Application of Robust Statistical Optimal Designs for a Growth Rate Model in Predictive Food Microbiology

Several statistical predictive models have been used in the food microbiology \u85eld in recent years to describe the growth or the inactivation of bacterial populations. These dynamic primary models (PMs) are nonlinear relative to their parameters. In addition, these parameters can themselves be modelled by nonlinear secondary models (SMs) as functions of environmental factors (EFs) such as temperature, pH, water activity, nitrites and phenol concentrations, etc. For example, the mumax parameter (representing the maximum growth rate of the PMs) can be modelled by several SMs. Typically, one e ¢ cient class of SMs deals with the nonlinear interactions between the EFs. A major objective for the microbiology community is to have the model that will lead to the best parameter estimates for the purpose of ensuring food safety, notably the minimal temperature and pH levels for which the growth of bacterial populations start. However, it remains di ¢ cult to obtain adequately accurate estimates because of the high variability of microbiological data. Obviously, some optimal experiments must be conducted in order to reach this objective. In this paper, for a published speci\u85c model, we propose an experimental strategy based on the use of some local and robust statistical optimal designs, followed by computer simulations, to compare the di¤erent designs. Key Words: D and X-optimal designs, bayesian D and X-optimal designs, accu-rate parameter estimation, food safety. 1