ANCOVA approach for shelf life analysis of stability study of multiple factor designs

For a traditional multiple batch stability design with no other factor, the conventional analysis is analysis of covariance (ANCOVA) modeling using F-tests based on type I sum of squares to determine whether the batches may be pooled for a common estimate of the linear regression line(s). In the last decade, many multiple factor designs were proposed in stability studies. With the objective of model selection, the generalization of the conventional ANCOVA model using type I sum of squares to designs with multiple factors requires a prespecified hierarchical pooling test ordering to determine whether any of the factors may be eliminated. Different shelf life estimates may be derived using different hierarchical pooling test orderings. On the other hand, setting the hierarchical ordering can be subjective and controversial. The stepwise modeling based on F-tests using type III sum of squares for model determination and factor elimination is proposed to eliminate such difficulties.

Significance levels for stability pooling test: a simulation study

Shelf life of a drug product is defined as the length of time under specific conditions of storage that the product will remain within specifications established to ensure its identity, strength, quality, and purity. The objective of an new drug application (NDA) stability study is to collect and evaluate the evidence in support of the sponsor-proposed shelf life. The proposed shelf life is supported when each batch of the drug products in the study has shelf life no shorter than the proposed shelf life. When the value of the batch mean changes linearly, sometimes batches of the same product may share the same slope or regression line. In practice, batches are pooled to have a common estimate of slope or regression line when there is no significant difference in slope or regression line. Such practice is often applied in pooling across levels of a design factor such as package or strength in a stability study designed with multiple factors. However, falsely pooling different slopes or intercepts may increase false positive rates on the decision of approval for the proposed shelf life. The proposed algorithm used with the simulation technique tries to reduce false pooling rates for testing slope or intercept differences in order to bring down the false positive rates on the decision of approval for the proposed shelf life to the prespecified Type-I error rate of 5 or 10%.

Overview of stability study designs

Stability requirements for the worldwide registration of pharmaceutical products have changed dramatically in the past few years. A series of guidelines on the design, conduct, and data analysis of stability studies of pharmaceuticals have been published by the International Conference on Harmonization (ICH); however, the statistical discussion on study design is limited. In this paper, stability designs including full, bracketing, and matrixing designs will be exemplified. The statistical aspects of these stability designs will be discussed in relation to the recent ICH guidelines. The statistical and regulatory considerations on the selection of stability design will also be presented. The stability study should be well designed so the shelf life of the drug product can be estimated with a high degree of accuracy and precision. Several commonly used criteria for design comparison will be presented. Finally, a case study is presented to illustrate the potential problems of an overreduced design from the statistical and regulatory perspectives.

Rank regression in stability analysis

Stability data are often collected to determine the shelf life of certain characteristics of a pharmaceutical product, for example, a drug's potency over time. Statistical approaches such as the linear regression models are considered as appropriate to analyze the stability data. However, most of these regression models in both theory and practice rely heavily on their underlying parametric assumptions, such as normality of the continuous characteristics or their transformations. In this article, we propose and study some rank-based regression procedures for the stability data when the linear regression models are semiparametric with unspecified error structure. Numerical studies including Monte Carlo simulations and practical example are demonstrated with the proposed procedures as well.