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Semiparametric regression analysis for left-truncated and interval-censored data without or with a cure fraction

Author

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  • Shen, Pao-sheng
  • Chen, Hsin-Jen
  • Pan, Wen-Harn
  • Chen, Chyong-Mei

Abstract

Interval censoring and truncation arise often in cohort studies, longitudinal and sociological research. In this article, we formulate the effects of covariates on left-truncated and mixed case interval-censored (LTIC) data without or with a cure fraction through a general class of semiparametric transformation models. We propose the conditional likelihood approach for statistical inference. For data without a cure fraction, we propose a computationally efficient EM algorithm, facilitated by a novel data augmentation method, to obtain the conditional maximum likelihood estimator (cMLE). For data with a cure fraction, we consider a semiparametric mixture cure model, which combines a logistic regression formula for the uncured probability with the class of transformation models for the failure time of uncured individuals. To overcome the computational complexity due to the presence of a cure fraction, by reparameterization of cure rate in the conditional likelihood function, we propose a computationally stable EM algorithm for obtaining the cMLE. We show that the cMLEs for the regression parameters are consistent and asymptotically normal. Based on the profile likelihood, we apply an EM-aided numerical differentiation method to compute the asymptotic variance estimates. We demonstrate the performance of our procedures through intensive simulation studies and application to the datasets from the Cardiovascular Disease Risk Factors Two-Township Study.

Suggested Citation

  • Shen, Pao-sheng & Chen, Hsin-Jen & Pan, Wen-Harn & Chen, Chyong-Mei, 2019. "Semiparametric regression analysis for left-truncated and interval-censored data without or with a cure fraction," Computational Statistics & Data Analysis, Elsevier, vol. 140(C), pages 74-87.
  • Handle: RePEc:eee:csdana:v:140:y:2019:i:c:p:74-87
    DOI: 10.1016/j.csda.2019.06.006
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    Cited by:

    1. Tianyi Lu & Shuwei Li & Liuquan Sun, 2023. "Combined estimating equation approaches for the additive hazards model with left-truncated and interval-censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 672-697, July.
    2. Prabhashi W. Withana Gamage & Christopher S. McMahan & Lianming Wang, 2023. "A flexible parametric approach for analyzing arbitrarily censored data that are potentially subject to left truncation under the proportional hazards model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 188-212, January.
    3. Pao-sheng Shen & Yingwei Peng & Hsin-Jen Chen & Chyong-Mei Chen, 2022. "Maximum likelihood estimation for length-biased and interval-censored data with a nonsusceptible fraction," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(1), pages 68-88, January.

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