What are non-parametric methods for survival analysis?

• A. Actuarial life tables
• B. Kaplan-Meier estimator of survivor function or product-limit estimate
• C. Nelson-Aalen estimator of cumulative hazard function
• D. Cox proportional hazards model

Answer: (B)

Non-parametric survival analysis estimates the time-to-event distribution without assuming a specific parametric form. The Kaplan-Meier estimator is the standard approach for the survivor function: it builds a stepwise curve using the product of the proportions at risk who remain event-free at each observed failure time. At each event time, you multiply the previous survival probability by (n_i − d_i)/n_i, where d_i is the number of events and n_i is the number at risk just before that time. This method naturally handles right-censoring (assuming censoring is independent of the event) and produces a practical, distribution-free estimate of S(t), with variance estimated by Greenwood’s formula for confidence intervals. While other non-parametric tools exist (like cumulative hazard estimators), the Kaplan-Meier curve is the quintessential non-parametric survival function estimator and is widely used for comparing groups via methods like the log-rank test.