Sequential Model-Based A- and V-Optimal Design of Experiments for Building Fundamental Models of Pharmaceutical Production Processes

Abstract

Sequential model-based A- and V-optimal experimental designs are known to be effective for maximizing the information content of data, leading to reliable parameter estimates and model predictions. A- and V-optimal designs require inversion of the Fisher Information Matrix (FIM), which may be noninvertible especially for fundamental models with many parameters. In this study, two different methodologies for selecting sequential approximately A- and V-optimal experiments are compared for situations where the FIM is noninvertible. The first approach, called Leave Out (LO) approach, finds and leaves out problematic parameters that make the FIM noninvertible and the second approach, called Pseudoinverse (PI) approach, uses a Moore-Penrose pseudoinverse of the FIM. Comparisons are carried out using a Michaelis Menten reaction dynamic model for production of a pharmaceutical agent. Monte Carlo simulations indicate, for both A- and V-optimal situations, that designed experiments using the LO approach are superior to designs obtained by the PI approach.