Summary

Competing risks analysis addresses situations in which participants under observation may experience one of several mutually exclusive events, each of which precludes the occurrence of the others. Traditional survival methods, such as the Kaplan–Meier estimator and standard Cox proportional hazards model, can yield biased measures of absolute or relative event probabilities when a competing event is treated as simple censoring. Modern approaches distinguish between cause-specific hazards, which quantify the instantaneous risk of each event type, and subdistribution hazards, which directly relate covariates to the cumulative incidence of an event in the presence of competing events. The cumulative incidence function (CIF) provides a direct estimate of the probability of an event over time, accounting for competing events. These methods underpin clinical trial design, epidemiological registry analyses and risk prediction in fields as diverse as oncology, cardiovascular science and orthopaedics. Recent methodological advances have improved flexibility through smooth hazard estimation, better handling of non-proportional hazards and time-dependent covariates, and the application of simulation frameworks for study planning. Practitioners now routinely employ multi-state modelling, flexible parametric forms and robust software implementations to yield more accurate absolute and relative risk estimates, guiding both policy decisions and individualized patient counselling.

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Competing Risks Analysis in Survival Data publication trend

The graph below shows the total number of articles in competing risks analysis in survival data across all publications each year (not limited to Nature Index journals).

Technical terms

Competing risk: An event type that precludes the occurrence or alters the probability of the primary event of interest.

Cumulative incidence function (CIF): The probability of experiencing a specific event by a given time, accounting for competing events.

Cause-specific hazard: The instantaneous rate at which a particular event occurs, assuming no prior occurrence of any event.

Subdistribution hazard: A hazard function that relates covariates directly to the CIF by retaining subjects in the risk set after competing events.

Non-proportional hazards: A situation in which the effect of a covariate on the hazard varies over time rather than remaining constant.

References

  1. Flexible parametric modelling of cause-specific hazards to estimate cumulative incidence functions. BMC Medical Research Methodology (2013).
  2. Understanding competing risks: a simulation point of view. BMC Medical Research Methodology (2011).
  3. Simulation shows undesirable results for competing risks analysis with time-dependent covariates for clinical outcomes. BMC Medical Research Methodology (2018).

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