Win statistics (win ratio, win odds, and net benefit): Noncollapsibility and standardization for randomized clinical trials

The win ratio, along with its stratified variant known as the stratified win ratio, has been widely utilized in many disease areas for both design and analysis of clinical trials. It is applied most prominently in cardiovascular diseases, followed by respiratory disease, diabetes, oncology, neurology, and other areas. Additionally, the win odds, which incorporates ties in its calculation, has also garnered attention in both prospective and retrospective analyses, alongside their utilization in study design. Researchers have invested considerable effort in the statistical inference of the win statistics (win ratio, win odds, and net benefit). However, despite their significance, the issue of noncollapsibility, highlighted as critical in the FDA's covariate adjustment guidance in 2023, has not been thoroughly investigated for these win statistics. In this article, we investigate the noncollapsibility of win statistics in three typical types of clinical trial data: binary, continuous, and time-to-event data. We demonstrate that (1) the win ratio is noncollapsible for all of these three types of data; (2) both win odds and net benefit exhibit collapsibility for binary data but are noncollapsible for continuous and time-to-event data. Therefore, win statistics are generally noncollapsible. In light of these findings, we propose the use of stratified win statistics as a standardization approach for analyzing prioritized multiple outcomes, particularly in scenarios where noncollapsibility is a concern.