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Biometrika 2009 96(4):873-886; doi:10.1093/biomet/asp064
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© 2009 Biometrika Trust

Article

Nonparametric estimation for right-censored length-biased data: a pseudo-partial likelihood approach

Xiaodong Luo

Department of Psychiatry, Mount Sinai School of Medicine, New York, New York, 10029, U.S.A. Xiaodong.Luo{at}mssm.edu

Wei Yann Tsai

Department of Biostatistics, Columbia University, New York, New York, 10032, U.S.A. wt5{at}columbia.edu

Received for publication 1 September 2008. Revision received 1 June 2009.
  Abstract

To estimate the lifetime distribution of right-censored length-biased data, we propose a pseudo-partial likelihood approach that allows us to derive two nonparametric estimators. With its closed-form estimators and explicit limiting variances, this approach retains the simplicity of conditional analysis, and has only a small efficiency loss compared with the unconditional analysis. Under some regularity conditions, we show that the two estimators are uniformly consistent and converge weakly to Gaussian processes. A simulation study demonstrates that the proposed estimators have satisfactory finite-sample performance. Application to an Alzheimer’s disease study is reported.

Key Words: Censoring on residual life • Left truncation • Length bias • Prevalent cohort studies • Pseudo-partial likelihood


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