title: A generalized analytic solution to the win ratio to analyze a composite endpoint considering the clinical importance order among components.
abstract: A composite endpoint consists of multiple endpoints combined in one outcome. It is frequently used as the primary endpoint in randomized clinical trials. There are two main disadvantages associated with the use of composite endpoints: a) in conventional analyses, all components are treated equally important; and b) in time-to-event analyses, the first event considered may not be the most important component. Recently Pocock et al. (2012) introduced the win ratio method to address these disadvantages. This method has two alternative approaches: the matched pair approach and the unmatched pair approach. In the unmatched pair approach, the confidence interval is constructed based on bootstrap resampling, and the hypothesis testing is based on the non-parametric method by Finkelstein and Schoenfeld (1999). Luo et al. (2015) developed a close-form variance estimator of the win ratio for the unmatched pair approach, based on a composite endpoint with two components and a specific algorithm determining winners, losers and ties. We extend the unmatched pair approach to provide a generalized analytical solution to both hypothesis testing and confidence interval construction for the win ratio, based on its logarithmic asymptotic distribution. This asymptotic distribution is derived via U-statistics following Wei and Johnson (1985). We perform simulations assessing the confidence intervals constructed based on our approach versus those per the bootstrap resampling and per Luo et al. We have also applied our approach to a liver transplant Phase III study. This application and the simulation studies show that the win ratio can be a better statistical measure than the odds ratio when the importance order among components matters; and the method per our approach and that by Luo et al., although derived based on large sample theory, are not limited to a large sample, but are also good for relatively small sample sizes. Different from Pocock et al. and Luo et al., our approach is a generalized analytical method, which is valid for any algorithm determining winners, losers and ties. Copyright © 2016 John Wiley & Sons, Ltd.
authors.affiliation: iStats Inc., Long Island City, NY, USA. Gaohong_Dong@iStats.org.
authors.forename: Gaohong
authors.initials: G
authors.lastname: Dong
authors.affiliation: Eisai Inc., Woodcliff Lake, NJ, USA.
authors.forename: Di
authors.initials: D
authors.lastname: Li
authors.affiliation: Novartis Pharma AG, Basel, Switzerland.
authors.forename: Steffen
authors.initials: S
authors.lastname: Ballerstedt
authors.affiliation: Novartis Pharma AG, Basel, Switzerland.
authors.forename: Marc
authors.initials: M
authors.lastname: Vandemeulebroecke
mesh_terms: D017326:Clinical Trials, Phase III as Topic / Q000379:methods / Q000706:statistics & numerical data*; D023381:Endpoint Determination / Q000379:methods / Q000706:statistics & numerical data*; D006801:Humans; D016031:Liver Transplantation / Q000706:statistics & numerical data*
keywords: U-statistic; Win ratio; composite endpoint; odds ratio; unmatched pair approach