Risk-adjusted Competing Risks Analysis
Risk-adjusted Competing Risks Survival Analysis · Also known as: competing risks regression, subdistribution hazard model, cause-specific hazard analysis, Fine-Gray model
Risk-adjusted competing risks analysis extends classical survival analysis to settings where subjects can experience more than one type of terminal event, and where the occurrence of one event prevents the occurrence of another. By modelling cause-specific or subdistribution hazards while adjusting for measured confounders, the method yields unbiased estimates of the absolute probability — the cumulative incidence function — of each event type over time in the presence of competing events.
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When to use it
Use risk-adjusted competing risks analysis whenever subjects can experience mutually exclusive terminal events and the absolute risk of one specific event is the inferential target — for example, disease-specific mortality vs. other-cause mortality in oncology, or graft failure vs. death with functioning graft in transplant research. It is mandatory when 1 − Kaplan-Meier overestimates the event probability because competing events are common. It is not necessary when competing events are rare (less than roughly 5% of failures) or when the causal question concerns only subjects still at risk (in which case a standard Cox model on cause-specific hazard suffices). The method requires individual-level time-to-event data with known event type; it cannot be applied to aggregated or grouped data without individual records.
Strengths & limitations
- Correctly estimates the absolute probability of each event type; does not inflate cumulative incidence by treating competing events as censored.
- The Fine-Gray subdistribution hazard model directly models the quantity of clinical interest — the CIF — making it suitable for risk prediction and individualized patient counselling.
- Allows full multivariable risk adjustment using standard covariate-entry or propensity-score methods.
- Provides a coherent framework: cumulative incidences of all event types sum to total failure probability, offering a natural consistency check.
- Widely implemented in R (cmprsk, riskRegression, timereg), Stata (stcrreg, stcrprep), and SAS (PROC PHREG).
- Requires individual-level time-to-event data with unambiguous event-type classification; not applicable to grouped or aggregate data.
- The subdistribution hazard has no simple biological interpretation — it is a mathematical construct linking to the CIF, not a direct hazard experienced by any real risk set.
- Risk adjustment controls only for measured confounders; unmeasured confounding in observational studies remains a threat.
- Proportionality assumptions (constant subdistribution or cause-specific hazard ratio over time) must be verified and may not hold over long follow-up.
Frequently asked
When should I use the Fine-Gray model versus the cause-specific hazard model?
Use the Fine-Gray subdistribution hazard model when your goal is predicting absolute risk or estimating the effect of a covariate on the CIF — the quantity directly relevant to clinical decision-making. Use the cause-specific hazard model when your goal is aetiological: understanding what drives the event process among those still at risk of experiencing it. Ideally, both analyses are reported and interpreted together.
Can I use Kaplan-Meier if competing events are rare?
If competing events constitute fewer than roughly 5% of all failures, the upward bias in 1 − Kaplan-Meier is negligible and a standard Kaplan-Meier plus Cox analysis is acceptable. When competing events are common — as in elderly or comorbid populations — the CIF must be used and Kaplan-Meier estimates should not be presented as event probabilities.
Does risk adjustment work the same way as in a standard Cox model?
Yes, in terms of syntax and covariate entry the Fine-Gray and cause-specific Cox models closely resemble a standard Cox model. The key difference is the risk set: in the Fine-Gray model, subjects who experienced a competing event remain in the risk set with diminishing weights, whereas in a standard Cox or cause-specific model they are censored. Propensity scores and IPTW can both be applied within the competing risks framework.
How do I check the proportional subdistribution hazard assumption?
Plot the log(−log(CIF)) against log(time) for categorical covariates: parallel curves indicate proportionality. For continuous covariates, scaled Schoenfeld-type residuals are available in R packages such as riskRegression and timereg. If non-proportionality is found, consider time-varying coefficient models or stratified analyses.
What software can I use?
In R, the cmprsk package provides the crr() function for Fine-Gray regression and cuminc() for CIF estimation. The riskRegression and timereg packages offer more flexible competing risks regression with diagnostics. In Stata, stcrreg implements the Fine-Gray model. SAS users can fit subdistribution hazard models with PROC PHREG using the EVENTCODE option.
Sources
- Fine, J. P., & Gray, R. J. (1999). A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association, 94(446), 496–509. DOI: 10.1080/01621459.1999.10474144 ↗
- Latouche, A., Allignol, A., Beyersmann, J., Labopin, M., & Fine, J. P. (2013). A competing risks analysis should report results on all cause-specific hazards and cumulative incidence functions. Journal of Clinical Epidemiology, 66(6), 648–653. DOI: 10.1016/j.jclinepi.2012.09.017 ↗
How to cite this page
ScholarGate. (2026, June 3). Risk-adjusted Competing Risks Survival Analysis. ScholarGate. https://scholargate.app/en/epidemiology/risk-adjusted-competing-risks-analysis
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Cox proportional hazardsEpidemiology↔ compare
- Kaplan-Meier EstimatorStatistics↔ compare
- Propensity Score MatchingResearch Statistics↔ compare
- Survival AnalysisResearch Statistics↔ compare