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This study extends the generalized competing event (GCE) framework to analyze the ratio between competing events in survival analysis using two additional scales: the subdistribution hazard ratio and the cumulative-incidence ratio. The authors develop statistical methods to estimate these ratios through stacked regression models and pseudo-observation techniques, demonstrating that while the cause-specific hazard ratio can be estimated efficiently, the cumulative-incidence scales involve covariance terms that reduce statistical efficiency. They provide mathematical relationships between the three ratio measures and validate their methods through simulations and clinical examples.
Why it matters
This work provides clinicians and researchers with new tools to directly compare the relative likelihood of competing events (such as disease-specific death versus other causes of death), which may reveal important differences between patient groups even when individual event rates appear similar. The gcemod R package makes these advanced statistical methods accessible for practical use in medical research.
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⚠️ Preprint – Noch nicht peer-reviewed
Dieser Artikel wurde noch nicht von unabhängigen Experten begutachtet. Die Ergebnisse sind vorläufig und sollten mit Vorsicht interpretiert werden.
In competing risks settings, covariate effects and group comparisons are usually assessed one event at a time – through log-rank or Cox tests on the cause-specific hazards, or Gray’s test or Fine-Gray regression on a cumulative incidence function (CIF). This can obscure a clinically important quantity: the ratio between the event of interest and the competing event, since groups may differ little on the individual events yet differ sharply in their ratio. The generalized competing event (GCE) framework makes this ratio the object of inference; on the cause-specific scale the hazard ratio omega+(t) = lambda_1(t)/lambda_2(t) is estimated efficiently from a single stacked (Lunn-McNeil) model. We extend the framework to two scales that describe realized incidence. The subdistribution hazard ratio omega-tilde+(t) = lambda-tilde_1(t)/lambda-tilde_2(t) is estimated by a stacked, risk-set-weighted extension of the Lunn-McNeil construction; the cumulative-incidence ratio rho(t) = F_1(t)/F_2(t) – the odds that a subject’s realized event by time t is the event of interest – by jackknife pseudo-observation regression of the Aalen-Johansen estimator. We relate the three contrasts: rho equals omega+ exactly under proportional cause-specific hazards, and equals omega-tilde+ only in the small-time limit under proportional subdistribution hazards, drifting toward 1 thereafter. The orthogonality that makes omega+ efficient is lost on both cumulative-incidence scales – omega tilde+ through overlapping weighted risk sets and shared censoring weights, rho through the shared all-cause survivor – so each carries a covariance term that must be handled and that bounds efficiency relative to the hazard-scale test. We derive the corresponding variances, study operating characteristics by simulation, illustrate on hypothetical prostate and head-and-neck cohorts, and provide an implementation in the gcemod R package.
Source: Competing event regression on the relative subdistribution and cumulative-incidence scales