ABSTRACT
Multivariate conditional regression using a Bayesian estimation approach for the development of a surrogate dissolution model as part of a comprehensive Process Analytical Technology (PAT) release strategy is the subject of this chapter. An appropriate experimental design provides the basis for constructing a process model in the first step, relating dissolution variables as the response to the critical process parameters (CPPs). Dissolution variables are either: Case 1: in vitro release measurements at one or several specific dissolution time points, or Case 2: the three parameters of the Weibull function describing the full profile at the tablet or batch or run average level. The dissolution variables are augmented with the measured API Content-by-NIR of the tablet to form the multivariate response vector in the process model. Then a conditional regression of the dissolution variables given API Content-by-NIR content and process parameters settings in the second step yields a predictive surrogate model of the dissolution variables. In the first case, the surrogate model directly yields predictions of the in vitro release measurement at the specific time point(s). In the second case, Weibull parameters are predicted, yielding a mean dissolution prediction at any time point on the dissolution profile. The Bayesian estimation approach to the conditional regression model permits simulations that can characterize the analytical performance of the surrogate model with respect to accuracy and precision for model qualification purposes. Two examples are given which show the statistical modeling details of both cases.
