Nonparametric and semiparametric estimation with sequentially truncated survival data

Rebecca A. Betensky, Jing Qian, Jingyao Hou

Research output: Contribution to journalArticlepeer-review


In observational cohort studies with complex sampling schemes, truncation arises when the time to event of interest is observed only when it falls below or exceeds another random time, that is, the truncation time. In more complex settings, observation may require a particular ordering of event times; we refer to this as sequential truncation. Estimators of the event time distribution have been developed for simple left-truncated or right-truncated data. However, these estimators may be inconsistent under sequential truncation. We propose nonparametric and semiparametric maximum likelihood estimators for the distribution of the event time of interest in the presence of sequential truncation, under two truncation models. We show the equivalence of an inverse probability weighted estimator and a product limit estimator under one of these models. We study the large sample properties of the proposed estimators and derive their asymptotic variance estimators. We evaluate the proposed methods through simulation studies and apply the methods to an Alzheimer's disease study. We have developed an R package, seqTrun, for implementation of our method.

Original languageEnglish (US)
Pages (from-to)1000-1013
Number of pages14
Issue number2
StatePublished - Jun 2023


  • Alzheimer's disease
  • biased sampling
  • inverse probability weighting
  • product limit estimator
  • quasi-independence
  • truncation

ASJC Scopus subject areas

  • Statistics and Probability
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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