A Modern Approach to Stability Studies via Bayesian Linear Mixed Models Incorporating Auxiliary Effects

Miguel Cordero; Florian Meinfelder; Tobias Eilert

doi:10.1016/j.xphs.2024.02.020

A Modern Approach to Stability Studies via Bayesian Linear Mixed Models Incorporating Auxiliary Effects

J Pharm Sci. 2024 Feb 28:S0022-3549(24)00061-3. doi: 10.1016/j.xphs.2024.02.020. Online ahead of print.

Authors

Miguel Cordero¹, Florian Meinfelder¹, Tobias Eilert²

Affiliations

¹ Chair of Statistics and Econometrics, University of Bamberg, Feldkirchenstraße 21, D-96052 Bamberg.
² Boehringer Ingelheim Pharma GmbH & Co. KG, CMC Statistics BioPharma, Birkendorfer Straße 65, D-88397 Biberach an der Riß, Germany.

PMID: 38417792
DOI: 10.1016/j.xphs.2024.02.020

Abstract

In preparation to the launch of a pharmaceutical product, an estimate of its shelf life via stability testing is required by regulatory agencies. The ICH-Q1E guidance has been the worldwide reference to reach this objective, but in recent years several authors have criticized many of its aspects. To that end we discuss a complete Bayesian transcript of the ICH-Q1E, treating all the apparent shortcomings, while also addressing the presence of multiple batches using a linear mixed model (LMM) for proper shelf life prediction by explicitly modelling the batch-to-batch variability. This comprises a redefinition of the linear models proposed in the ICH-Q1E by suitable LMM counterparts, and a Bayesian analogue for model selection, which is more intuitive and remedies detrimental features of the ICH approach. In that context, a proper mathematical foundation of shelf life is provided that we use to investigate and mathematically compare the two available approaches to shelf life determination via shelf life distribution and batch distribution. The discussed method is then tested and evaluated using real data in comparison with the ICH-Q1E approach demonstrating their approximate equivalency for 6 batches. As a major objective, we extended the LMM with auxiliary fixed effects, here the concentration, which interconnect data sets allowing a prediction of shelf lives for concentrations lacking a sufficient number of batches. This establishes a novel approach to accelerate the speed to submission while retaining the patients' safety. Both case studies underline the inherent superiority of LMMs within a Bayesian framework regarding predictability and interpretability, and we hope that the relevant authorities will accept this approach in the future.

Keywords: Auxiliary effects; Batch distribution; Bayes factor; Bayesian borrowing; Bayesian modelling; ICH-Q1E; Linear mixed model; Model selection; Shelf life; Shelf life distribution; Stability study.