Group Sequential Methods for the Win Ratio
Tracy Bergemann, Tim Hanson
TL;DR
This paper addresses how to implement group sequential designs when the primary endpoint is a win ratio. It derives the covariance structure for incremental U-statistics testing both the win difference and the win ratio, proving the independent increments property under the asymptotic distribution (for complete information) and providing an approximate result for the log win ratio. Through simulations, it demonstrates that Lan-DeMets alpha-spending maintains Type I error across interim looks, and it illustrates the practical utility with a re-analysis of the IN.PACT SFA trial, showing that early stopping could have occurred. The work enables applying standard group sequential boundaries to win-ratio trials under common conditions, with implications for adaptive designs involving hierarchical composite endpoints in cardiovascular trials.
Abstract
The win ratio is increasingly used in randomized trials due to its intuitive clinical interpretation, ability to incorporate the relative importance of composite endpoints, and its capacity for combining different types of outcomes (e.g. time-to-event, binary, counts, etc.) to be combined. There are open questions, however, about how to implement adaptive design approaches when the primary endpoint is a win ratio, including in group sequential designs. A key requirement allowing for straightforward application of classical group sequential methods is the independence of incremental interim test statistics. This paper derives the covariance structure of incremental U-statistics that evaluate the win ratio under its asymptotic distribution. The derived covariance shows that the independent increments assumption holds for the asymptotic distribution of U-statistics that test the win ratio. Simulations confirm that traditional $α$-spending preserves Type I error across interim looks. A retrospective look at the IN.PACT SFA clinical trial data illustrates the potential for stopping early in a group sequential design using the win ratio. We have demonstrated that straightforward use of Lan-De\uppercase{M}ets $α$-spending is possible for randomized trials involving the win ratio under certain common conditions. Thus, existing software capable of computing traditional group sequential boundaries can be employed.