Design Space Definition Using a Variational Bayes' Approximation

The design space may be interpreted as the constrained region of the key manufacturing parameters space which provides assurance of quality of a drug given that manufacturing occurs in this region. The metric used to represent this assurance should not be deterministic, rather it should be stated in probabilistic terms. In this work, we report on the use of Bayesian methods to develop a suitable risk metric based on statistical models of the manufacturing processes and product properties. The Bayesian inference is carried out to determine the posterior distribution of the probability of the product meeting quality specifications. Here, we propose an alternative optimization based procedure, the variational Bayes’ approximation, to obtain the posterior distribution. A sequential methodology is proposed to deal with non-linear models and the consideration of covariance. The results are compared to the widely used but computationally intensive Markov Chain Monte Carlo method. The proposed approached is illustrated with information drawn from a QbD study on Gabapentin.