A Bayesian Approach to Pharmaceutical Product Quality Risk Quantification

The FDA’s Quality by Design initiative and associated design space construct (ICH, 2009), have stimulated the use of quantitative methods, mathematical and statistical models, and designed experiments in the process of drug development and manufacture. For a given drug product, the design space may be interpreted as the constrained region of the manufacturing operating variable space within which assurance can be provided that drug product quality specifications will be met. It is now understood, at least conceptually, that this assurance is not deterministic, rather it must be stated in probabilistic terms. In this paper, we report on the use of Bayesian methods to develop a suitable risk metric based on both mathematical and statistical models of the manufacturing processes and product properties. The Bayesian estimation is carried out to determine the joint posterior distribution of the probability of the product meeting quality specifications. The computations are executed using a novel Variational Bayes approximation. In this paper the direct computational approach using this approximation is compared to the widely used but computationally very intensive Markov Chain Monte Carlo method. The approach is illustrated using experimental data and models drawn from a recent QbD study on the drug gabapentin in which the authors were participants.