Reliable estimation of prediction errors for QSAR models under model uncertainty using double cross-validation

Désirée Baumann, Knut Baumann

Generally, QSAR modelling requires both model selection and validation since there is no a priori knowledge about the optimal QSAR model. Prediction errors (PE) are frequently used to select and to assess the models under study. Reliable estimation of prediction errors is challenging - especially under model uncertainty - and requires independent test objects. These test objects must not be involved in model building nor in model selection. Double cross-validation, sometimes also termed nested cross-validation, offers an attractive possibility to generate test data and to select QSAR models since it uses the data very efficiently. Nevertheless, there is a controversy in the literature with respect to the reliability of double cross-validation under model uncertainty. Moreover, systematic studies investigating the adequate parameterization of double cross-validation are still missing. Here, the cross-validation design in the inner loop and the influence of the test set size in the outer loop is systematically studied for regression models in combination with variable selection.