Competing Risks

Competing risks arise when a subject can experience one of several mutually exclusive event types, and the occurrence of one event prevents or alters the chance of observing another — for example, death from a cause other than the one under study removes the subject from the possibility of that event. Standard single-event survival methods can mislead in this setting, so competing-risks analysis uses tailored estimators.

Definition

A competing risk is an event whose occurrence precludes or fundamentally alters the probability of the event of primary interest; competing-risks analysis estimates the probability of each event type over time while accounting for the others, principally through cause-specific hazards and the cumulative incidence function.

Scope

This topic covers why naive Kaplan-Meier estimation overstates the risk of one event when others compete, the distinction between the cause-specific hazard and the cumulative incidence function, and regression approaches including cause-specific Cox models and the Fine-Gray subdistribution model. It is methodological reference material and not clinical guidance.

Core questions

• Why does treating competing events as ordinary censoring bias the estimated probability of an event?
• How do the cause-specific hazard and the cumulative incidence function differ in what they describe?
• When should a cause-specific Cox model versus a Fine-Gray subdistribution model be used?
• How are competing-risks results interpreted and reported?

Key concepts

• Mutually exclusive event types
• Cause-specific hazard
• Cumulative incidence function (CIF)
• Subdistribution hazard
• Fine-Gray model
• Gray's test
• Independent-censoring violation
• One-minus-Kaplan-Meier overestimation

Mechanisms

When competing events are treated as ordinary censoring, the independent-censoring assumption is violated, and one minus the Kaplan-Meier estimate overstates the probability of the event of interest because it implicitly assumes censored subjects could still have that event. The cumulative incidence function instead estimates the probability of each specific event by a given time in the real world where the other events also occur, and it sums across event types to the total probability of any event. Two regression frameworks address covariate effects: cause-specific Cox models, which model the hazard of each event among those still event-free and answer aetiologic questions, and the Fine-Gray model, which models the subdistribution hazard directly tied to the cumulative incidence and is suited to prediction. Group comparison of cumulative incidence uses Gray's test (Fine & Gray, 1999; Gray, 1988; Putter et al., 2007; Austin et al., 2016).

Clinical relevance

Competing risks are common in older or sicker populations where, for instance, death from other causes competes with the outcome under study; ignoring them can substantially overstate the risk of that outcome and distort comparisons. Recognising this is important for appraising prognostic studies; the entry describes methodology and is not a basis for individual clinical decisions.

Epidemiology

Competing-risks settings are frequent in cardiology, oncology, transplantation, and geriatrics, where multiple causes of failure coexist; methodological tutorials in major clinical journals have promoted appropriate analysis as awareness has grown (Austin et al., 2016).

Evidence & guidelines

There are no clinical guidelines for competing-risks analysis itself; the methodological references are Gray's test for cumulative incidence (Gray, 1988), the Fine-Gray subdistribution model (Fine & Gray, 1999), tutorials for biostatistics and clinical audiences (Putter et al., 2007; Austin et al., 2016), and survival-analysis texts (Klein & Moeschberger, 2003).

History

The cumulative incidence function and cause-specific hazards have long roots in actuarial and biostatistical work on multiple decrement, but modern practice was shaped by Gray's 1988 K-sample test for cumulative incidence and the Fine-Gray 1999 subdistribution hazard model, which together provided practical estimation, testing, and regression. Tutorials in the 2000s and 2010s carried these methods into routine clinical research (Putter et al., 2007; Austin et al., 2016).

Debates

Cause-specific hazard versus subdistribution (Fine-Gray) model?

Cause-specific models address aetiologic questions about the rate of an event among those at risk, while Fine-Gray models target the cumulative incidence for prediction; analysts debate which to report, and many recommend presenting both rather than choosing one.

Key figures

• Jason P. Fine
• Robert J. Gray
• Hein Putter
• Peter C. Austin

Seminal works

• fine-gray-1999
• gray-1988

Frequently asked questions

Why can't I just use a Kaplan-Meier curve when there are competing risks?

Treating competing events as censoring violates the independence assumption and makes one minus the Kaplan-Meier estimate overstate the event's probability; the cumulative incidence function should be used instead.

What is the difference between the cause-specific hazard and the cumulative incidence function?

The cause-specific hazard is the rate of a particular event among subjects still event-free and answers aetiologic questions, whereas the cumulative incidence function gives the actual probability of that event by a given time in the presence of the competing events.