Which function is estimated by the Kaplan-Meier estimator?

• A. Hazard function
• B. Survivor function
• C. Cumulative distribution function
• D. Probability density function

Answer: (B)

Kaplan-Meier estimates the survivor function, S(t) = P(T > t). It represents the probability of surviving beyond a given time and is built to handle right-censored data. At each observed event time, it looks at how many are at risk just before that time (n_i) and how many experience the event (d_i), forming a conditional survival probability of 1 − d_i/n_i. By multiplying these conditional probabilities across all event times up to t, we get Ŝ(t) = ∏(1 − d_i/n_i). This stepwise survival curve decreases only when events occur and can include censored observations without altering the product unless an event happens. Since the cumulative distribution function is F(t) = 1 − S(t), the KM estimator indirectly relates to F(t) but it directly estimates the survivor function, not the hazard or the density. Hazard describes instantaneous risk at time t given survival to t, which KM does not estimate directly.