Stability analysis using mixed models: A critique of tolerance interval methods and a probabilistic solution.

Recently, tolerance interval approaches to the calculation of a shelf life of a drug product have been proposed in the literature. These address the belief that shelf life should be related to control of a certain proportion of batches being out of specification. We question the appropriateness of the tolerance interval approach. Our concerns relate to the computational challenges and practical interpretations of the method. We provide an alternative Bayesian approach, which directly controls the desired proportion of batches falling out of specification assuming a controlled manufacturing process. The approach has an intuitive interpretation and posterior distributions are straightforward to compute. If prior information on the fixed and random parameters is available, a Bayesian approach can provide additional benefits both to the company and the consumer. It also avoids many of the computational challenges with the tolerance interval methodology.

A Bayesian Approach to Kinetic Modeling of Accelerated Stability Studies and Shelf Life Determination.

Kinetic modeling of accelerated stability data serves an important purpose in the development of pharmaceutical products, providing support for shelf life claims and expediting the path to clinical implementation. In this context, a Bayesian kinetic modeling framework is considered, accommodating different types of nonlinear kinetics with temperature and humidity dependent rates of degradation and accounting for the humidity conditions within the packaging to predict the shelf life. In comparison to kinetic modeling based on nonlinear least-squares regression, the Bayesian approach allows for interpretable posterior inference, flexible error modeling and the opportunity to include prior information based on historical data or expert knowledge. While both frameworks perform comparably for high-quality data from well-designed studies, the Bayesian approach provides additional robustness when the data are sparse or of limited quality. This is illustrated by modeling accelerated stability data from two solid dosage forms and is further examined by means of artificial data subsets and simulated data.

Dissolution curve comparisons through the F(2) parameter, a Bayesian extension of the f(2) statistic.

Dissolution (or in vitro release) studies constitute an important aspect of pharmaceutical drug development. One important use of such studies is for justifying a biowaiver for post-approval changes which requires establishing equivalence between the new and old product. We propose a statistically rigorous modeling approach for this purpose based on the estimation of what we refer to as the F2 parameter, an extension of the commonly used f2 statistic. A Bayesian test procedure is proposed in relation to a set of composite hypotheses that capture the similarity requirement on the absolute mean differences between test and reference dissolution profiles. Several examples are provided to illustrate the application. Results of our simulation study comparing the performance of f2 and the proposed method show that our Bayesian approach is comparable to or in many cases superior to the f2 statistic as a decision rule. Further useful extensions of the method, such as the use of continuous-time dissolution modeling, are considered.

DISSOLUTION PROFILE SIMILARITY ANALYSES-STATISTICAL PRINCIPLES, METHODS AND CONSIDERATIONS.

The pharmaceutical industry and regulatory agencies rely on dissolution similarity testing to make critical product decisions as part of drug product life cycle management. Accordingly, the application of mathematical approaches to evaluate dissolution profile similarity is described in regulatory guidance with the emphasis given to the similarity factor f2 with little discussion of alternative methods. In an effort to highlight current practices to assess dissolution profile similarity and to strive toward global harmonization, a workshop entitled "In Vitro Dissolution Similarity Assessment in Support of Drug Product Quality: What, How, When" was held on May 21-22, 2019 at the University of Maryland, Baltimore. This manuscript provides in-depth discussion of the mathematical principles of the model-independent statistical methods for dissolution profile similarity analyses presented in the workshop. Deeper understanding of the testing objective and statistical properties of the available statistical methods is essential to identify methods which are appropriate for application in practice. A decision tree is provided to aid in the selection of an appropriate statistical method based on the underlying characteristics of the drug product. Finally, the design of dissolution profile studies is addressed regarding analytical and statistical recommendations to sufficiently power the study. This includes a detailed discussion on evaluation of dissolution profile data for which several batches per reference and/or test product are available.

Block designs in method transfer experiments.

Method transfer is a part of the pharmaceutical development process in which an analytical (chemical) procedure developed in one laboratory (typically the research laboratory) is about to be adopted by one or more recipient laboratories (production or commercial operations). The objective is to show that the recipient laboratory is capable of performing the procedure in an acceptable manner. In the course of carrying out a method transfer, other questions may arise related to fixed or random factors of interest, such as analyst, apparatus, batch, supplier of analytical reagents, and so forth. Estimates of reproducibility and repeatability may also be of interest. This article focuses on the application of various block designs that have been found useful in the comprehensive study of method transfer beyond the laboratory effect alone. An equivalence approach to the comparison of laboratories can still be carried out on either the least squares means or subject-specific means of the laboratories to justify a method transfer or to compare analytical methods.

Serially balanced designs for two sets of treatments.

Serially balanced designs are useful in applications in which repeated measurements of multiple samples (treatments) are being taken according to an ordered sequence. The design permits the estimation of direct treatment and carryover effects. When the samples comprise two groups, where the sequence requires samples from one group to be separated by samples from another group (e.g., when a wash step has to be performed between treated samples), then the sequence has to be arranged in such a way as to accommodate this requirement. The solution to the construction of such a serially balanced sequence is given according to the construction method given by Altan et al. (2004) for the first group of treatments in combination with the use of an F-square to dictate placement of the second group of treatments.

Double bootstrapping a tolerance limit.

We consider the problem of constructing tolerance limits in the context of a one-way random effects model The usual parametric method for calculating tolerance intervals is based on the normality assumption. However, in practice, we frequently observe nonnormally distributed data. We propose the use of the double bootstrap (or nested bootstrap) method to estimate tolerance limits, which allows us to relax the normality assumption.

A note on kinetic modeling of stability data and implications on pooling.

In this note we discuss the relationship between the underlying kinetic model and the statistical (or analytic) model used to study degradation. For small degradation rates, the zeroth, first, and second order statistical models give approximately the same fits and predictions on either the original assay scale or the percent of label claim scale. However, It is shown that the zeroth and second order statistical models artificially induce differential degradation rates across strengths when the percent of label claim response data are analyzed and poolability is not allowed across strengths. The first order model is free of this problem when the true degradation kinetics are first order. We make some recommendations in pooling stability data across strengths.