Questions: Cumulative Incidence and Risk Estimation

Question 1

A study follows 500 people for 5 years to estimate cumulative incidence. By year 5, 50 people developed the outcome. Another 100 people were lost to follow-up at various points. A researcher computes 5-year CI as 50/500 = 10%. What is the fundamental problem?

• A. The numerator should include people lost to follow-up as potential cases
• B. The denominator treats all 500 as followed for the full 5 years, ignoring that censored individuals contributed less than 5 years of risk time — overstating the at-risk pool and underestimating true risk
• C. Cumulative incidence cannot be calculated over 5 years; it requires 10-year follow-up
• D. The formula is correct; loss to follow-up does not affect the denominator

Answer: (B)

Censored individuals were not followed to the event endpoint. Including them as full observations assumes they were at risk the entire period — overstating the denominator and underestimating risk. The Kaplan-Meier estimator corrects this by updating the at-risk count at each event time.

Question 2

In a 5-year study, the incidence rate is 0.02 per person-year. A colleague argues that the 5-year cumulative incidence is simply 0.02 × 5 = 0.10. This approximation is:

• A. Always correct — cumulative incidence equals rate × time by definition
• B. A valid approximation when outcomes are rare and follow-up is short, but increasingly incorrect as rates rise or durations lengthen
• C. Only valid for propagated outbreaks, not cohort studies
• D. Correct only when there is no censoring

Answer: (B)

When the outcome is rare and the time window short, CI ≈ rate × time. At longer durations or higher rates, this diverges substantially — the incidence rate is an instantaneous measure that assumes a constant hazard, while cumulative incidence is bounded at 1.0 and accounts for the shrinking at-risk pool.

Question 3

A cumulative incidence of 15% is fully interpretable without knowing the time period over which it was calculated.

• T. True
• F. False

Answer: False

Time horizon is integral to the definition of cumulative incidence — it answers 'probability of outcome within a specified window.' Without specifying that window (e.g., '5-year cumulative incidence'), the figure is meaningless. An annual CI of 15% and a 20-year CI of 15% convey entirely different levels of risk.

Question 4

The Kaplan-Meier estimator handles censoring by updating the at-risk denominator at each event time, allowing survival probability to be estimated even when participants leave the study at different times.

• T. True
• F. False

Answer: True

Kaplan-Meier works step by step: at each event time, it multiplies the cumulative survival probability by the conditional probability of surviving that step, using only individuals still under observation. Censored individuals are removed from the at-risk count before the next step — they neither inflate nor deflate the denominator inappropriately.

Question 5

Why can't competing events (such as deaths from other causes) simply be treated as ordinary censored observations when calculating cumulative incidence for a specific outcome?

Model answer: Ordinary censoring assumes the individual remains at risk of the outcome after they leave observation — it treats their future as unobserved but possible. A participant who dies of cardiovascular disease is no longer at risk of dying from cancer; treating their death as censoring implies they could still develop cancer, which inflates the cumulative incidence of cancer. Competing risks methods (e.g., cause-specific hazards, Gray's method) correctly account for this by recognizing that one event permanently removes the individual from the risk set for the other.

This is the central conceptual gap between simple cumulative incidence and competing risks analysis. Censoring is appropriate for dropout or administrative end-of-study; it is inappropriate for events that biologically preclude the outcome of interest. Ignoring competing risks systematically overstates the probability of the primary outcome.