Estimating Shelf Life Through Tolerance Intervals Extended to Nonlinear Response Trends

Methods for estimating pharmaceutical shelf life based on tolerance intervals are proposed by Schwenke, et al. AAPS PharmSciTech. 2020;21:290, [1] where a critical quality attribute that follows a simple linear (straight line) response trend across storage time is presented as the traditional example. A random coefficient mixed linear regression model is used to characterize the between batch and within batch variation. These methods are further discussed for various stability study scenarios, number of stability batches, and levels of assumed risk in Schwenke, et al. AAPS PharmSciTech. 2021;22:273, [4] through a simulation study, again based on a critical quality attribute assuming a simple linear response. However, in practice, not all stability response profiles conveniently follow straight line or linear trends. The purpose of this paper is to extend the proposed tolerance interval and random coefficient mixed regression methods for estimating pharmaceutical shelf life to critical quality attributes that follow more complex stability response profiles. As an example, a nonlinear response is typically characterized by either an increasing or decreasing response, starting from an initial concentration, trending with storage time towards some limiting response or asymptote. Nonlinear responses cannot be statistically analyzed with linear model methods. Practical information supported by simulation results based on a pharmaceutical stability study are discussed to allow for appropriate statistical analyses and shelf life estimates through random coefficient mixed nonlinear regression and tolerance interval methods.