Nonparametric Smooth Estimation of Conditional Survival Functions under Various Sampling Schemes

10.29973/JCSA.200812.0001

You-Jun Yang

Censoring ； conditional survival distribution ； dependent truncation ； nonparametric estimation ； smooth estimator ； truncation

中國統計學報

46卷4期（2008 / 12 / 01）

245 - 268

英文

In many follow-up studies, survival data are often collected by a cross-sectional sampling scheme. Such sampling schemes causes censoring or truncation in the data. We consider the case that the survival time distribution depends on the occurrence time of the initiating event in right-censored data and left-truncated data. When the survival time distribution does not depend on the censoring period of time (or the truncation period of time), the Kaplan-Meier estimator (or the product-limit estimator) is the nonparametric MLE for the censored data (or truncated data, respectively). But this may not be true if the survival time distribution depends on the initiating time. Here we construct a generalized Kaplan-Meier estimator to estimate the conditional survival function of the survival time given the initiating time, and then kernel smooth it with respect to the survival time to obtain a smooth estimator. Theoretical and numerical justifications are given.

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