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Empirical likelihood MLE for joint modeling right censored survival data with longitudinal covariates

Author

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  • Jian-Jian Ren

    (University of Maryland)

  • Yuyin Shi

    (U.S. Food and Drug Administration, Center for Biologics Evaluation and Research (CBER))

Abstract

Up to now, almost all existing methods for joint modeling survival data and longitudinal data rely on parametric/semiparametric assumptions on longitudinal covariate process, and the resulting inferences critically depend on the validity of these assumptions that are difficult to verify in practice. The kernel method-based procedures rely on choices of kernel function and bandwidth, and none of the existing methods provides estimate for the baseline distribution in proportional hazards model. This article proposes a proportional hazards model for joint modeling right censored survival data and intensive longitudinal data taking into account of within-subject historic change patterns. Without any parametric/semiparametric assumptions or use of kernel method, we derive empirical likelihood-based maximum likelihood estimators and partial likelihood estimators for the regression parameter and the baseline distribution function. We develop stable computing algorithms and present some simulation results. Analyses of real dataset are conducted for smoking cessation data and liver disease data.

Suggested Citation

  • Jian-Jian Ren & Yuyin Shi, 2024. "Empirical likelihood MLE for joint modeling right censored survival data with longitudinal covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(4), pages 617-648, August.
    • Handle: RePEc:spr:aistmt:v:76:y:2024:i:4:d:10.1007_s10463-024-00899-5
    DOI: 10.1007/s10463-024-00899-5
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    References listed on IDEAS

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    1. Hongyuan Cao & Mathew M. Churpek & Donglin Zeng & Jason P. Fine, 2015. "Analysis of the Proportional Hazards Model With Sparse Longitudinal Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1187-1196, September.
    2. Ursula U. Müller & Hanxiang Peng & Anton Schick, 2019. "Inference about the slope in linear regression: an empirical likelihood approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 181-211, February.
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    4. Jian-Jian Ren, 2001. "Weighted Empirical Likelihood Ratio Confidence Intervals for the Mean with Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 498-516, September.
    5. Jian-Jian Ren & Mai Zhou, 2011. "Full likelihood inferences in the Cox model: an empirical likelihood approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(5), pages 1005-1018, October.
    6. Jian-Jian Ren & Tonya Riddlesworth, 2014. "Empirical likelihood bivariate nonparametric maximum likelihood estimator with right censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 913-930, October.
    7. Mai Zhou, 2005. "Empirical likelihood analysis of the rank estimator for the censored accelerated failure time model," Biometrika, Biometrika Trust, vol. 92(2), pages 492-498, June.
    8. Jimin Ding & Jane-Ling Wang, 2008. "Modeling Longitudinal Data with Nonparametric Multiplicative Random Effects Jointly with Survival Data," Biometrics, The International Biometric Society, vol. 64(2), pages 546-556, June.
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