The homogenetic estimate for the variance of survival rate.

The homogenetic estimate for the variance of survival rate is proposed based on generalization and reduction between the complement of the empirical distribution function and the Kaplan--Meier or Berkson--Gage estimate. It reduces to the binomial variance estimate when there is no censoring. A Monte Carlo simulation study was carried out under various sample sizes, survival and censoring configurations, number of tied observations, and confidence levels with 2000 replications. It verifies that the commonly employed Greenwood estimate understimates, and the Simon and Lee expression for the Peto estimate strictly overestimates, the variance of survival rate to an extent dependent on the censoring distributions. The conclusions are identical with those of Peto et al. (1977) and Slud et al. (1984). The bias of the homogenetic estimate is less than that of both the Greenwood estimate and the Simon and Lee expression for the Peto estimate. The homogenetic estimate slightly overestimates when there are no ties and becomes unbiased and then slightly underestimates as the number of tied observations increases.