Probabilistic Design space determination in pharmaceutical product development: A Bayesian/latent variable approach

To find the design space (DS) of a pharmaceutical process, quantification of the “assurance of quality” for the product under development is required. In this study, latent‐variable modeling is combined with multivariate Bayesian regression to identify a subset of input combinations (process operating conditions and raw materials properties) within which the DS of the product will lie at a probability equal to, or greater than, an assigned threshold. Partial least‐squares regression is used to obtain a linear transformation between the original multidimensional input space and a low‐dimensional latent space. The input domain is then discretized on its lower dimensional representation and a Bayesian posterior predictive approach is used to quantify the probability that the critical quality attributes of the product will meet their specifications for each discretization point. The methodology is tested on two case studies taken from the literature, one of which involving experimental data. The ability of the proposed approach to obtain a probabilistic identification of the DS, while simultaneously reducing the computational burden for the discretization of the input domain and providing a simple graphical representation of the DS, is shown.