Nonparametric estimation for length-biased and right-censored data

Chiung Yu Huang, Jing Qin

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


This paper considers survival data arising from length-biased sampling, where the survival times are left truncated by uniformly distributed random truncation times. We propose a nonparametric estimator that incorporates the information about the length-biased sampling scheme. The new estimator retains the simplicity of the truncation product-limit estimator with a closed-form expression, and has a small efficiency loss compared with the nonparametric maximum likelihood estimator, which requires an iterative algorithm. Moreover, the asymptotic variance of the proposed estimator has a closed form, and a variance estimator is easily obtained by plug-in methods. Numerical simulation studies with practical sample sizes are conducted to compare the performance of the proposed method with its competitors. A data analysis of the Canadian Study of Health and Aging is conducted to illustrate the methods and theory.

Original languageEnglish (US)
Pages (from-to)177-186
Number of pages10
Issue number1
StatePublished - Mar 2011
Externally publishedYes


  • Backward and forward recurrence time
  • Cross-sectional sampling
  • Partial likelihood
  • Random truncation
  • Renewal process

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Agricultural and Biological Sciences (miscellaneous)
  • General Agricultural and Biological Sciences
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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