Competing Risks — Fine-Gray + Aalen-Johansen CIF (multi-cause survival)

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Time-to-event analysis when subjects can experience one of ≥ 2 mutually exclusive event types (e.g., cancer death vs other-cause death; graft rejection vs patient death).

Standard KM overestimates the cumulative incidence of each cause when competing events exist; the Aalen-Johansen estimator gives the correct CIF. Reports cause-specific CIF per group, Gray's test for between-group differences in CIF, plus cause-specific Cox AND Fine-Gray subdistribution-hazards regression. Standard tool in oncology, transplantation, cardiology, and aging research.

Worked example

Does a drug change the chance of relapse when death is a competing event?

Patients could relapse OR die without relapsing (a competing event). Cumulative incidence functions and Gray's test compare relapse incidence across arms without over-counting.

Result

The end-of-follow-up cumulative incidence of relapse was lower on the drug (18% vs 30%), while death-without-relapse did not differ.

How you'd report it (APA)

In a competing-risks analysis, the cumulative incidence of relapse was lower on the drug (18% vs 30%).

Try it yourself: Load this ready-made sample and follow the run above.

When to use it

  • Two-group competing-risks comparison
    Trial of adjuvant chemotherapy vs control in early-stage cancer.
  • k-group competing-risks comparison
    Comparing 5-year cardiovascular death across 4 statin regimens (low, moderate, high intensity, ezetimibe), with non-CV death as competing event.
  • Covariate-adjusted competing-risks regression
    Cancer-specific mortality adjusted for age, tumour stage, and treatment arm via Fine-Gray regression with non-cancer death as competing event.

When NOT to — use instead

Hypotheses

H₀: CIFs for cause k are equal across groups (Gray's test) AND all sHR β_j = 0 (Fine-Gray regression).
Hₐ: At least one group's CIF differs OR at least one β_j ≠ 0.

Parameter tested: CIF per cause per group; log-subdistribution-hazard coefficients β + log-cause-specific-hazard coefficients β.

Assumptions (and what to do if they fail)

Each covariate's subdistribution hazard ratio is CONSTANT over time. Violation means the effect on the CIF is time-varying.medium

Check: Visual −log(1 − CIF) plot — parallel lines indicate PH.

If violated: Non-PH inflates / attenuates the subdistribution HR; the effect on the CIF may be time-varying.

Censoring is INDEPENDENT of the cause-specific hazards — censored subjects would have had the same CIF as remaining at-risk subjects.high

Check: Per-group censoring rates within 30 pct pts.

If violated: Informative censoring biases the CIF and the subdistribution HR.

No single subject dominates the sHR estimates. DFBETAS or score residuals flag influence.low

Check: Max |score residual| per subject.

If violated: An outlier can drive a single subdistribution coefficient.

Ready to run a Competing Risks — Fine-Gray + Aalen-Johansen CIF (multi-cause survival) on your own data?

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