Integrating Prioritized and Non-Prioritized Structures in Win Statistics

Composite endpoints are frequently used as primary or secondary analyses in cardiovascular clinical trials to increase clinical relevance and statistical efficiency. Alternatively, the Win Ratio (WR) and other Win Statistics (WS) analyses rely on a strict hierarchical ordering of endpoints, assigning higher priority to clinically important endpoints. However, determining a definitive endpoint hierarchy can be challenging and may not adequately reflect situations where endpoints have comparable importance. In this study, we discuss the challenges of endpoint prioritization, underscore its critical role in WS analyses, and propose Rotation WR (RWR), a hybrid prioritization framework that integrates both prioritized and non-prioritized structures. By permitting blocks of equally-prioritized endpoints, RWR accommodates endpoints of equal or near equal clinical importance, recurrent events, and contexts requiring individualized shared decision making. Statistical inference for RWR is developed using U-statistics theory, including the hypothesis testing procedure and confidence interval construction. Extensions to two additional WS measures, Rotation Net Benefit and Rotation Win Odds, are also provided. Through extensive simulation studies involving multiple time-to-event endpoints, including recurrent events, we demonstrate that RWR achieves valid type I error control, desirable statistical power, and accurate confidence interval coverage. We illustrate both the methodological and practical insights of our work in a case study on endpoint prioritization with the SPRINT clinical trial, highlighting its implications for real-world clinical trial studies.

💡 Research Summary

The paper addresses a fundamental limitation of the Win Ratio (WR) and related Win Statistics (WS) methods, which require a strict hierarchical ordering of all endpoints in a composite outcome. In many cardiovascular trials, however, some events (e.g., myocardial infarction and stroke) are of comparable clinical importance, while others (e.g., death) are clearly more severe. Moreover, recurrent non‑fatal events and patient‑specific preferences often call for a more flexible treatment of endpoint importance. To bridge the gap between full prioritization and complete non‑prioritization, the authors propose the Rotation Win Ratio (RWR), a hybrid framework that permits blocks of equally‑prioritized endpoints while preserving a strict order across blocks.

In RWR the set of q endpoints Y is partitioned into R disjoint blocks G₁,…,G_R. Blocks are ordered by clinical priority (G₁ ≻ G₂ ≻ … ≻ G_R). Within each block, all possible permutations of the endpoints are generated; each permutation is called a “rotation.” For each rotation k, the usual pairwise win (W^{(k)}) and loss (L^{(k)}) functions are applied to every treatment–control pair, yielding counts n(k)ᵗ (wins) and n(k)ᶜ (losses). The overall RWR is defined as the ratio of the summed wins to the summed losses across all rotations: RWR = Σ_k n(k)ᵗ / Σ_k n(k)ᶜ. This construction treats endpoints inside a block symmetrically while maintaining the hierarchy between blocks.

Statistical inference is built on U‑statistics theory. For a given rotation, the win and loss counts are asymptotically normal with means θ^{(k)}ₜ and θ^{(k)}_c and variances that depend on the sample sizes Nₜ and N_c. Covariances between counts from different rotations are derived analytically, allowing the full vector of counts (wins and losses for all rotations) to be modeled as a multivariate normal distribution. By applying a linear transformation that aggregates wins and losses across rotations, the authors obtain the asymptotic distribution of log(RWR) via the delta method. Consequently, a Wald confidence interval and a z‑test for H₀: RWR = 1 are readily available. Under the null hypothesis the win and loss probabilities are set to ½, providing a variance estimator that respects the symmetry of the null.

The framework is extended to stratified trials. For each stratum s, a separate RWR is computed and then combined using pre‑specified weights w(s), yielding a stratified RWR that retains the block‑rotation structure.

Simulation studies evaluate the operating characteristics of RWR under two realistic scenarios. The first scenario places death at the top of the hierarchy and three non‑fatal time‑to‑event endpoints of comparable importance in a single block. The second scenario includes a fatal event above a recurrent non‑fatal event, where the recurrent event is summarized by three statistics (total count, time to first recurrence, time to last recurrence) forming a block. Across a range of event rates, censoring proportions, block sizes, and sample sizes, RWR consistently controls type I error at the nominal 5 % level, achieves power comparable to or slightly higher than the standard WR, and provides confidence intervals with coverage close to the nominal level. Notably, when recurrent information is incorporated, the rotation approach captures additional information that would be lost under a strict first‑event analysis.

The methodology is illustrated with data from the Systolic Blood Pressure Intervention Trial (SPRINT). Five endpoints—death, major cardiovascular events, hospitalization, blood‑pressure target failure, and a composite of non‑fatal events—are grouped into three blocks: {death}, {major cardiovascular events, hospitalization}, and {blood‑pressure target failure}. Applying RWR yields an estimate of 1.27 (95 % CI 1.08–1.49), indicating a modestly stronger treatment effect than the conventional WR estimate of 1.22. The authors also present block‑level win, loss, and tie proportions, facilitating clinical interpretation of which endpoint groups drive the overall benefit.

The authors discuss the practical implications of RWR. By allowing equal priority within blocks, the method aligns with clinical situations where several outcomes are judged to have similar importance, accommodates recurrent event summaries, and supports shared decision‑making where patient preferences may dictate equal weighting of certain outcomes. The U‑statistics‑based inference avoids computationally intensive bootstrapping or permutation tests, offering analytic variance estimates and straightforward confidence interval construction. A limitation is the potential combinatorial explosion of rotations when blocks contain many endpoints (p = ∏_r |G_r|!), which can increase computational burden; the authors suggest future work on approximation or sampling strategies to mitigate this issue.

In conclusion, the Rotation Win Ratio provides a statistically rigorous yet flexible extension of win‑ratio methodology. It preserves the interpretability of hierarchical analyses while introducing the ability to treat subsets of endpoints as equally important. Simulation results and the SPRINT case study demonstrate valid inference, good power, and practical utility. The approach broadens the applicability of win‑statistics to a wider range of clinical trial designs, especially those involving recurrent events, composite endpoints with mixed importance, and patient‑centered outcome weighting.