Empirical comparison of win ratio and joint frailty models for recurrent event endpoints with applications in oncology and cardiology

Technical Summary: Empirical Comparison of Win Ratio and Joint Frailty Models for Recurrent Event Endpoints

Problem Statement
Composite endpoints (CEs) combining recurrent non-fatal events (e.g., hospitalizations, relapses) with a terminal event (e.g., death) are increasingly utilized in randomized clinical trials (RCTs) to capture disease burden more comprehensively than single components. However, conventional time-to-first-event analyses often obscure clinically relevant information by discarding data after the first non-fatal event and treating death as non-informative censoring. This approach fails to account for three critical methodological challenges: (1) within-subject dependence due to unobserved heterogeneity and state dependence; (2) the semi-competing risks structure where death precludes further recurrences; and (3) the informative nature of death, which is often correlated with the recurrent event process.

This study addresses the need to compare two statistical frameworks tailored to such endpoints: the Joint Frailty Model (JFM) and the Last-Event Assisted Recurrent-Event Win Ratio (LWR). While JFM provides component-specific hazard ratios accounting for dependence, LWR offers a nonparametric, prioritized pairwise comparison summarizing population-level treatment benefit.

Methodology
The authors conducted a comprehensive empirical comparison involving simulation studies and real-world applications.

• Statistical Frameworks:

  • Joint Frailty Model (JFM): A model-based approach specifying proportional hazards for recurrent and terminal events linked by a shared gamma frailty term ($\omega_i$). This induces dependence between the processes and accounts for unobserved heterogeneity. Estimation is performed via penalized likelihood (using M-splines or parametric Weibull baselines) in the frailtypack R package.
  • Win Ratio (WR): A nonparametric approach based on pairwise comparisons of patients from treatment and control arms. The study focuses on the Last-Event Assisted Win Ratio (LWR), which prioritizes death, then compares the total count of recurrent events, and finally breaks ties using the time of the last recurrence. This utilizes the full history of events rather than just the first. Inference relies on asymptotic normality of the log win ratio.

• Simulation Design:

  • Data Generation: 500 datasets were simulated per scenario ($N=400$ subjects, 1:1 allocation) using inverse transform sampling from a gamma-frailty JFM.
  • Scenarios: Six scenarios varied the frailty variance ($\theta$), event rates (high/low death vs. high/low recurrence), and baseline hazard misspecification (log-logistic vs. Weibull).
  • Performance Metrics: Bias, coverage rates, empirical power, and sample size estimation capabilities were evaluated.

• Applications:

  • Oncology (Readmission): A prospective cohort of colorectal cancer patients analyzing readmissions and death.
  • Cardiology (HF-ACTION): A subgroup of heart failure patients analyzing rehospitalizations and death.

• Sample Size Calculation:

  • JFM: Utilized a Monte Carlo-based approach (via frailtyDesign) to estimate power and required sample sizes based on Fisher information.
  • LWR: The authors modified the existing WR package to implement a simulation-based sample size calculation, as standard formulas (e.g., Mao et al.) do not account for recurrent events.

Key Results

• Estimation Performance: Both methods provided well-calibrated point estimates. JFM regression coefficients were essentially unbiased, though the frailty variance ($\theta$) was difficult to estimate under near-homogeneity or model misspecification. LWR estimates showed small relative bias and maintained nominal coverage.
• Statistical Power: The JFM consistently demonstrated superior statistical power compared to the LWR across all simulation scenarios. For instance, in the base scenario, JFM power was 82% versus 40.6% for LWR. The power advantage of JFM persisted even under baseline hazard misspecification. LWR power was highest in scenarios with frequent recurrent events (Scenario 5) but remained lower than JFM.
• Stratification: Stratifying the LWR by baseline covariates yielded negligible improvements in power unless those covariates directly modified the baseline hazards, a finding that contrasts with some previous literature.
• Real-World Applications:
  • In the Readmission dataset, JFM revealed opposing effects of chemotherapy (reducing readmissions but increasing death risk), leading to a non-significant net effect in LWR. The LWR could not disentangle these opposing component effects.
  • In the HF-ACTION dataset, both methods detected a beneficial treatment effect, with JFM showing significance for readmissions and LWR showing significance for the composite.
• Sample Size: The Schoenfeld formula (time-to-first-event) required the largest sample sizes. The JFM-based approach generally required fewer subjects than the standard Win Ratio approach. However, simulation-based LWR sample sizes were highly sensitive to assumptions regarding heterogeneity and event rates, often yielding much larger requirements than JFM when heterogeneity was high.

Significance and Claims
The paper claims that for composite endpoints involving recurrent events and death, the Joint Frailty Model is the most reliable approach for inference and sample size estimation due to its superior statistical power and ability to provide component-specific estimates.

The authors highlight that while the Win Ratio (specifically LWR) is a valuable nonparametric tool that respects clinical hierarchies and utilizes full event histories, it suffers from lower power in the presence of unobserved heterogeneity and cannot separate treatment effects on individual components. This limitation is critical when treatments have opposing effects on different endpoints (e.g., reducing recurrences while increasing mortality), as the LWR may obscure these nuances.

The study concludes that JFM should be preferred as the primary analysis method when:

1. Treatment effects on components may differ in direction.
2. Component-specific estimates or covariate adjustments are required.
3. High statistical power is needed for sample size planning.

Conversely, the LWR remains a promising direction for future research, particularly if methodological extensions are developed to handle censoring robustly (e.g., via IPCW) and to formalize causal estimands at the individual level. The authors provide a modified R package to facilitate simulation-based sample size calculations for recurrent-event win ratios, addressing a current gap in the literature.