Using Random Forest To Model the Domain Applicability of Another Random Forest Model

In QSAR, a statistical model is generated from a training set of molecules (represented by chemical descriptors) and their biological activities. We will call this traditional type of QSAR model an "activity model". The activity model can be used to predict the activities of molecules not in the training set. A relatively new subfield for QSAR is domain applicability. The aim is to estimate the reliability of prediction of a specific molecule on a specific activity model. A number of different metrics have been proposed in the literature for this purpose. It is desirable to build a quantitative model of reliability against one or more of these metrics. We can call this an "error model". A previous publication from our laboratory (Sheridan J. Chem. Inf. Model., 2012, 52, 814-823.) suggested the simultaneous use of three metrics would be more discriminating than any one metric. An error model could be built in the form of a three-dimensional set of bins. When the number of metrics exceeds three, however, the bin paradigm is not practical. An obvious solution for constructing an error model using multiple metrics is to use a QSAR method, in our case random forest. In this paper we demonstrate the usefulness of this paradigm, specifically for determining whether a useful error model can be built and which metrics are most useful for a given problem. For the ten data sets and for the seven metrics we examine here, it appears that it is possible to construct a useful error model using only two metrics (TREE_SD and PREDICTED). These do not require calculating similarities/distances between the molecules being predicted and the molecules used to build the activity model, which can be rate-limiting.