Optimal Piecewise Linear Regression Algorithm for QSAR Modelling

Quantitative Structure-Activity Relationship (QSAR) models have been successfully applied to lead optimisation, virtual screening and other areas of drug discovery over the years. Recent studies, however, have focused on the development of models that are predictive but often not interpretable. In this article, we propose the application of a piecewise linear regression algorithm, OPLRAreg, to develop both predictive and interpretable QSAR models. The algorithm determines a feature to best separate the data into regions and identifies linear equations to predict the outcome variable in each region. A regularisation term is introduced to prevent overfitting problems and implicitly selects the most informative features. As OPLRAreg is based on mathematical programming, a flexible and transparent representation for optimisation problems, the algorithm also permits customised constraints to be easily added to the model. The proposed algorithm is presented as a more interpretable alternative to other commonly used machine learning algorithms and has shown comparable predictive accuracy to Random Forest, Support Vector Machine and Random Generalised Linear Model on tests with five QSAR data sets compiled from the ChEMBL database.