In a study of cardiac mortality among elderly patients, deaths from cancer are treated as censored in a standard Kaplan-Meier analysis. Why does this overestimate cardiac mortality risk?
ACancer deaths reduce the sample size, widening confidence intervals
BCensoring cancer deaths implies those patients could still die from cardiac causes, but they cannot — they are already dead. The KM estimator overestimates the cumulative probability of cardiac death by assuming censored subjects remain at risk
CCancer deaths should be combined with cardiac deaths as a single outcome
DThe KM estimator underestimates cardiac mortality when competing risks are present
The KM estimator assumes that censored subjects have the same future risk as those remaining — an assumption violated by competing risks. A patient who died of cancer is removed from the risk set as if they were merely lost to follow-up and could still have a cardiac event. The cumulative incidence function (CIF), which properly accounts for competing risks, will always be lower than or equal to the KM complement (1 - KM) because it recognizes that some subjects will experience competing events instead.
Question 2 True / False
A cause-specific hazard model and a Fine-Gray subdistribution model can give contradictory results for the same exposure-outcome relationship. This occurs because they answer fundamentally different questions.
TTrue
FFalse
Answer: True
The cause-specific hazard asks: among those currently alive (event-free), what is the instantaneous rate of the event of interest? The subdistribution hazard asks: what is the rate of the event of interest in a hypothetical world where subjects who experienced competing events remain in the risk set? A treatment that reduces cardiac death but increases cancer death might show a reduced cause-specific cardiac hazard but an unchanged subdistribution hazard (because fewer cardiac deaths are offset by the subjects remaining at risk longer due to increased cancer deaths). The cause-specific model is better for understanding etiology; the Fine-Gray model is better for prediction and clinical decision-making about overall risk.
Question 3 Short Answer
Explain why the cumulative incidence function (CIF) must sum across all event types to a value less than or equal to 1, and why this constraint distinguishes it from the Kaplan-Meier complement.
Think about your answer, then reveal below.
Model answer: The CIF for each event type represents the probability of experiencing that specific event by time t, given that competing events are possible. Since a subject can only experience one event, the CIFs across all event types sum to the total probability of experiencing any event — which cannot exceed 1. The KM complement (1 - S(t)) computed separately for each event type treats competing events as censored and can exceed the true probability because it imagines a world without competing risks. The CIFs properly partition the total failure probability among event types.
At any time t, CIF_cardiac(t) + CIF_cancer(t) + CIF_other(t) = total failure probability ≤ 1. Each individual CIF is bounded above by the total failure probability. The KM complement for cardiac death, computed by censoring cancer and other deaths, estimates the probability of cardiac death in a hypothetical world where competing events do not exist — a quantity that may be of scientific interest but does not correspond to what patients actually experience.