Competing Risks – Part 2
Bryan Lau, Johns Hopkins University
A complication of time to event analyses is when there is an event that prevents the event of interest from occurring. The discussion of this idea of competing events has been contemplated for centuries and dates back at least to the 17000s when Bernoulli estimated mortality rates. However, while common in epidemiologic research, the interest in competing risk methods in epidemiology has seemed greatly increased over the past decade or two. This perhaps may be due in part to the resulting debate in the statistical literature in the 1970s. Prior approaches used a latent failure time approach in which identification of the joint survival distribution across multiple events is problematic. A shift towards estimating the hazards (specifically the so called cause-specific hazards) was then promulgated since identification is not a concern. Then in 1999, Fine and Gray published their seminal paper for estimating a proportional hazards model based upon the “subdistribution”-hazard function. These two realizations has made competing risk methods more approachable. Additionally of late, I have seen more and more papers focusing on a multi-state approach to competing risks rather than a latent failure time approach. This is interesting as in a latent failure time framework, one has to be concerned about the events being dependent on one another. However under a multi-state framework, the outcome is a realization of a single random variable in which each event is a part of. Therefore the idea of (in)dependence is not applicable. Nevertheless, the jargon (e.g. hazard, cause-specific hazard, subdistribution-hazard, latent failure time, multi-state framework, etc.) has perhaps made the field somewhat difficult to navigate. The following playlist will hopefully help unpack the concepts behind competing risk methods such that one will be able to understand the difference between what a cause-specific hazard ratio is measuring as compared to a subhazard hazard ratio as well as expose you to different approaches and study design.
The playlist (Part 2):
While the papers in Part 1 focus on semi-parametric approaches in which one needs to choose between a cause-specific or subdistribution, I would like to point out one can estimate the cumulative incidence function, subdistribution hazards, and cause-specific hazards in a fully parametric mixture model (Checkley; Lau, 2011) an approach which was promulgated by Larson and Dinse (1985, Applied Statistics) as well as a non-parametric approach for competing risks using a random forest (Ishwaran). Briefly, as epidemiologists we are just as concerned if not more so about study design than the analytical methods. The last two papers in the list refers to competing risks in nested study designs (Wolkewitz; Pintilie).