Modelling Structure Activity Landscapes with Cliffs: a Kernel Regression-Based Approach

Quantitative Structure-Activity Relationship (QSAR) models are increasingly used in hazard and risk assessment. Even when models with linear relationships between activity and a small number of descriptors are built and validated regarding predictivity and statistical assumptions, similar structures can exhibit large differences in activity known as similarity paradoxes or activity cliffs. In order to reduce the impact that similarity paradoxes can have on predictions we have devised a statistical method based on Nadaraya-Watson kernel regression. According to our method, activity cliffs filter out contributions of neighbouring chemicals especially along the cliff axis. Our method decreases density-based certainty in particular for chemicals with strong prediction errors and the implementation of Structure-Activity Landscape Index (SALI) curves shows that our method improves the prediction of activity cliff ranks. We also provide useful indications on the density-based applicability domain and the reliability of individual predictions.