Using Prior Parameter Knowledge in Model-Based Design of Experiments for Pharmaceutical Production

Ali Shahmohammadi,Kimberley Mcauley

doi:10.22541/au.158531777.72018148

Abstract

Sequential model-based design of experiments (MBDoE) uses information from previous experiments to select run conditions for new experiments. Computation of the objective functions for popular MBDoE can be impossible due to a non-invertible Fisher Information Matrix (FIM). Previously, we evaluated a leave-out (LO) approach that design experiments by removing problematic model parameters from the design process. However, the LO approach can be computationally expensive due to its iterative nature and some model parameters are ignored. In this study, we propose a simple Bayesian approach that makes the FIM invertible by accounting for prior parameter information. We compare the proposed Bayesian approach to the LO approach for designing sequential A-optimal experiments. Results from a pharmaceutical case study show that the Bayesian approach is superior, on average, to the LO approach for design of experiments. However, for subsequent parameter estimation, a subset-selection-based LO approach gives better parameter values than the Bayesian approach.

Highlights

We suggest that simplified Bayesian model-based design of experiments (MBDoE) should be combined with a subset-selection-based approach for parameter estimation
Consider the nonlinear model: YY = gg(dd, θθ) + εε where YY ∈ RRNN is a vector of stacked measured responses, g is the solution of equations that describe the system, dd ∈ RRrr×DD is a matrix of experimental settings, θθ ∈ RRpp is the vector of model parameters and εε ∈ RRNN is a vector of a measurement noise with diagonal covariance matrix ΣΣyy ∈ RRNN×NN
The focus of this study is on the design of experiments, we investigate the effectiveness of Bayesian and LO parameter estimation using the new data obtained following MBDoE

Summary

INTRODUCTION

Mathematical models are used in chemical and pharmaceutical industries for analysis, design and control of chemical processes and for maximizing product quality and profit.[1,2] 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] 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]. G- and V-optimal designs focus on obtaining accurate model predictions at specified operating conditions of interest to the modeler.[20,23–25] Biochemical and pharmacological systems, models often contain a large number of kinetic and transport parameters (e.g., 10-80 parameters) which may result in noninvertible/ill-conditioned FIMs.[35–39] To avoid this problem, several approaches have been considered during sequential MBDoE calculations including parameter-subset selection,[14,40,41] pseudoinverse methods,[25,42] Tikhonov regularization,[43–46] and Bayesian approaches.[13,47,48]. We developed a new Tikhonov-based approach for MBDoE to address the problem of ill-conditioned/singular FIMs. The Tikhonov weightings are specified by using Bayesian arguments based on the modeler’s prior knowledge about plausible values of the parameters. Results obtained using Monte Carlo (MC) simulations are provided, revealing that the proposed Bayesian approach is superior to the LO approach for this case study

BACKGROUND

CONCLUSIONS

Use Xk to predict columns in Z using ordinary least squares