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

## TL;DR

This paper introduces a new method for analyzing complex health outcomes in trials by combining win ratio analysis with regularization techniques, improving prediction accuracy.

## Contribution

The paper proposes an elastic net-type regularization approach for win ratio regression, enabling variable selection and risk prediction in high-dimensional settings.

## Key findings

- The wrnet method outperforms regularized Cox regression in scenarios with differing covariate effects on mortality and nonfatal events.
- Application to the HF-ACTION trial showed superior predictive accuracy compared to traditional models.
- The method is implemented in the wrnet R-package, offering a user-friendly interface for clinical researchers.

## Abstract

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.