The use of the win odds in the design of non-inferiority clinical trials

In 2012, Pocock and colleagues proposed the win ratio (WR) statistics for the analysis of controlled clinical trials with a composite endpoint. This approach takes into account clinical priorities among multiple components of the composite. Subjects in the test group are compared with subjects in the control group in all possible pairwise comparisons. The WR is calculated as the number of "winners" divided by the number of "losers" in the test group. The WR statistic is intuitive; however, it is not clear how it should be applied when the number of ties is substantial. To handle the ties, Dong et al. recently introduced the win odds (WO) statistics, which assigns 50% of the ties to both the numerator and the denominator of the WR statistic. In this work, we discuss the WO in the design of a Non-Inferiority (NI) trial with a composite endpoint, as ties in NI trials may reflect comparable treatment effect and the number of ties may be substantial. We extend the large sample inference for the WR to the WO and demonstrate the utility of the WO in the design of NI trials through simulations.