  Most clinical trials conducted in drug development contain multiple endpoints
in order to collectively assess the intended effects of the drug on various
disease characteristics. Focusing on the estimation of the global win
probability, defined as the average win probability (WinP) across 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 variance is allowed. Simulation results suggest that the
method performs very well. We illustrate the proposed formula using a
Parkinson's disease clinical trial design example.
