Nonlinear hierarchical modeling of experimental infection data.

In this paper, we propose a nonlinear hierarchical model (NLHM) for analyzing longitudinal experimental infection (EI) data. The NLHM offers several improvements over commonly used alternatives such as repeated measures analysis of variance (RM-ANOVA) and the linear mixed model (LMM). It enables comparison of relevant biological properties of the course of infection including peak intensity, duration and time to peak, rather than simply comparing mean responses at each observation time. We illustrate the practical benefits of this model and the insights it yields using data from experimental infection studies on equine arteritis virus. Finally, we demonstrate via simulation studies that the NLHM substantially reduces bias and improves the power to detect differences in relevant features of the infection response between two populations. For example, to detect a 20% difference in response duration between two groups (n=15) in which the peak time and peak intensity were identical, the RM-ANOVA test had a power of just 11%, and LMM a power of just 12%. By comparison, the nonlinear model we propose had a power of 58% in the same scenario, while controlling the Type I error rate better than the other two methods.