Nonparametric estimation of the survival distribution under covariate-induced dependent truncation

Bella Vakulenko-Lagun, Jing Qian, Sy Han Chiou, Nancy Wang, Rebecca A. Betensky

Research output: Contribution to journalArticlepeer-review


There is often delayed entry into observational studies, which results in left truncation. In the estimation of the distribution of time-to-event from left-truncated data, standard survival analysis methods require quasi-independence between the truncation time and event time. Incorrectly assuming quasi-independence may lead to biased estimation. We address the problem of estimation of the survival distribution when dependence between the event time and its left truncation time is induced by shared covariates. We introduce propensity scores for truncated data and propose two inverse probability weighting methods that adjust for both truncation and dependence, if all of the shared covariates are measured. The proposed methods additionally allow for right censoring. We evaluate the proposed methods in simulations, conduct sensitivity analyses, and provide guidelines for use in practice. We illustrate our approach in application to data from a central nervous system lymphoma study. The proposed methods are implemented in the R package, depLT.

Original languageEnglish
Pages (from-to)1390-1401
Number of pages12
Issue number4
StatePublished - Dec 2022

Bibliographical note

Funding Information:
This research was supported by NIH (grant no. R01NS094610).

Publisher Copyright:
© 2021 The International Biometric Society


  • delayed entry
  • nonparametric estimation
  • positivity
  • propensity scores

ASJC Scopus subject areas

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


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