Multiobjective Optimization in Quantitative Structure−Activity Relationships:  Deriving Accurate and Interpretable QSARs

Deriving quantitative structure-activity relationship (QSAR) models that are accurate, reliable, and easily interpretable is a difficult task. In this study, two new methods have been developed that aim to find useful QSAR models that represent an appropriate balance between model accuracy and complexity. Both methods are based on genetic programming (GP). The first method, referred to as genetic QSAR (or GPQSAR), uses a penalty function to control model complexity. GPQSAR is designed to derive a single linear model that represents an appropriate balance between the variance and the number of descriptors selected for the model. The second method, referred to as multiobjective genetic QSAR (MoQSAR), is based on multiobjective GP and represents a new way of thinking of QSAR. Specifically, QSAR is considered as a multiobjective optimization problem that comprises a number of competitive objectives. Typical objectives include model fitting, the total number of terms, and the occurrence of nonlinear terms. MoQSAR results in a family of equivalent QSAR models where each QSAR represents a different tradeoff in the objectives. A practical consideration often overlooked in QSAR studies is the need for the model to promote an understanding of the biochemical response under investigation. To accomplish this, chemically intuitive descriptors are needed but do not always give rise to statistically robust models. This problem is addressed by the addition of a further objective, called chemical desirability, that aims to reward models that consist of descriptors that are easily interpretable by chemists. GPQSAR and MoQSAR have been tested on various data sets including the Selwood data set and two different solubility data sets. The study demonstrates that the MoQSAR method is able to find models that are at least as good as models derived using standard statistical approaches and also yields models that allow a medicinal chemist to trade statistical robustness for chemical interpretability.