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.