One- and two-stage Arrhenius models for pharmaceutical shelf life prediction

One of the most challenging aspects of the pharmaceutical development is the demonstration and estimation of chemical stability. It is imperative that pharmaceutical products be stable for two or more years. Long-term stability studies are required to support such shelf life claim at registration. However, during drug development to facilitate formulation and dosage form selection, an accelerated stability study with stressed storage condition is preferred to quickly obtain a good prediction of shelf life under ambient storage conditions. Such a prediction typically uses Arrhenius equation that describes relationship between degradation rate and temperature (and humidity). Existing methods usually rely on the assumption of normality of the errors. In addition, shelf life projection is usually based on confidence band of a regression line. However, the coverage probability of a method is often overlooked or under-reported. In this paper, we introduce two nonparametric bootstrap procedures for shelf life estimation based on accelerated stability testing, and compare them with a one-stage nonlinear Arrhenius prediction model. Our simulation results demonstrate that one-stage nonlinear Arrhenius method has significant lower coverage than nominal levels. Our bootstrap method gave better coverage and led to a shelf life prediction closer to that based on long-term stability data.