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Nonparametric and semiparametric estimation with sequentially truncated survival data

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  • Rebecca A. Betensky
  • Jing Qian
  • Jingyao Hou

Abstract

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.

Suggested Citation

  • Rebecca A. Betensky & Jing Qian & Jingyao Hou, 2023. "Nonparametric and semiparametric estimation with sequentially truncated survival data," Biometrics, The International Biometric Society, vol. 79(2), pages 1000-1013, June.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:2:p:1000-1013
    DOI: 10.1111/biom.13678
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    References listed on IDEAS

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    1. Martin, Emily C. & Betensky, Rebecca A., 2005. "Testing Quasi-Independence of Failure and Truncation Times via Conditional Kendall's Tau," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 484-492, June.
    2. Mandel, Micha, 2007. "Censoring and TruncationHighlighting the Differences," The American Statistician, American Statistical Association, vol. 61, pages 321-324, November.
    3. Pao-sheng Shen, 2010. "Nonparametric analysis of doubly truncated data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(5), pages 835-853, October.
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