Multi-Dimensional Composite Endpoint Analysis via the Choquet Integral: Block Recurrent Encoding and Comparative Advantage Mapping

TL;DR

This paper introduces CWOT-CE, a novel Choquet integral-based method for analyzing composite endpoints in cardiovascular trials, effectively capturing multiple outcome dimensions and outperforming traditional methods in simulations.

Contribution

The paper presents a new non-additive fuzzy measure approach that encodes six outcome dimensions, with permutation inference and component attribution, improving analysis of complex composite endpoints.

Findings

CWOT-CE maintains nominal Type I error in simulations.

Outperforms Cox TTFE, Win Ratio, and WLW in most scenarios.

Shows advantages in high-correlation, mortality-driven, and balanced effects.

Abstract

Background: Composite endpoints in cardiovascular trials combine heterogeneous outcomes-mortality, nonfatal events, hospitalizations, and biomarkers-yet conventional analytical methods sacrifice information by targeting a single dimension. Cox time-to-first-event ignores post-first-event data; Win Ratio discards tied pairs; negative binomial regression treats death as noninformative censoring. Methods: We propose CWOT-CE: a Choquet integral-based composite endpoint analysis that encodes K = 6 outcome dimensions-survival, event-free time, AUC recurrent burden, last event time, biomarker, and alive status-and aggregates them through a non-additive fuzzy measure with pairwise interaction terms. The recurrent event process is represented as two complementary scalar summaries: the area under the cumulative count curve (AUC burden) and the last event time. Inference is via permutation test with exact finite-sample Type I error control and dual confidence interval by inversion. We conducted a simulation study comparing CWOT-CE against Cox TTFE, Win Ratio (WRrec), and WLW across 20 clinically motivated scenarios (1,000-5,000 replications). Results: Under the sharp null (5,000 replications), all methods maintained nominal Type I error (CWOT-CE: 4.8%, MCSE 0.3%). Across 17 non-null scenarios, CWOT-CE outperformed Cox TTFE in 15 (mean +28.8 pp), WLW in 14 (mean +27.2 pp), and Win Ratio in 10, with 5 ties and only 2 narrow losses (mean +5.6 pp). CWOT-CE showed particular advantages in high-correlation settings (+35.4 pp vs. WR), mortality-driven effects (+10.7 pp), and balanced multi-component effects (+10.1 pp). Shapley decomposition correctly identified effect-bearing components across all calibration scenarios. Conclusions: CWOT-CE with block recurrent encoding is broadly effective across clinically relevant scenarios while offering unique interpretive advantages through component attribution.