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Empirical likelihood inference for the panel count data with informative observation process

Author

Listed:
  • Faysal Satter

    (Data Analytics and Computational Intelligence, Lowe’s Companies, Inc.)

  • Yichuan Zhao

    (Georgia State University)

  • Ni Li

    (Hainan Normal University)

Abstract

Panel count data refer to interval-censored recurrent event data. Each study subject can only be observed at discrete time points, leading to knowledge about the total number of events occurring between observations. The observation times can be also different among subjects and carry important information about the underlying recurrent process. In this paper, an empirical likelihood (EL) method for panel count data with informative observation times is proposed. Based on the influence function, we formulate an empirical likelihood ratio for the vector of regression coefficients, and the Wilks’ theorem is established. Simulation studies are carried out to compare the performance of empirical likelihood with normal approximation methods. Finally, the EL method is compared with existing approaches, utilizing an illustrative example drawn from a bladder cancer study.

Suggested Citation

  • Faysal Satter & Yichuan Zhao & Ni Li, 2024. "Empirical likelihood inference for the panel count data with informative observation process," Statistical Papers, Springer, vol. 65(5), pages 3039-3061, July.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:5:d:10.1007_s00362-023-01506-0
    DOI: 10.1007/s00362-023-01506-0
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    References listed on IDEAS

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    1. Chiung-Yu Huang & Mei-Cheng Wang & Ying Zhang, 2006. "Analysing panel count data with informative observation times," Biometrika, Biometrika Trust, vol. 93(4), pages 763-775, December.
    2. Jianguo Sun, 2003. "A nonparametric test for panel count data," Biometrika, Biometrika Trust, vol. 90(1), pages 199-208, March.
    3. Suojin Wang & Lianfen Qian & Raymond J. Carroll, 2010. "Generalized empirical likelihood methods for analyzing longitudinal data," Biometrika, Biometrika Trust, vol. 97(1), pages 79-93.
    4. Jianguo Sun & Xingwei Tong & Xin He, 2007. "Regression Analysis of Panel Count Data with Dependent Observation Times," Biometrics, The International Biometric Society, vol. 63(4), pages 1053-1059, December.
    5. Yichuan Zhao & Song Yang, 2012. "Empirical likelihood confidence intervals for regression parameters of the survival rate," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 59-70.
    6. Ying Zhang, 2002. "A semiparametric pseudolikelihood estimation method for panel count data," Biometrika, Biometrika Trust, vol. 89(1), pages 39-48, March.
    7. Zhang, Haixiang & Zhao, Hui & Sun, Jianguo & Wang, Dehui & Kim, KyungMann, 2013. "Regression analysis of multivariate panel count data with an informative observation process," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 71-80.
    8. Xue Yu & Yichuan Zhao, 2019. "Jackknife empirical likelihood inference for the accelerated failure time model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 269-288, March.
    9. Buzkova Petra, 2010. "Panel Count Data Regression with Informative Observation Times," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-24, September.
    10. Zhang, Zhigang & Zhao, Yichuan, 2013. "Empirical likelihood for linear transformation models with interval-censored failure time data," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 398-409.
    11. Shuyuan He & Wei Liang & Junshan Shen & Grace Yang, 2016. "Empirical Likelihood for Right Censored Lifetime Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 646-655, April.
    12. Yanqing Sun & Rajeshwari Sundaram & Yichuan Zhao, 2009. "Empirical Likelihood Inference for the Cox Model with Time‐dependent Coefficients via Local Partial Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 444-462, September.
    13. D. Y. Lin & L. J. Wei & I. Yang & Z. Ying, 2000. "Semiparametric regression for the mean and rate functions of recurrent events," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 711-730.
    14. Wen Yu & Yunting Sun & Ming Zheng, 2011. "Empirical likelihood method for linear transformation models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 331-346, April.
    15. Hui Zhao & Yang Li & Jianguo Sun, 2013. "Semiparametric analysis of multivariate panel count data with dependent observation processes and a terminal event," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 379-394, June.
    16. Zhao, Xingqiu & Tong, Xingwei & Sun, Jianguo, 2013. "Robust estimation for panel count data with informative observation times," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 33-40.
    17. J. Sun & L. J. Wei, 2000. "Regression analysis of panel count data with covariate‐dependent observation and censoring times," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 293-302.
    18. Song Xi Chen & Hengjian Cui, 2006. "On Bartlett correction of empirical likelihood in the presence of nuisance parameters," Biometrika, Biometrika Trust, vol. 93(1), pages 215-220, March.
    19. Zhao, Yichuan, 2011. "Empirical likelihood inference for the accelerated failure time model," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 603-610, May.
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