A win ratio approach to comparing continuous non-normal outcomes in clinical trials.

Clinical trials are often designed to compare continuous non-normal outcomes. The conventional statistical method for such a comparison is a non-parametric Mann-Whitney test, which provides a P-value for testing the hypothesis that the distributions of both treatment groups are identical, but does not provide a simple and straightforward estimate of treatment effect. For that, Hodges and Lehmann proposed estimating the shift parameter between two populations and its confidence interval (CI). However, such a shift parameter does not have a straightforward interpretation, and its CI contains zero in some cases when Mann-Whitney test produces a significant result. To overcome the aforementioned problems, we introduce the use of the win ratio for analysing such data. Patients in the new and control treatment are formed into all possible pairs. For each pair, the new treatment patient is labelled a 'winner' or a 'loser' if it is known who had the more favourable outcome. The win ratio is the total number of winners divided by the total numbers of losers. A 95% CI for the win ratio can be obtained using the bootstrap method. Statistical properties of the win ratio statistic are investigated using two real trial data sets and six simulation studies. Results show that the win ratio method has about the same power as the Mann-Whitney method. We recommend the use of the win ratio method for estimating the treatment effect (and CI) and the Mann-Whitney method for calculating the P-value for comparing continuous non-Normal outcomes when the amount of tied pairs is small.