Kaplan–Meier and Nelson–Aalen Estimation › Disadvantages

Kaplan-Meier and Nelson-Aalen are marginal estimators. They describe the survival experience of the entire sample, not the effect of a treatment or covariate after adjustment. If treated and untreated patients differ in prognostic factors such as age or disease severity, comparing two Kaplan-Meier curves can mix the treatment effect with those differences. Covariate adjustment requires an additional modeling, weighting, or standardization step; the Cox proportional hazards model we will meet next is one such approach.

For these unadjusted marginal curves, censoring must leave the observed risk sets representative of the event risk in the population. Independence of event and censoring times is a simple sufficient assumption. Independence only after conditioning on predictors of both failure and censoring can require stratification or weighting. Selective dropout of patients with higher subsequent event risk can leave a healthier observed risk set and bias estimated survival upward. Competing risks are another failure mode: if a patient dies from another cause, coding that death as censored and interpreting one minus Kaplan–Meier as cumulative incidence can overestimate the cumulative incidence of the event of interest.

The tails of the curves are fragile. As follow-up progresses, fewer subjects remain at risk, so tail estimates depend on less information. Absolute Greenwood standard errors and pointwise interval widths need not increase monotonically. If the largest observed time is censored, the Kaplan-Meier curve never reaches zero, and we have no direct estimate of survival beyond the last follow-up. A median may not be reached at all, even in a large study, if follow-up is short. Ties and small risk sets also make the finite-sample difference between Kaplan-Meier and the exponential transform of Nelson-Aalen more noticeable.