Comparison of applicability domains of QSAR models: application to the modelling of the environmental toxicity against Tetrahymena pyriformis

The estimation of the applicability domains and the accuracy of predictions are the critical problems in QSAR modelling. In this presentation we propose a new approach to compare different estimates of applicability domains based on “distances to models” as well as their significance. The “distance to model” is a measure of similarity between training and test sets compounds, which could be expressed in many different ways (e.g., Tanimoto coefficient, Euclidian distance, leverage, etc.). The main idea of our analysis is that the errors can be described by a mixture of Gaussian distributions rather than a single Gaussian distribution. Here, we analyse 12 QSAR models for aqueous toxicity against Tetrahymena pyriformis obtained with different machine-learning methods and various types of descriptors. The models were obtained and tested for a dataset of 1093 compounds measured in the same laboratory [1–4]. The dataset has been divided into training and test sets using a diversity sampling algorithm. The majority of examined distances to models provided significantly lower statistical scores (bootstrap test, p<0.05) for description of errors when using a mixture of Gaussian distributions. The use of the mixture distributions fitted to the training set affords a significantly better assessment of the test set errors as compared to the assumption of identical distribution of errors in training and test sets.