The price of Kaplan-Meier

Miller has studied the asymptotic efficiency of the nonparametric, Kaplan-Meier survival estimator relative to parametric estimates based on the exponential and Weibull distributions. He concluded that in certain cases, the asymptotic efficiency is low and recommended that analysts give more consideration to parametric estimators, particularly for estimation of small tail probabilities. In this article we revisit this issue and examine the performance of the nonparametric procedure for estimation not only of a point on the survival curve, but also of the mean (or restricted mean) lifetime. In addition to the exponential and Weibull families, we consider the performance of the Kaplan-Meier procedure relative to a more flexible parametric model proposed by Efron. We find that the reduction in efficiency of the Kaplan-Meier survival estimate becomes negligible fairly quickly as the number of parameters in the parametric model increases. Moreover, for estimation of the mean or restricted mean, the loss in efficiency, even relative to the exponential distribution, is small or nil. We conclude that a parametric estimate of the survival curve may be necessary in certain extreme situations, such as when the sample size is very small. In these cases, careful attention must be given to considering the degree of fit, although with sparse data, this must be assessed from outside sources. For certain functionals of the survival curve, such as the mean or restricted mean, the nonparametric approach is unbiased and entails little or no loss in efficiency, and therefore would generally be preferred over a parametric-based estimate.