Sample size planning for estimating the global win probability with precision and assurance

Randomized controlled trials commonly employ multiple endpoints to collectively assess the intended effects of the new intervention on multiple aspects of the disease. Focusing on the estimation of the global win probability (WinP), defined as the (weighted) mean of the WinPs across the endpoints that a treated participant would have a better outcome than a control participant, we propose a closed-form sample size formula incorporating pre-specified precision and assurance, with precision denoted by the lower limit of confidence interval and assurance denoted by the probability of achieving that lower limit. We make use of the equivalence of the WinP and the area under the receiver operating characteristic curve (AUC) and adapt a formula originally developed for the difference between two AUCs to handle the global WinP. Unequal variances between treatment groups are allowed. Simulation results suggest that the method performs very well. We illustrate the proposed formula using a Parkinson's disease clinical trial design example.