on the microbial growth rate. Again, equidistant level selection is compared to a D-optimal (based) experimental design. In addition, a full factorial and a Latin-square approach are evaluated. From the simulation case studies presented, it can be stated that all parameters can be equally well defined from an equidistant design as from a D-optimal-based design. In addition, reducing the experimental load by constructing a Latin-square design does not hamper the parameter estimation procedure. This work confirms the observation of a previous study, i.e., for complex cases a Latin-square design is an attractive alternative for a full factorial design as it yields equally accurate and reliable parameter estimates while reducing the experimental workload.