Competing risks

The Competing Risk Problem - More Than One Way Out

• A competing risk is an event that prevents the primary outcome of interest from occurring or fundamentally alters its probability.
• In a cohort study, individuals experiencing a competing event are removed from the at-risk population for the primary outcome.
  • Classic Example: In a study on death due to cardiovascular disease, death from cancer is a competing risk.
• Analytical Issue: Standard survival methods like Kaplan-Meier curves treat competing events as non-informative censoring. This violates the method's core assumption and leads to biased results.
  • Specifically, it causes an overestimation of the cumulative incidence of the event of interest.
• Solution: Use statistical models designed for this scenario.
  • The Cumulative Incidence Function (CIF) is the appropriate method to estimate the probability of an event in the presence of competing risks.

⭐ Using a standard Kaplan-Meier analysis when competing risks are present will incorrectly estimate the event probability. The resulting survival curve is often referred to as "immortal time bias" because it doesn't account for events that removed the patient from risk.

Cumulative Incidence (CIF) - The Right Tool for the Job

• The Problem: In cohort studies, a competing risk is an event that either prevents the event of interest from occurring or fundamentally alters the chance of its occurrence.

  • Example: In a study tracking death from prostate cancer, death from a heart attack is a competing risk.

• Why Kaplan-Meier (KM) Fails: The standard KM method is inappropriate when competing risks are present.

  • KM analysis censors subjects who experience a competing event.
  • This violates the core assumption of non-informative censoring, as the competing event is indeed informative.
  • Result: KM systematically overestimates the incidence of the event of interest.

• Solution: Cumulative Incidence Function (CIF): CIF provides a realistic estimate of incidence. It calculates the cumulative probability of a specific event occurring by a certain time, acknowledging the presence of competing risks.

  • The formula is conceptually: $CIF_k(t) = \sum [S(t_{j-1}) \times I_k(t_j)]$, where $S(t)$ is the overall event-free survival probability and $I_k(t)$ is the incidence of event k at time $t_j$.

• Graphical Interpretation:

  • A CIF curve for an event will plateau at a value < 1, representing the true proportion of individuals who experience that event.

⭐ In the presence of a significant competing risk, the sum of the probabilities from a standard Kaplan-Meier analysis for the event of interest and the competing risk can exceed 100%, which is impossible. CIF avoids this by correctly partitioning the probabilities.

Advanced Modeling - Cause-Specific vs. Fine-Gray

• Competing Risk: An event that prevents the primary outcome of interest from occurring.
• The choice of model hinges on the research question.

Flowchart? YES

High‑Yield Points - ⚡ Biggest Takeaways

• A competing risk is an event that precludes the occurrence of the primary outcome of interest.
• Traditional survival analyses (e.g., Kaplan-Meier) are invalid because they overestimate the probability of the event.
• They incorrectly treat competing events as non-informative censoring, which introduces bias.
• The correct approach uses competing risk regression (e.g., Fine-Gray model) to estimate the cumulative incidence function (CIF).
• The CIF provides a realistic probability of the event of interest.