Competing Risk Analysis
Competing Risk Analysis handles survival data with multiple possible failure types — where a subject can experience one of several mutually exclusive events and occurrence of one prevents the others from being observed.
Step 1 — Define events and provide data
- Time — follow-up time
- Event Type — 0 (censored), 1 (event of interest), 2+ (competing events)
- Group — optional grouping variable
- Covariates — optional for regression
Define an Event Type Definition table labelling each code.
Supports Excel Import, Sample Data Generator, and Manual Entry.
Step 2 — Results
Cumulative Incidence Functions (CIFs):
- For each (group, event type): CIF estimate, SE, 95% CI at each time
- CIF Plot — step curves per event type
Gray's Test (when >= 2 groups):
- Chi-square, df, p-value per event type
- Tests whether CIFs differ across groups
Cause-Specific Cox Regression:
- Cox model per event type (other events treated as censoring)
- Coefficients, HRs, 95% CI, p-values
Fine-Gray Subdistribution-Hazard Regression:
- Subdistribution HRs (sHR) per event type
- Directly interpretable on cumulative incidence scale
A UniversalChatBot is available for discussion.
Statistical methods used
CIF — Aalen-Johansen estimator
F_k(t) = sum(S(t_i-) * d_ik / n_i) where S accounts for ALL event types.
Corrects the overestimation of standard Kaplan-Meier when competing events exist.
Gray's Test
Competing-risks analogue of log-rank. Tests CIF equality across groups per event type.
Cause-Specific Cox
Separate Cox per event type; other events censored. Gives cause-specific HRs (biological interpretation).
Fine-Gray
Modified risk set keeps competing-event subjects. Gives subdistribution HRs (prognostic interpretation).
When to use which
| Goal | Use |
|---|---|
| Biological mechanism | Cause-specific HR |
| Prognosis/prediction | Fine-Gray sHR |
| Clinical papers | Both |