Multicenter Competing Risks Analysis

Kaplan-Meier assumes that censored individuals have the same future risk as those still under observation. Competing events violate this assumption because a patient who dies from another cause truly cannot experience the primary event. Treating them as censored overestimates the cumulative incidence of the primary event. The Aalen-Johansen estimator and the Fine-Gray model avoid this by explicitly accounting for the probability mass absorbed by competing events.

Use the Fine-Gray subdistribution hazard model when your primary question is about absolute risk — the probability that a patient with given characteristics will experience the event by a particular time, factoring in competing risks. Use cause-specific Cox models when your question is etiological — whether a risk factor accelerates the biological process leading to the event, independent of competing events. In most multicenter clinical studies, both should be reported.

The most common approaches are stratification (allowing each center its own baseline hazard), inclusion of a center fixed effect as a covariate, robust sandwich standard errors clustered at the center level, and random-effects frailty models. Stratification is preferred when center-specific baseline hazards are expected to differ substantially; frailty models are preferred when the number of centers is large and center effects are of scientific interest.

Sample size depends on the expected cumulative incidence of the primary event (not the overall event rate), the number of covariates in the model, and the degree of clustering. Rules of thumb from cause-specific Cox regression (roughly 10–15 events per covariate) provide a starting point, but simulation-based power calculations using the Fine-Gray model are preferred when competing event rates are substantial.

Yes. Meta-analytic approaches (analyzing center-level summary statistics and pooling estimates) and federated learning frameworks that compute gradients or sufficient statistics locally are viable when data sharing is legally or logistically infeasible. However, federated approaches for the Fine-Gray model require specialized algorithms and may lose some efficiency relative to individual patient data pooling.