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Estimating Shelf Life Through Tolerance Intervals Extended to Nonlinear Response Trends

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Abstract

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.

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References

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Acknowledgements

This work is a direct result of the authors’ discussions as cofounders, original members, and chairs of the Product Quality Research Institute (PQRI) Stability Shelf Life Working Group which was established in 2006 and disbanded in late 2019. The authors wish to thank all past colleagues of the Working Group over the years and hope that the discussions in stability studies and shelf life estimation will continue. The authors thank the reviewers of our past PharmSciTech shelf life papers who encouraged the writing of this paper through their comments. The authors also thank the reviewers of this paper who suggested edits that kept this paper focused.

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Authors and Affiliations

  1. Applied Research Consultants, LLC, 119 Town Farm Road, New Milford, Connecticut, 06776-3718, USA

    James Schwenke

  2. Statistics, University of Nebraska-Lincoln, Lincoln, Nebraska, USA

    Walter Stroup

  3. Early Development Biostatistics, Novartis, East Hanover, New Jersey, USA

    Michelle Quinlan

  4. RA CMC, Novartis, East Hanover, New Jersey, USA

    Patrick Forenzo

Authors
  1. James Schwenke
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  2. Walter Stroup
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  3. Michelle Quinlan
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  4. Patrick Forenzo
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by all authors. The first draft of the manuscript was written by James Schwenke, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to James Schwenke.

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Schwenke, J., Stroup, W., Quinlan, M. et al. Estimating Shelf Life Through Tolerance Intervals Extended to Nonlinear Response Trends. AAPS PharmSciTech 24, 80 (2023). https://doi.org/10.1208/s12249-023-02532-9

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  • DOI: https://doi.org/10.1208/s12249-023-02532-9

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