Finding Design Space and a Reliable Operating Region Using a Multivariate Bayesian Approach with Experimental Design

The posterior predictive approach for multiple response surface optimization presented by Peterson [7] is used to identify a region of process operating conditions where all quality attributes of the product are highly likely to meet specifications. The approach consists of calculating the probability that future responses will meet specification over a multidimensional grid of operating conditions. Examples from the pharmaceutical industry are used to show how the method is applied to statistically designed experiments and the results are used to generate reliability surface plots. The approach supplements traditional analysis and optimization techniques with calculated values that capture the maturity of the process under development, and provide a useful figure of merit in the definition of Design Space [5]. Also considered is the distinction between determining a Design Space to meet the specifications of critical quality attributes (CQA's) [2] for the active pharmaceutical ingredient (API), and a reliable operating region (ROR) that also satisfies desirable manufacturing attributes, such as cost, yield, or throughput. A Bayesian posterior predictive approach offers benefits over traditional frequentist approaches to optimization. The traditional approaches, such as desirability functions or overlapping contours, do not account for model parameter uncertainty and the correlation of the responses at fixed operating conditions.