The Analysis of Failure Times in the Presence of Competing Risks

TLDR

Analysis of failure times with competing risks faces challenges such as estimating treatment effects on specific failure types, studying interrelations among causes, and estimating failure rates when certain causes are removed, yet conventional latent‑time formulations are criticized for unwarranted assumptions, lack of physical interpretation, and identifiability issues. The study proposes an alternative approach that uses cause‑specific hazard functions for observable quantities, including time‑dependent covariates. The authors propose estimating parameters linking time‑dependent risk indicators for some causes to cause‑specific hazard functions for other causes, and illustrate this framework using a bone‑marrow transplantation program for leukemia and a survivorship study with censoring. The study demonstrates that cause‑specific hazard functions are the fundamental estimable quantities in competing‑risks analysis, and that estimating failure rates after removing certain causes is ill‑posed without a specified removal mechanism, though once specified, sensible extrapolations from available data become possible.

Abstract

Distinct problems in the analysis of failure times with competing causes of failure include the estimation of treatment or exposure effects on specific failure types, the study of interrelations among failure types, and the estimation of failure rates for some causes given the removal of certain other failure types. The usual formation of these problems is in terms of conceptual or latent failure times for each failure type. This approach is criticized on the basis of unwarranted assumptions, lack of physical interpretation and identifiability problems. An alternative approach utilizing cause-specific hazard functions for observable quantities, including time-dependent covariates, is proposed. Cause-specific hazard functions are shown to be the basic estimable quantities in the competing risks framework. A method, involving the estimation of parameters that relate time-dependent risk indicators for some causes to cause-specific hazard functions for other causes, is proposed for the study of interrelations among failure types. Further, it is argued that the problem of estimation of failure rates under the removal of certain causes is not well posed until a mechanism for cause removal is specified. Following such a specification, one will sometimes be in a position to make sensible extrapolations from available data to situations involving cause removal. A clinical program in bone marrow transplantation for leukemia provides a setting for discussion and illustration of each of these ideas. Failure due to censoring in a survivorship study leads to further discussion.