On the implications of proportional hazards assumptions for competing risks modelling

TL;DR

This paper explores how proportional hazards assumptions in competing risks models can overly restrict the possible data-generating processes, potentially leading to misleading inferences about risks.

Contribution

It provides new insights into the limitations imposed by PH models on copulas and marginal hazards in competing risks analysis.

Findings

PH models can restrict copula and hazard classes

Cause-specific hazard estimates may be uninformative

Restrictions can lead to degenerate or independent risks

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.