The Relative Importance of Domain Applicability Metrics for Estimating Prediction Errors in QSAR Varies with Training Set Diversity.

In QSAR, a statistical model is generated from a training set of molecules (represented by chemical descriptors) and their biological activities (an "activity model"). The aim of the field of domain applicability (DA) is to estimate the uncertainty of prediction of a specific molecule on a specific activity model. A number of DA metrics have been proposed in the literature for this purpose. A quantitative model of the prediction uncertainty (an "error model") can be built using one or more of these metrics. A previous publication from our laboratory (Sheridan, R. P. J. Chem. Inf. Model. 2013, 53, 2837-2850) suggested that QSAR methods such as random forest could be used to build error models by fitting unsigned prediction errors against DA metrics. The QSAR paradigm contains two useful techniques: descriptor importance can determine which DA metrics are most useful, and cross-validation can be used to tell which subset of DA metrics is sufficient to estimate the unsigned errors. Previously we studied 10 large, diverse data sets and seven DA metrics. For those data sets for which it is possible to build a significant error model from those seven metrics, only two metrics were sufficient to account for almost all of the information in the error model. These were TREE_SD (the variation of prediction among random forest trees) and PREDICTED (the predicted activity itself). In this paper we show that when data sets are less diverse, as for example in QSAR models of molecules in a single chemical series, these two DA metrics become less important in explaining prediction error, and the DA metric SIMILARITYNEAREST1 (the similarity of the molecule being predicted to the closest training set compound) becomes more important. Our recommendation is that when the mean pairwise similarity (measured with the Carhart AP descriptor and the Dice similarity index) within a QSAR training set is less than 0.5, one can use only TREE_SD, PREDICTED to form the error model, but otherwise one should use TREE_SD, PREDICTED, SIMILARITYNEAREST1.