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