On the implications of proportional hazards assumptions for competing risks modelling

2025-08-14

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.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

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.

Problem

• Examines implications of proportional hazards in competing risks models
• Shows PH models restrict copulas and marginal hazards compatibility
• Highlights risks of degenerate or independent models in empirical research

Innovation

• Analyzes PH implications in competing risks
• Identifies restrictive copulas and hazards
• Shows PH models limit risk compatibility