Optimal Material Selection for Oral Dosage Development and Manufacture Using Optimization Techniques and Multivariate Latent Variable Models
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Multivariate latent variable models (such as Principal Components Analysis –PCA, and Projection to Latent Structures –PLS) have been reported in literature to transform a collection of physical properties measured for multiple materials into scores (or principal properties) with the ultimate objective of aiding a selection or screening process, which is ultimately done by the practitioner. Even when using principal properties, it is not uncommon to find situations where there are more than two principal components (and hence principal properties) and the decision of which materials to use for an experimental design is not obvious and will require an exhaustive manual exercise to select materials with the optimal position in the score space such that the covariance of the principal properties of the selected materials is kept orthogonal and centered around the mean to avoid bias. This work presents the application of multivariate methods coupled with mixed integer non-linear optimization methods to aid the selection process from a finite population of materials when the objective is to maximize the balanced and orthogonal information from the materials onto an experimental design. An objective function is formulated such that the off diagonals of the variance-covariance matrix of the sub-set of scores for the selected materials is minimized, while maximizing the main diagonal of the variance-covariance matrix while keeping the “design” centered around the mean to avoid bias. Furthermore, when the properties of the materials are considered as a mixture, modifications to the PLS algorithm have been proposed to model the covariance structure of such data and aid the decision making process that involves the selection of materials from a given pool. In this work we also present two examples of such exercise: one for process development and one for commercial manufacture in support of a process improvement effort. For the process development example a formulation for a wet granulated tablet is optimized in order to maximize the slope of the hardness compression profile. The commercial manufacture example presents the case where historical data for the physical chemical properties of the different lots of raw materials were regressed to the final dissolution of the product, and the model is then used to determine which of the available lots in inventory are the optimal to be blended to minimize the variability in the quality of the final product.