Nonlinear regression technique to estimate kinetic parameters and confidence intervals in unsteady-state conduction-heated foods

Due to difficulty in computing, confidence intervals (CIs) for kinetic parameters and the predicted dependent variable (Y) in nonlinear models are often not reported. The purpose of this work was to present a straightforward method to calculate asymptotic CIs for kinetic parameters and the associated Y variable for nonisothermal survivor or retention curves. The novelty of this work was that (1) confidence bands (CBs) and prediction bands (PBs) for predicted Y (microbial survival ratio or nutrient retention) were computed along with CIs for the parameters (using Matlab®), and (2) confidence regions for the parameters were computed by an iterative method. Both the k–E and the D–z model were used. Three case studies were used. Kinetic parameters for microbial death (Cases 1 and 2) in an unsteady-state conduction-heated canned food and for thiamin concentration (Case 3) were estimated using a nonlinear regression technique. Upper 95% prediction bands gave a more conservative (safer) limit than the Y value predicted by the model, up to a 0.84 log difference. Given the availability and ease of use of nonlinear regression software, researchers can consider using the proposed method as a template for kinetic parameter estimation, confidence interval, and confidence region computation. These data are essential for accurate estimates of food safety.