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 life-table (LT) or Kaplan–Meier (KM) estimators, even when the LT and KM techniques are optimized for the purpose of long-term survival estimation. In addition to conventional survival applications, one can also estimate the probability of being disease-free 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.

Key Words:

• Curve estimation
• Kaplan–Meier estimator
• Life tables
• Long-term survival
• Mean integrated squared error
• Weighting