On the implications of proportional hazards assumptions for competing risks modelling

Simon M. S. Lo, Ralf Wilke and Takeshi Emura

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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.

Date: 2025-08
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