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

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Listed:
  • Bella Vakulenko‐Lagun
  • Jing Qian
  • Sy Han Chiou
  • Nancy Wang
  • Rebecca A. Betensky

Abstract

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.

Suggested Citation

  • Bella Vakulenko‐Lagun & Jing Qian & Sy Han Chiou & Nancy Wang & Rebecca A. Betensky, 2022. "Nonparametric estimation of the survival distribution under covariate‐induced dependent truncation," Biometrics, The International Biometric Society, vol. 78(4), pages 1390-1401, December.
    • Handle: RePEc:bla:biomet:v:78:y:2022:i:4:p:1390-1401
    DOI: 10.1111/biom.13545
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    References listed on IDEAS

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    1. T. Emura & K. Murotani, 2015. "An algorithm for estimating survival under a copula-based dependent truncation model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 734-751, December.
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    3. Lajmi Lakhal Chaieb & Louis-Paul Rivest & Belkacem Abdous, 2006. "Estimating survival under a dependent truncation," Biometrika, Biometrika Trust, vol. 93(3), pages 655-669, September.
    4. Emura, Takeshi & Wang, Weijing, 2012. "Nonparametric maximum likelihood estimation for dependent truncation data based on copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 171-188.
    5. Yu-Jen Cheng & Mei-Cheng Wang, 2015. "Causal estimation using semiparametric transformation models under prevalent sampling," Biometrics, The International Biometric Society, vol. 71(2), pages 302-312, June.
    6. Qian, Jing & Betensky, Rebecca A., 2014. "Assumptions regarding right censoring in the presence of left truncation," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 12-17.
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