The stratified win statistics (win ratio, win odds, and net benefit)

• Published in: Pharmaceutical statistics : the journal of the pharmaceutical industry Vol. 22; no. 4; pp. 748 - 756
• Main Authors: Dong, Gaohong, Hoaglin, David C., Huang, Bo, Cui, Ying, Wang, Duolao, Cheng, Yu, Gamalo‐Siebers, Margaret
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Inc 01.07.2023; Wiley Subscription Services, Inc
• Subjects: Finkelstein‐Schoenfeld test; generalized pairwise comparisons; Humans; mantel–Haenszel method; net benefit; Odds Ratio; Probability; Statistical analysis; win odds; win ratio; win ratio; mantel-Haenszel method; Finkelstein-Schoenfeld test; net benefit; generalized pairwise comparisons; win odds
• DOI: 10.1002/pst.2293
• ISSN: 1539-1604

The win odds and the net benefit are related directly to each other and indirectly, through ties, to the win ratio. These three win statistics test the same null hypothesis of equal win probabilities between two groups. They provide similar p‐values and powers, because the Z‐values of their statistical tests are approximately equal. Thus, they can complement one another to show the strength of a treatment effect. In this article, we show that the estimated variances of the win statistics are also directly related regardless of ties or indirectly related through ties. Since its introduction in 2018, the stratified win ratio has been applied in designs and analyses of clinical trials, including Phase III and Phase IV studies. This article generalizes the stratified method to the win odds and the net benefit. As a result, the relations of the three win statistics and the approximate equivalence of their statistical tests also hold for the stratified win statistics.