Analysis of Design of Experiments with Dynamic Responses

Abstract

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.

Using prior parameter knowledge in model‐based design of experiments for pharmaceutical production

“…Especially in pharmaceutical industries, models are important for quality by design and development of continuous manufacturing processes, which are becoming more widespread 3‐5 . Mathematical models for pharmaceutical product development can be either empirical or mechanistic 5‐7 . Although empirical models are commonly used for pharmaceutical processes, they cannot reliably predict the system behavior outside the range of operating conditions used for model development 8 .…”

“…While Bayesian MBDoE explicitly uses prior parameter information for designing new experiments, the LO MBDoE approach implicitly incorporates prior parameter information using appropriate scaling factors. We use the pharmaceutical case study of Domagalski et al, which is of interest to our industrial sponsor 6,25 . The associated dynamic model uses Michaelis–Menten kinetics and enzyme‐catalyzed reactions to describe the production of a pharmaceutical agent 59 .…”

From dynamic response surface models to the identification of the reaction stoichiometry in a complex pharmaceutical case study

“…The limitation of the RSM model to appropriately represent time‐resolved data was identified 10 years ago and an interesting initial effort to model such data has been recently presented for a pharmaceutical process by Domagalski et al They initially discussed four different possible ways of addressing the challenge and focused their attention mostly on a statistical approach that incorporates the effect of time as a factor and allows terms of high polynomial orders in time to be regressed against the time‐resolved output data. However, the possible numerous time instants at which measurements of concentrations might be available opens the possibility for a substantially large number of powers of time to be considered as regressors against the output data.…”

“…However, the possible numerous time instants at which measurements of concentrations might be available opens the possibility for a substantially large number of powers of time to be considered as regressors against the output data. Domagalski et al resolved this issue using a genetic algorithm to select the important ones from all of the possible regression terms.…”

“…Treating time as an input parameter different from the traditional factors bypasses the challenge of having to select the type and number of regression terms involving time if the time‐resolved data are very numerous, as in the case of spectroscopic measurements. As Domagalski et al correctly observed, how would one design the experiments if time were seen as one of the factors? Should the DOE algorithm/software decide at what time instants to take measurements or should one measure as frequently as possible using the measurement technology available?…”