Variance of the Kaplan-Meier Estimator and Its Quantiles Under Certain Fixed Censoring Models

Abstract

For fixed censoring models that contain at most one intermediate censoring point, we obtain exact algebraic expressions for the asymptotic variances of (i) the quantiles of the Kaplan-Meier (KM, 1958) survival estimator and (ii) the KM estimator itself at fixed time points. The relationship between (i) and (ii) is found to be the same as the one derived by Sander (1975) and Reid (1981b) for the random censorship model. Confidence intervals for the quantiles based on (i) are briefly discussed and compared to previously known procedures. Although Greenwood's Formula is recommended over (ii) in practice because of its (desirable) conditioning on the observed censoring pattern, (ii) is of theoretical interest as an asymptotic limit for Greenwood's Formula in closed form.