Estimating Shelf Life Through Tolerance Intervals
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Research Article Estimating Shelf Life Through Tolerance Intervals James Schwenke,1,5 Michelle Quinlan,2 Walter Stroup,3 and Patrick Forenzo4
Received 1 July 2020; accepted 21 August 2020 Abstract.
This paper is a continuation of the research published by the Stability Shelf Life Working Group as chartered under the Product Quality Research Institute. The Working Group was formed in 2006 and disbanded in late 2019. Following the philosophy presented by the Working Group on how to characterize the stability shelf life paradigm (Capen et al., 2012), shelf life is estimated here in terms of defining risk as a specified proportion of the pharmaceutical stability distribution of interest being out of specification. Shelf life can be defined for the batch mean distribution for regulatory issues, as well as for the product distributions for patient interests. Estimates of shelf life are proposed corresponding to each stability distribution through the use of statistical tolerance intervals. Appropriate estimates of the between-batch and within-batch variance components are obtained through a random coefficient mixed regression model analysis based on the best fit to batch stability response data. Tolerance interval estimates are computed as part of the mixed model analysis and computed directly using the statistical definition of the stability distributions. A proposed rationale is offered on how to select an appropriate proportion allowed out of specification to define a meaningful shelf life. Examples of the proposed shelf life estimates are presented using industry stability batch data. For each example, the traditional ICH shelf life estimate is given for comparison. KEY WORDS: stability analysis; shelf life estimation; random coefficient regression; tolerance interval.
INTRODUCTION A common mistake made in discussions on estimating the shelf life of a pharmaceutical product is to assume only one generic error term in the statistical regression model used to characterize the stability study batch results. For example, in ICH guidance Q1A(R2) (1) and Q1E (2), a simple linear regression response model with one residual error term is assumed to characterize multiple batch data in a stability study. The assumed assumption is that batch differences are a quantifiable effect in the stability study, versus a random component of the manufacturing process as discussed in Stroup et al. (3). This approach dictates that the one residual error variance component is estimated primarily or exclusively by the within-batch or residual variation in the observed data, depending on the structure of the system of regression equations used to characterize batch responses. Following ICH guidance, the ideal stability study response is 1
Applied Research Consultants, LLC, 119 Town Farm Road, New Milford, Connecticut 06776, USA. 2 Early Development Biostatistics, Novartis, East Hanover, New Jersey, USA. 3 Statistics, University of Nebraska-Lincoln, Lincoln, Nebraska, USA. 4 RA CMC Team, Novartis, East Hanover, New Jersey, USA. 5 To whom correspondenc
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