Imputation for semiparametric transformation models with biased-sampling data

Hao Liu, Jing Qin, Yu Shen

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Widely recognized in many fields including economics, engineering, epidemiology, health sciences, technology and wildlife management, length-biased sampling generates biased and right-censored data but often provide the best information available for statistical inference. Different from traditional right-censored data, length-biased data have unique aspects resulting from their sampling procedures. We exploit these unique aspects and propose a general imputation-based estimation method for analyzing length-biased data under a class of flexible semiparametric transformation models. We present new computational algorithms that can jointly estimate the regression coefficients and the baseline function semiparametrically. The imputation-based method under the transformation model provides an unbiased estimator regardless whether the censoring is independent or not on the covariates. We establish large-sample properties using the empirical processes method. Simulation studies show that under small to moderate sample sizes, the proposed procedure has smaller mean square errors than two existing estimation procedures. Finally, we demonstrate the estimation procedure by a real data example.

Original languageEnglish (US)
Pages (from-to)470-503
Number of pages34
JournalLifetime data analysis
Issue number4
StatePublished - Aug 20 2012
Externally publishedYes


  • Biased sampling
  • Estimating equation
  • Imputation
  • Transformation models

ASJC Scopus subject areas

  • Applied Mathematics

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