Generalized win fraction regression for composite survival endpoints

TL;DR

This paper introduces a flexible regression framework for composite survival endpoints that models the probability of winning across multiple time-to-event outcomes, accommodating censoring and ties.

Contribution

It develops a unified approach using different link functions for modeling win fractions, including a novel logit link, with theoretical properties and practical performance evaluation.

Findings

The proposed estimators are consistent and asymptotically normal.

Simulation studies show good finite-sample performance across various scenarios.

Application to clinical trial data demonstrates practical utility.

Abstract

We propose a generalized win fraction regression framework for prioritized composite survival outcomes. The framework models the conditional win fraction through a chosen link function (including identity, logit, or probit), thereby accommodating multi-component time-to-event endpoints within a unified regression structure. To handle right censoring, we construct inverse-probability-of-censoring-weighted estimating equations that target the win fraction as if censoring were absent. Under the identity link, regression parameters characterize covariate associations on the natural win fraction scale. Under the logit link, they characterize the log odds of winning -- a new and complementary effect measure that treats ties as failures to win, imposing a more conservative standard than the win ratio or win odds. When there are no ties, the logit win fraction model reduces to proportional win fraction regression; moreover, the unweighted version of our estimating equations numerically coincides with the proportional win fraction point estimator regardless of ties. We establish large-sample properties of the proposed estimators and derive a consistent sandwich variance estimator that accounts for uncertainty from the estimated censoring weights. Extensive simulations examine finite-sample performance across link functions and censoring rates, and our method is illustrated through a reanalysis of the HF-ACTION clinical trial.