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Regression Analysis of Dependent Current Status Data with Left Truncation

Author

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  • Mengyue Zhang

    (Center for Applied Statistical Research, School of Mathematics, Jilin University, Changchun 130012, China)

  • Shishun Zhao

    (Center for Applied Statistical Research, School of Mathematics, Jilin University, Changchun 130012, China)

  • Tao Hu

    (School of Mathematical Sciences, Capital Normal University, Beijing 100048, China)

  • Da Xu

    (Key Laboratory of Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China)

  • Jianguo Sun

    (Department of Statistics, University of Missouri, Columbia, MO 65211, USA)

Abstract

Current status data are encountered in a wide range of applications, including tumorigenic experiments and demographic studies. In this case, each subject has one observation, and the only information obtained is whether the event of interest happened at the moment of observation. In addition to censoring, truncating is also very common in practice. This paper examines the regression analysis of current status data with informative censoring times, considering the presence of left truncation. In addition, we propose an inference approach based on sieve maximum likelihood estimation (SMLE). A copula-based approach is used to describe the relationship between the failure time of interest and the censoring time. The spline function is employed to approximate the unknown nonparametric function. We have established the asymptotic properties of the proposed estimator. Simulation studies suggest that the developed procedure works well in practice. We also applied the developed method to a real dataset derived from an AIDS cohort research.

Suggested Citation

  • Mengyue Zhang & Shishun Zhao & Tao Hu & Da Xu & Jianguo Sun, 2023. "Regression Analysis of Dependent Current Status Data with Left Truncation," Mathematics, MDPI, vol. 11(16), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3539-:d:1218379
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    References listed on IDEAS

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    2. Minggen Lu & Ying Zhang & Jian Huang, 2007. "Estimation of the mean function with panel count data using monotone polynomial splines," Biometrika, Biometrika Trust, vol. 94(3), pages 705-718.
    3. Achim Dörre, 2020. "Bayesian estimation of a lifetime distribution under double truncation caused by time-restricted data collection," Statistical Papers, Springer, vol. 61(3), pages 945-965, June.
    4. 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.
    5. Ling Ma & Tao Hu & Jianguo Sun, 2015. "Sieve maximum likelihood regression analysis of dependent current status data," Biometrika, Biometrika Trust, vol. 102(3), pages 731-738.
    6. Da Xu & Shishun Zhao & Tao Hu & Jianguo Sun, 2019. "Regression analysis of informatively interval-censored failure time data with semiparametric linear transformation model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 31(3), pages 663-679, July.
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