Validation of 3D-QSAR models

The partial least squares (PLS)34,35 was used for cross-validation analysis, which regarded the descriptors of force fields as independent variables and the pIC₅₀ values as the dependent variables for 3D-QSAR modeling analysis. Then the leave-one-out (LOO) method was applied and a series of internal validation parameters were obtained including the q², r², ONC, SEE and F values. In general, for internal validation, the robust and reliable ability of the CoMFA/CoMSIA model should meet q² > 0.5, r² > 0.9.36 The Topomer CoMFA model satisfies q² > 0.2 as for internal validation.

However, these internal validation parameters appeared to be the necessary but not the sufficient condition for a model with high predictive power. Therefore, a set of external validation methods were adopted for evaluating the predictive ability of 3D-QSAR models. The correlation coefficient R_pred² and MAE (mean absolute error) were expressed as the following formulas ((1) and (2)). For a high predictive ability of the model, the R_pred² value should be higher than 0.5,37,38 the MAE value should meet MAE ≤ 0.1 × training set range.39

In eqn (1): the PRESS value was the sum of squared deviations between the actual and the predicted pIC₅₀ of the test compounds. The SD meant the sum of squared deviation between pIC₅₀ of test molecules and the average pIC₅₀ of the training molecules. In eqn (2): the Y_pred and Y_actu were the value of predicted and actual activities.

The fitness and predictability of the models were also checked based on Golbraikh and Tropsha statistical characteristics criteria40,41 for external validation. The three criteria were evaluated the predicted pIC₅₀ values:(1) R² > 0.6; (2) 0.85 < k < 1.15; (3) [(R² – R₀²)/R²] < 0.1.

The value of correlation coefficient R, the slope k and correlation coefficient R₀² for regressions were calculated as following formulas ((3)–(5)):

The predictive and reliable power of the 3D-QSAR models were further accessed by calculating additional validation parameters r_m² proposed by Roy.42 The r_m² was described as the following formula (6).