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Background <p>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.</p> Methods <p>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 <Emphasis FontCategory="NonProportional">wrnet</Emphasis> R-package, publicly available at <a href="https://lmaowisc.github.io/wrnet/">https://lmaowisc.github.io/wrnet/</a>.</p> Results <p>Simulation studies demonstrate that <Emphasis FontCategory="NonProportional">wrnet</Emphasis> 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.</p> Conclusion <p>The <Emphasis FontCategory="NonProportional">wrnet</Emphasis> 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.</p>

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Regularized win ratio regression for variable selection and risk prediction, with an application to a cardiovascular trial

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月17日

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  • Lu Mao

摘要

Background

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.

Methods

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/.

Results

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.

Conclusion

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.