Competing Risk Analysis in Cardiovascular Outcome Trials: A Simulation Comparison of Cox and Fine-Gray Models

TL;DR

This work tackles competing risks in cardiovascular outcome trials by comparing Cox proportional hazards and Fine-Gray subdistribution hazard models through a comprehensive copula-based simulation. It shows that in typical CVOT contexts with low competing risks, both methods yield similar conclusions, while divergence arises mainly under high competing risk rates and discordant treatment effects on competing events; neither approach reliably recovers the true marginal hazard ratio except under special conditions. The authors emphasize prespecified primary analyses (Cox) and cautious use of Fine-Gray as supplementary descriptive analysis, with alternatives like Aalen-Johansen-based cumulative incidence, IPCW, or multistate models considered in high-risk scenarios. The findings have practical implications for trial design, analysis planning, and regulatory discussions, supporting interpretability and integrity of CVOT results while acknowledging limitations and context-specific method benefits.

Abstract

Cardiovascular outcome trials commonly face competing risks when non-CV death prevents observation of major adverse cardiovascular events (MACE). While Cox proportional hazards models treat competing events as independent censoring, Fine-Gray subdistribution hazard models explicitly handle competing risks, targeting different estimands. This simulation study using bivariate copula models systematically varies competing event rates (0.5%-5% annually), treatment effects on competing events (50% reduction to 50% increase), and correlation structures to compare these approaches. At competing event rates typical of CV outcome trials (~1% annually), Cox and Fine-Gray produce nearly identical hazard ratio estimates regardless of correlation strength or treatment effect direction. Substantial divergence occurs only with high competing rates and directionally discordant treatment effects, though neither estimator provides unbiased estimates of true marginal hazard ratios under these conditions. In typical CV trial settings with low competing event rates, Cox models remain appropriate for primary analysis due to superior interpretability. Pre-specified Cox models should not be abandoned for competing risk methods. Importantly, Fine-Gray models do not constitute proper sensitivity analyses to Cox models per ICH E9(R1), as they target different estimands rather than testing assumptions. As supplementary analysis, cumulative incidence using Aalen-Johansen estimator can provide transparency about competing risk impact. Under high competing-risk scenarios, alternative approaches such as inverse probability of censoring weighting, multiple imputation, or inclusion of all-cause mortality in primary endpoints warrant consideration.

Figures (6)

• Figure 1: Estimated (subdistribution) hazard ratio by $\theta_2$ ($\alpha = 1.0$). True HR = 0.80 (horizontal dashed line)
• Figure 2: Estimated (subdistribution) hazard ratio by $\theta_2$ ($\alpha = 1.2$). True HR = 0.80 (horizontal dashed line)
• Figure 3: Estimated (subdistribution) hazard ratio by $\theta_2$ ($\alpha = 1.5$). True HR = 0.80 (horizontal dashed line)
• Figure 4: Estimated (subdistribution) hazard ratio by $\theta_2$ ($\alpha = 2.0$). True HR = 0.80 (horizontal dashed line)
• Figure 5: Cox HR Bias by $\theta_2$ across correlation levels. The figure shows bias in Cox HR estimates (deviation from true HR = 0.80) across different treatment effects on competing risk ($\theta_2$, x-axis) for different competing event rates. Four panels represent different correlation strengths ($\alpha = 1.0, 1.2, 1.5, 2.0$). The shaded region ($\theta_2 = 0.7-0.9$) demonstrates minimal bias when treatment effects are directionally consistent across primary and competing events. When $\theta_2 \approx \theta_1 = 0.80$, all curves converge near zero bias regardless of competing event rate or correlation level.