On Two Novel Parameters for Validation of Predictive QSAR Models

Abstract: Validation is a crucial aspect of quantitative structure–activity relationship (QSAR) modeling. The present paper shows that traditionally used validation parameters (leave-one-out Q² for internal validation and predictive R² for external validation) may be supplemented with two novel parameters r_m² and R_p² for a stricter test of validation. The parameter r_m²_(overall) penalizes a model for large differences between observed and predicted values of the compounds of the whole set (considering both training and test sets) while the parameter R_p² penalizes model R² for large differences between determination coefficient of nonrandom model and square of mean correlation coefficient of random models in case of a randomization test. Two other variants of r_m² parameter, r_m²_(LOO) and r_m²_(test), penalize a model more strictly than Q² and R²_pred respectively. Three different data sets of moderate to large size have been used to develop multiple models in order to indicate the suitability of the novel parameters in QSAR studies. The results show that in many cases the developed models could satisfy the requirements of conventional parameters (Q² and R²_pred) but fail to achieve the required values for the novel parameters r_m² and R_p². Moreover, these parameters also help in identifying the best models from among a set of comparable models. Thus, a test for these two parameters is suggested to be a more stringent requirement than the traditional validation parameters to decide acceptability of a predictive QSAR model, especially when a regulatory decision is involved.