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Abstract
Implicit in ICH Q1E (International Conference on Harmonization [ICH], Citation2003b) are definitions of batch shelf life (the time the batch mean crosses the acceptance limit) and product shelf life (the minimum batch shelf life). The distribution of batch means over time projects to a distribution of batch shelf lives on the x-axis. Assuming multivariate normality, shelf life is the ratio of correlated Gaussian variables. Using Hinkley (Citation1969), we describe the relationship between quantiles of the distributions of batch shelf lives and batch means. Exploiting this relationship, a linear mixed model is used to estimate a target quantile of batch shelf lives to address the ICH objective.
ACKNOWLEDGMENTS
Funding for this research was provided by the Product Quality Research Institute (PQRI) through the PQRI Stability Shelf Life Working Group. PQRI, located in Arlington, VA, is a nonprofit consortium of organizations working together to generate and share timely, relevant, and impactful information that advances drug product quality and development. The authors thank all the members of the PQRI Stability Shelf Life Working Group for providing resources, guidance, ideas, and advice that greatly contributed to this research. This research was presented to the faculty of the Graduate College at the University of Nebraska–Lincoln in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Statistics for Michelle Quinlan, June 2010.