Adjusted win ratio using the inverse probability of treatment weighting

The win ratio method has been increasingly applied in the design and analysis of clinical trials. However, the win ratio method is a univariate approach that does not allow for adjusting for baseline imbalances in covariates, although a stratified win ratio can be calculated when the number of strata is small. This paper proposes an adjusted win ratio to control for such imbalances by inverse probability of treatment weighting (IPTW) method. We derive the adjusted win ratio with its variance and suggest three IPTW adjustments: IPTW-average treatment effect (IPTW-ATE), stabilized IPTW-ATE (SIPTW-ATE) and IPTW-average treatment effect in the treated (IPTW-ATT). The proposed adjusted methods are applied to analyse a composite outcome in the CHARM trial. The statistical properties of the methods are assessed through simulations. Results show that adjusted win ratio methods can correct the win ratio for covariate imbalances at baseline. Simulation results show that the three proposed adjusted win ratios have similar power to detect the treatment difference and have slightly lower power than the corresponding adjusted Cox models when the assumption of proportional hazards holds true but have consistently higher power than adjusted Cox models when the proportional hazard assumption is violated.