Modular Nonparametric Subsurvival Estimation

Abstract

This article describes new methods for estimating survival distributions based on nonparametric curve estimators. One approach improves the estimation of long-term survival rates. Simulation studies using Weibull and lognormal data show that even in the case found to be least favorable, the new method has less than one-seventh the prediction error of all conventional lifetable (LT) or Kaplan-Meier (KM) estimators, even when the LT and KM techniques a~e optimized for t~e purp~se o~long-term survival estimation. In addition to conventional survival applications, one can also estimate the probability of being diseasefree at different ages and following different exposures to possibly harmful environmental contaminants. This approach is particularly useful in situations where the effects of a confounding, nuisance, or effect-modifying variable cannot be confidently modeled in a parametric form. The new techniques are based on a closed-form nonparametric maximum likelihood curve estimator expressed in terms of separate curve estimates obtained from samples of randomly censored and uncensored times to failure-that is, subsurvival populations.