Generalized win-odds regression models for composite endpoints

The time-to-first-event analysis is often used for studies involving multiple event times, where each component is treated equally, regardless of their clinical importance. Alternative summaries such as Win Ratio, Net Benefit, and Win Odds (WO) have drawn attention lately because they can handle different types of outcomes and allow for a hierarchical ordering in component outcomes. In this paper, we focus on WO and propose proportional WO regression models to evaluate the treatment effect on multiple outcomes while controlling for other risk factors. The models are easily interpretable as a standard logistic regression model. However, the proposed WO regression is more advanced; multiple outcomes of different types can be modeled together, and the estimating equation is constructed based on all possible and potentially dependent pairings of a treated individual with a control one under the functional response modeling framework. In addition, informative ties are carefully distinguished from those inconclusive comparisons due to censoring, and the latter is handled via the inverse probability of censoring weighting method. We establish the asymptotic properties of the estimated regression coefficients using the U-statistic theory and demonstrate the finite sample performance through numerical studies.