Nonadditivity Analysis

We introduce the statistics behind a novel type of SAR analysis named “nonadditivity analysis”. On the basis of all pairs of matched pairs within a given data set, the approach analyzes whether the same transformations between related molecules have the same effect, i.e., whether they are additive. Assuming that the experimental uncertainty is normally distributed, the additivities can be analyzed with statistical rigor and sets of compounds can be found that show significant nonadditivity. Nonadditivity analysis can not only detect nonadditivity, potential SAR outliers, and sets of key compounds but also allow estimating an upper limit of the experimental uncertainty in the data set. We demonstrate how complex SAR features that inform medicinal chemistry can be found in large SAR data sets. Finally, we show how the upper limit of experimental uncertainty for a given biochemical assay can be estimated without the need for repeated measurements of the same protein–ligand system.