Multicenter Cox Proportional Hazards — Survival Regression Across Multiple Sites

In a stratified Cox model, each center has its own non-parametric baseline hazard; covariate effects are assumed to be the same across centers. It is non-parametric with respect to center differences and makes no assumption about the distribution of center effects. A frailty model treats center as a random effect drawn from a specified distribution (usually gamma or log-normal), explicitly estimating the variance of center effects and producing shrinkage estimates of center-specific hazards. Frailty models are more powerful when the number of centers is large and center effects are genuinely random; stratified models are safer with few centers or when between-center differences are structural rather than random.

Individual patient data (IPD) are strongly preferred because they allow proper handling of clustering, testing of the proportional hazards assumption at the individual level, and adjustment for patient-level confounders. Aggregate-data meta-analysis using published log hazard ratios and standard errors is a secondary option when IPD are unavailable, but it cannot account for within-study heterogeneity or verify model assumptions.

Include a center-by-treatment interaction term in the Cox model and assess its statistical significance. Visually, plot center-specific Kaplan-Meier curves and center-specific hazard ratio estimates with their confidence intervals (forest plot). Substantial heterogeneity of effect across centers (significant interaction, wide spread in forest plot) indicates that a single pooled effect estimate should be interpreted cautiously.

First identify whether the violation is global or restricted to specific covariates or centers. Options include: adding time-varying coefficients (interacting predictors with log-time), stratifying the analysis at a time split point, switching to a parametric accelerated failure time model if the hazard form is known, or reporting restricted mean survival time (RMST) differences as a summary measure that does not require the PH assumption.

Yes. The cause-specific Cox model fits a separate Cox model for each event type, treating other events as censored — this extends naturally to multicenter data with stratification or frailty terms per center. Alternatively, the Fine-Gray subdistribution hazard model for the cumulative incidence function can be stratified by center. The choice depends on whether the scientific question is about the biological hazard of a specific event (cause-specific) or the actual probability of occurrence in the presence of competing events (Fine-Gray).