Reflections on the use of robust and least-squares non-linear regression to model challenge tests conducted in/on food products

In this research, we question the straight-forward use of the classical sum of squared error criterion for identifying the typical parameters of a primary model (like growth rate μmax and lag time λ) when applied to growth curves obtained in and on food products. Firstly, we base our reflections on 62 Listeria monocytogenes laboratory challenge tests collected in various environments (broth, crushed cold-smoked salmon, and surface of cold-smoked salmon slices). Whereas growth data in broth resulted in residual values consistent with a Gaussian distribution, growth data in the crushed product and even more on the surface of slices appeared different. Secondly, we propose the use of an alternative so-called robust non-linear regression method suitable when experimental error is non-normally distributed, which seems, according to this research, typical for microbial challenge tests in/on food products, and which lead to apparent outliers or leverage points in the experimental data. Properties of the robust regression procedure are illustrated on simulated data first, whereafter its use on the considered challenge tests is illustrated. To conclude, reflections on the assumptions and related realism underlying challenge tests and recommendations for fitting growth curves obtained in and on food products are presented.