Weighted win loss statistics
Steven Bai, U.S. Food and Drug Administration  *Xiaodong Luo, Sanofi R&D US  Junshan Qiu, FDA CDER  Hong Tian, Jenssen R&D 

Keywords: CV trials, composite endpoints, prioritized outcomes, weighting, variance estimation

There are more and more objectives to achieve in a single CV trial. This results in more than one primary outcome. In addition to assessing several primary endpoints with a pre-specified testing procedure, combining multiple endpoints into a univariate effect measure is used as an alternative. The traditional analyses assign equal weight to all types of events irrespective of their clinical relevance. Effect measures accounting for different priorities, which are called prioritized outcomes, were proposed by Buyes (2010) and Pocock et al. (2012) for evaluation of drug efficacy. A generalized pairwise comparison of prioritized outcomes based on extension of the U-statistic of the Wilcoxon-Mann-Whitney test was proposed by Buyse (2010). This method can assign higher weight to more important endpoints and reducing masking effects when using a traditional univariate outcome. Also based on prioritized outcomes, Pocock et al. (2012) proposed a win ratio approach. Comparing with other non-parametric approaches, the win ratio approach can yield a confidence interval and P-value for the win ratio statistic. Luo et al. (2015) established a statistical framework for the win ratio approach for the semi-competing risks data. A more general framework was developed by Bebu and Lachin (2016) using the large sample distribution of certain multivariate multi-sample U-statistic. Both the approaches by Buyse (2010) and Pocock et al. (2012) can be expressed as weighted sum of univariate effect measures for the components which share common disadvantages in weighting strategies: considerable dependence on the censoring and follow-up distributions, independence of the priority of the individual endpoints, and non-standardized weights. As a result, these combined univariate approaches could be hard to interpret (Rauch et al., 2014). Sample size estimation is one of the issues in planning clinical trials with composite endpoints (Rauch et al., 2015). There is a need for deriving appropriate statistics such as variance estimator for sample size estimation. Here we propose a weighted win ratio approach to further improve the traditional win ratio approach and also derive the variance estimator under the null hypothesis. These efforts improve the performance of the win ratio approach in analyzing prioritized outcomes and facilitate its implementation in planning clinical trials.