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 $Q_{int}^2$, $Q_{\mathrm{L}\mathrm{G}\mathrm{O}}^2$, $Q_{\mathrm{B}\mathrm{o}\mathrm{o}\mathrm{t}}^2$, $\mathrm{M}\mathrm{S}{\mathrm{E}}_{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}}$, Y-randomization test, $Q_{\mathrm{e}\mathrm{x}\mathrm{t}}^2$, $\mathrm{M}\mathrm{S}{\mathrm{E}}_{\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}}$ 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 $Q_{int}^2$, $Q_{\mathrm{L}\mathrm{G}\mathrm{O}}^2$ and $Q_{\mathrm{B}\mathrm{o}\mathrm{o}\mathrm{t}}^2$, and the lowest $\mathrm{M}\mathrm{S}{\mathrm{E}}_{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}}$. For the test dataset, rank-bridge model shows higher external validation value ($Q_{\mathrm{e}\mathrm{x}\mathrm{t}}^2$ = 0.824), and lower value of $\mathrm{M}\mathrm{S}{\mathrm{E}}_{\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}}$ compared with the other methods, indicating its higher predictive ability.

在定量结构-活性关系（QSAR）建模中经常遇到线性回归模型。回归模型参数的传统估计是基于响应变量（生物活动）的正常假设，因此，它对异常值或重尾分布敏感。鲁棒的惩罚回归方法已经得到了广泛的关注，因为它们将鲁棒的估计方法与惩罚项相结合，以同时执行QSAR参数估计和变量选择（描述符选择）。在本文中，基于桥梁罚则，提出了一种可靠的QSAR模型的流感神经氨酸酶a / PR / 8/34（H1N1）抑制剂，作为对异常值或重尾错误的抵抗方法。基本思想是将秩回归和桥罚结合在一起以产生秩桥方法。等级桥模型是基于以下方面进行内部和外部验证的${问}_{整型}^2$， ${问}_{\mathrm{大号}\mathrm{G}\mathrm{Ø}}^2$， ${问}_{\mathrm{乙}\mathrm{Ø}\mathrm{Ø}\mathrm{Ť}}^2$， $\mathrm{中号}\mathrm{小号}{\mathrm{Ë}}_{\mathrm{Ť}\mathrm{[R}\mathrm{一种}\mathrm{一世}\mathrm{ñ}}$，Y随机检验， ${问}_{\mathrm{Ë}\mathrm{X}\mathrm{Ť}}^2$， $\mathrm{中号}\mathrm{小号}{\mathrm{Ë}}_{\mathrm{Ť}\mathrm{Ë}\mathrm{s}\mathrm{Ť}}$和适用范围（AD）。验证结果表明，秩桥模型是鲁棒的，而不是由于机会相关性。此外，结果表明，用于训练数据集的秩桥模型的描述符选择和预测性能优于其他两种使用的建模方法。等级桥模型显示最高${问}_{整型}^2$， ${问}_{\mathrm{大号}\mathrm{G}\mathrm{Ø}}^2$ 和 ${问}_{\mathrm{乙}\mathrm{Ø}\mathrm{Ø}\mathrm{Ť}}^2$，最低 $\mathrm{中号}\mathrm{小号}{\mathrm{Ë}}_{\mathrm{Ť}\mathrm{[R}\mathrm{一种}\mathrm{一世}\mathrm{ñ}}$。对于测试数据集，秩桥模型显示出更高的外部验证值（${问}_{\mathrm{Ë}\mathrm{X}\mathrm{Ť}}^2$ = 0.824），而较低的值 $\mathrm{中号}\mathrm{小号}{\mathrm{Ë}}_{\mathrm{Ť}\mathrm{Ë}\mathrm{s}\mathrm{Ť}}$ 与其他方法相比，表明其更高的预测能力。