Analysis of Design of Experiments with Dynamic Responses

Multivariate understanding offers information that is critical to the successful evaluation of risk within a pharmaceutical process. A common means to acquire such data in the absence of detailed prior knowledge is a design of experiments (DoE). A significant challenge in the implementation of conventional DoE methodology is the analysis of processes with transient responses. A large number of processes in the pharmaceutical industry are described by kinetic processes which results in severe difficulties in the interpretation of the DoE analysis. In this paper we describe a workflow utilizing classic DoE practices, data visualization, and techniques extracted from the larger field of machine learning to facilitate the interpretation of DoE results in process development. The resulting analysis is appropriate for use in surveying the knowledge space for a chemical reaction and identifying areas of risk that merit verification. For clarity the workflow is described using a numerical solution to a well-defined reaction network with specified kinetic responses. Case studies are subsequently presented from the development of two late-stage API processes.