Meta-analysis of individual patient data with semi-competing risks under the Weibull joint frailty–copula model

Computational Statistics volume 35, pages1525–1552(2020)Cite this article

Abstract

In meta-analysis of individual patient data with semi-competing risks, the joint frailty–copula model has been proposed, where frailty terms account for the between-study heterogeneity and copulas account for dependence between terminal and nonterminal event times. In the previous works, the baseline hazard functions in the joint frailty–copula model are estimated by the nonparametric model or the penalized spline model, which requires complex maximization schemes and resampling-based interval estimation. In this article, we propose the Weibull distribution for the baseline hazard functions under the joint frailty–copula model. We show that the Weibull model constitutes a conjugate model for the gamma frailty, leading to explicit expressions for the moments, survival functions, hazard functions, quantiles, and mean residual lifetimes. These results facilitate the parameter interpretation of prognostic inference. We propose a maximum likelihood estimation method and make our computer programs available in the R package, joint.Cox. We also show that the delta method is feasible to calculate interval estimates, which is a useful alternative to the resampling-based method. We conduct simulation studies to examine the accuracy of the proposed methods. Finally, we use the data on ovarian cancer patients to illustrate the proposed method.

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Acknowledgements

The authors kindly thank the associate editor and two anonymous referees for their valuable suggestions that improved the paper. We are grateful to Jia-Han Shih for his technical assistance for the data analysis and simulation studies. The research of Emura T is funded by the grant from the Ministry of Science and Technology of Taiwan (MOST, 107-2118-M-008 -003 -MY3).

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Affiliations

  1. Graduate Institute of Statistics, National Central University, Taoyuan, Taiwan

    Bo-Hong Wu

  2. Department of Clinical Medicine (Biostatistics), School of Pharmacy, Kitasato University, Tokyo, Japan

    Hirofumi Michimae

  3. Department of Information Management, Chang Gung University, No. 259, Wenhua 1st Rd., Guishan Dist., Taoyuan City, 333, Taiwan

    Takeshi Emura

Authors
  1. Bo-Hong Wu
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  2. Hirofumi Michimae
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  3. Takeshi Emura
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Correspondence to Takeshi Emura.

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Wu, B., Michimae, H. & Emura, T. Meta-analysis of individual patient data with semi-competing risks under the Weibull joint frailty–copula model. Comput Stat 35, 1525–1552 (2020). https://doi.org/10.1007/s00180-020-00977-1

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Keywords

  • Clustered survival data
  • Gamma frailty
  • Mean residual life
  • Hierarchical model
  • Random effects
  • Survival analysis