Uncertainty back-propagation in PLS model inversion for design space determination in pharmaceutical product development

The inversion of latent-variable models is an effective tool to assist the determination of the design space (DS) of a new pharmaceutical product. A challenging issue in partial least-square (PLS) regression model inversion is to describe how the uncertainty on the model outputs (product quality) relates to the uncertainty on the model inputs (raw material properties and process parameters). In this study, a methodology to relate the uncertainty on the output of a PLS model to the uncertainty on the model inputs is proposed. Two uncertainty back-propagation models are formulated and critically compared. Frequentist confidence regions (CRs) for the solution of the inversion problem are built. These CRs represent a subspace of the historical knowledge space within which the DS of the product to be developed is likely to lie with assigned confidence level. The input combinations that belong to these CRs (and that are consistent with the historical calibration data set) should be primarily investigated when an experimental campaign is to be performed to determine the DS. The proposed methodology is tested on three different case studies, two of which involve experimental data taken from the literature, respectively, on a roller compactor and on a wet granulator. It is shown that both uncertainty back-propagation models are effective in bracketing the DS, with the second model outperforming the first one in terms of shrinkage of the space within which experiments should be carried out to identify the DS.