A robust quantitative structure–activity relationship modelling of influenza neuraminidase a/PR/8/34 (H1N1) inhibitors based on the rank-bridge estimator

Linear regression model is frequently encountered in quantitative structure–activity relationship (QSAR) modelling. The traditional estimation of regression model parameters is based on the normal assumption of the response variable (biological activity) and therefore, it is sensitive to outliers or heavy-tailed distributions. Robust penalized regression methods have been given considerable attention because they combine the robust estimation method with penalty terms to perform QSAR parameter estimation and variable selection (descriptor selection) simultaneously. In this paper, based on bridge penalty, a robust QSAR model of the influenza neuraminidase a/PR/8/34 (H1N1) inhibitors is proposed as a resistant method to the existence of outliers or heavy-tailed errors. The basic idea is to combine the rank regression and the bridge penalty together to produce the rank-bridge method. The rank-bridge model is internally and externally validated based on $Q_{int}^2$, $Q_{LGO}^2$, $Q_{Boot}^2$, $MS{E}_{train}$, Y-randomization test, $Q_{ext}^2$, $MS{E}_{test}$ and the applicability domain (AD). The validation results indicate that the rank-bridge model is robust and not due to chance correlation. In addition, the results indicate that the descriptor selection and prediction performance of the rank-bridge model for training dataset outperforms the other two used modelling methods. Rank-bridge model shows the highest $Q_{int}^2$, $Q_{LGO}^2$ and $Q_{Boot}^2$, and the lowest $MS{E}_{train}$. For the test dataset, rank-bridge model shows higher external validation value ($Q_{ext}^2$ = 0.824), and lower value of $MS{E}_{test}$ compared with the other methods, indicating its higher predictive ability.