Mao Lu
Department of Biostatistics and Medical Informatics, School of Medicine and Public Health, University of Wisconsin-Madison, 610 Walnut St, Room 207 A, Madison, 53726, WI, USA.
BMC Med Res Methodol. 2025 Apr 17;25(1):102. doi: 10.1186/s12874-025-02554-w.
The win ratio has been widely used in the analysis of hierarchical composite endpoints, which prioritize critical outcomes such as mortality over nonfatal, secondary events. Although a regression framework exists to incorporate covariates, it is limited to low-dimensional datasets and may struggle with numerous predictors. This gap necessitates a robust variable selection method tailored to the win ratio framework.
We propose an elastic net-type regularization approach for win ratio regression, extending the proportional win-fractions (PW) model in low-dimensional settings. The method addresses key challenges, including adapting pairwise comparisons to penalized regression, optimizing model selection through subject-level cross-validation, and defining performance metrics via a generalized concordance index. The procedures are implemented in the wrnet R-package, publicly available at https://lmaowisc.github.io/wrnet/ .
Simulation studies demonstrate that wrnet outperforms traditional (regularized) Cox regression for time-to-first-event analysis, particularly in scenarios with differing covariate effects on mortality and nonfatal events. When applied to data from the HF-ACTION trial, the method identified prognostic variables and achieved superior predictive accuracy compared to regularized Cox models, as measured by overall and component-specific concordance indices.
The wrnet approach combines the interpretability and clinical relevance of the win ratio with the scalability and robustness of elastic net regularization. The accompanying R-package provides a user-friendly interface for routine application of the procedures, whenever appropriate. Future research could explore additional applications or refine the methodology to address non-proportionalities in win-loss risks and nonlinearities in covariate effects.
胜率已广泛用于分层复合终点的分析，在这种分析中，诸如死亡率等关键结局比非致命性次要事件具有更高优先级。尽管存在一个纳入协变量的回归框架，但它仅限于低维数据集，并且可能难以处理众多预测变量。这一差距需要一种专门针对胜率框架的稳健变量选择方法。
我们提出一种用于胜率回归的弹性网络型正则化方法，扩展了低维情况下的比例赢率（PW）模型。该方法解决了关键挑战，包括使成对比较适应惩罚回归、通过个体水平交叉验证优化模型选择以及通过广义一致性指数定义性能指标。这些程序在wrnet R包中实现，可在https://lmaowisc.github.io/wrnet/ 上公开获取。
模拟研究表明，在首次事件发生时间分析中，wrnet优于传统（正则化）Cox回归，特别是在协变量对死亡率和非致命事件有不同影响的情况下。当应用于HF-ACTION试验的数据时，与正则化Cox模型相比，该方法识别出了预后变量，并在总体和特定成分一致性指数的衡量下实现了更高的预测准确性。
wrnet方法将胜率的可解释性和临床相关性与弹性网络正则化的可扩展性和稳健性相结合。随附的R包提供了一个用户友好的界面，以便在适当的时候对这些程序进行常规应用。未来的研究可以探索更多应用或改进该方法，以解决输赢风险的非比例性和协变量效应的非线性问题。
