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

Abstract

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.