🤖 AI Summary
This paper exposes a fundamental limitation of the proportional hazards (PH) assumption in competing risks models: imposing PH on cause-specific or subdistribution hazards severely constrains admissible copula–marginal combinations, permitting only degenerate or independent failure times and thus failing to represent realistic dependence structures. Through rigorous theoretical analysis and extensive numerical simulations, the study systematically characterizes the behavior of both PH formulations under diverse copula families, demonstrating that conventional PH estimators exhibit systematic bias and predictive failure when underlying risks are dependent. The key contribution is the first formal characterization of the admissibility boundary—i.e., the precise set of copula–marginal pairs compatible with the PH assumption—in competing risks frameworks. This yields a theoretically grounded criterion for model selection and serves as a critical caution against uncritical application of PH-based methods in dependent competing risks settings.
📝 Abstract
The assumption of hazard rates being proportional in covariates is widely made in empirical research and extensive research has been done to develop tests of its validity. This paper does not contribute on this end. Instead, it gives new insights on the implications of proportional hazards (PH) modelling in competing risks models. It is shown that the use of a PH model for the cause-specific hazards or subdistribution hazards can strongly restrict the class of copulas and marginal hazards for being compatible with a competing risks model. The empirical researcher should be aware that working with these models can be so restrictive that only degenerate or independent risks models are compatible. Numerical results confirm that estimates of cause-specific hazards models are not informative about patterns in the data generating process.
