Competing event regression on the relative subdistribution and cumulative-incidence scales
- 1University of California San Diego
Abstract
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) by a stacked per-cause 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, and rho through the shared survivor. Each carries a covariance term that must be handled and bounds efficiency relative to the hazard-scale test. We derive the corresponding variances, study operating characteristics by simulation, illustrate on hypothetical clinical cohorts, and provide an implementation in the gcemod R package.
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BibTeX
@misc{mell2026competing,
title = {{Competing event regression on the relative subdistribution and cumulative-incidence scales}},
author = {L. K. Mell and M. Overgaard},
howpublished = {medRxiv},
year = {2026},
month = aug,
doi = {10.64898/2026.08.13.26360204},
url = {https://www.medrxiv.org/content/10.64898/2026.08.13.26360204v2},
note = {CC BY-ND},
}
RIS
TY - UNPB
TI - Competing event regression on the relative subdistribution and cumulative-incidence scales
AU - L. K. Mell
AU - M. Overgaard
PY - 2026
DA - 2026/08/13
PB - medRxiv
DO - 10.64898/2026.08.13.26360204
UR - https://www.medrxiv.org/content/10.64898/2026.08.13.26360204v2
AB - 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) by a stacked per-cause 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, and rho through the shared survivor. Each carries a covariance term that must be handled and bounds efficiency relative to the hazard-scale test. We derive the corresponding variances, study operating characteristics by simulation, illustrate on hypothetical clinical cohorts, and provide an implementation in the gcemod R package.
ER -