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

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  • Bo-Hong Wu

    (National Central University)

  • Hirofumi Michimae

    (Kitasato University)

  • Takeshi Emura

    (Chang Gung University)

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.

Suggested Citation

  • Bo-Hong Wu & Hirofumi Michimae & Takeshi Emura, 2020. "Meta-analysis of individual patient data with semi-competing risks under the Weibull joint frailty–copula model," Computational Statistics, Springer, vol. 35(4), pages 1525-1552, December.
  • Handle: RePEc:spr:compst:v:35:y:2020:i:4:d:10.1007_s00180-020-00977-1
    DOI: 10.1007/s00180-020-00977-1
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    References listed on IDEAS

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    1. Kyu Ha Lee & Francesca Dominici & Deborah Schrag & Sebastien Haneuse, 2016. "Hierarchical Models for Semicompeting Risks Data With Application to Quality of End-of-Life Care for Pancreatic Cancer," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1075-1095, July.
    2. Rotolo, Federico & Legrand, Catherine & Van Keilegom, Ingrid, 2013. "A simulation procedure based on copulas to generate clustered multi-state survival data," LIDAM Reprints ISBA 2013021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Duchateau, Luc & Janssen, Paul & Lindsey, Patrick & Legrand, Catherine & Nguti, Rosemary & Sylvester, Richard, 2002. "The shared frailty model and the power for heterogeneity tests in multicenter trials," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 603-620, September.
    4. Peng, Mengjiao & Xiang, Liming & Wang, Shanshan, 2018. "Semiparametric regression analysis of clustered survival data with semi-competing risks," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 53-70.
    5. R. Arabi Belaghi & M. Noori Asl, 2019. "Estimation based on progressively type-I hybrid censored data from the Burr XII distribution," Statistical Papers, Springer, vol. 60(3), pages 761-803, June.
    6. Kyu Ha Lee & Sebastien Haneuse & Deborah Schrag & Francesca Dominici, 2015. "Bayesian semiparametric analysis of semicompeting risks data: investigating hospital readmission after a pancreatic cancer diagnosis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 64(2), pages 253-273, February.
    7. Tomasz Burzykowski & Geert Molenberghs & Marc Buyse & Helena Geys & Didier Renard, 2001. "Validation of surrogate end points in multiple randomized clinical trials with failure time end points," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(4), pages 405-422.
    8. Rashad M. EL-Sagheer, 2018. "Estimation of parameters of Weibull–Gamma distribution based on progressively censored data," Statistical Papers, Springer, vol. 59(2), pages 725-757, June.
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    2. Xifen Huang & Jinfeng Xu & Hao Guo & Jianhua Shi & Wenjie Zhao, 2022. "An MM Algorithm for the Frailty-Based Illness Death Model with Semi-Competing Risks Data," Mathematics, MDPI, vol. 10(19), pages 1-13, October.

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