Survival analysis for the missing censoring indicator model using kernel density estimation techniques

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Abstract

This article concerns asymptotic theory for a new estimator of a survival function in the missing censoring indicator model of random censorship. Specifically, the large sample results for an inverse probability-of-non- missingness weighted estimator of the cumulative hazard function, so far not available, are derived, including an almost sure representation with rate for a remainder term, and uniform strong consistency with rate of convergence. The estimator is based on a kernel estimate for the conditional probability of non-missingness of the censoring indicator. Expressions for its bias and variance, in turn leading to an expression for the mean squared error as a function of the bandwidth, are also obtained. The corresponding estimator of the survival function, whose weak convergence is derived, is asymptotically efficient. A numerical study, comparing the performances of the proposed and two other currently existing efficient estimators, is presented.

Original languageEnglish (US)
Pages (from-to)125-136
Number of pages12
JournalStatistical Methodology
Volume3
Issue number2
DOIs
StatePublished - Apr 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Keywords

  • Bandwidth sequence
  • Functional delta method
  • Independent increments
  • Kernel density estimator
  • Lyapounov central limit theorem
  • Standard Wiener process

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