Model-based confidence bands for survival functions

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Abstract

This paper focuses on a novel method of developing one-sample confidence bands for survival functions from right censored data. The approach is model-based, relying on a parametric model for the conditional expectation of the censoring indicator given the observed minimum, and derives its strength from easy access to a good-fitting model among a plethora of choices available for binary response data. The substantive methodological contribution is in exploiting a semiparametric estimator of the survival function to produce improved simultaneous confidence bands. To obtain critical values for computing the confidence bands, a two-stage bootstrap approach that combines the classical bootstrap with the more recent model-based regeneration of censoring indicators is proposed and a justification of its asymptotic validity is also provided. Several different confidence bands are studied using the proposed approach. Numerical studies, including robustness of the proposed bands to misspecification, are carried out to check efficacy. The method is illustrated using two lung cancer data sets.

Original languageEnglish (US)
Pages (from-to)1166-1185
Number of pages20
JournalJournal of Statistical Planning and Inference
Volume143
Issue number7
DOIs
StatePublished - Jul 2013

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Keywords

  • Bivariate Gaussian process
  • Continuous mapping theorem
  • Empirical coverage probability
  • Functional central limit theorem
  • Maximum likelihood estimator
  • Semiparametric random censorship models

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