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Generalized inverse-Gaussian frailty models with application to TARGET neuroblastoma data

Author

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  • Luiza S. C. Piancastelli

    (University College Dublin
    Universidade Federal de Minas Gerais)

  • Wagner Barreto-Souza

    (King Abdullah University of Science and Technology
    Universidade Federal de Minas Gerais)

  • Vinícius D. Mayrink

    (Universidade Federal de Minas Gerais)

Abstract

A new class of survival frailty models based on the generalized inverse-Gaussian (GIG) distributions is proposed. We show that the GIG frailty models are flexible and mathematically convenient like the popular gamma frailty model. A piecewise-exponential baseline hazard function is employed, yielding flexibility for the proposed class. Although a closed-form observed log-likelihood function is available, simulation studies show that employing an EM-algorithm is advantageous concerning the direct maximization of this function. Further simulated results address the comparison of different methods for obtaining standard errors of the estimates and confidence intervals for the parameters. Additionally, the finite-sample behavior of the EM-estimators is investigated and the performance of the GIG models under misspecification assessed. We apply our methodology to a TARGET (Therapeutically Applicable Research to Generate Effective Treatments) data about the survival time of patients with neuroblastoma cancer and show some advantages of the GIG frailties over existing models in the literature.

Suggested Citation

  • Luiza S. C. Piancastelli & Wagner Barreto-Souza & Vinícius D. Mayrink, 2021. "Generalized inverse-Gaussian frailty models with application to TARGET neuroblastoma data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 979-1010, October.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:5:d:10.1007_s10463-020-00774-z
    DOI: 10.1007/s10463-020-00774-z
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    References listed on IDEAS

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    1. Wagner Barreto-Souza & Vinícius Diniz Mayrink, 2019. "Semiparametric generalized exponential frailty model for clustered survival data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 679-701, June.
    2. 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.
    3. Donglin Zeng & D. Y. Lin, 2006. "Efficient estimation of semiparametric transformation models for counting processes," Biometrika, Biometrika Trust, vol. 93(3), pages 627-640, September.
    4. D. Zeng & D. Y. Lin, 2007. "Maximum likelihood estimation in semiparametric regression models with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 507-564, September.
    5. 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.
    6. Vu, Hien T. V. & Knuiman, Matthew W., 2002. "A hybrid ML-EM algorithm for calculation of maximum likelihood estimates in semiparametric shared frailty models," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 173-187, July.
    7. Chen, Pengcheng & Zhang, Jiajia & Zhang, Riquan, 2013. "Estimation of the accelerated failure time frailty model under generalized gamma frailty," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 171-180.
    8. C. Paddy Farrington & Steffen Unkel & Karim Anaya-Izquierdo, 2012. "The relative frailty variance and shared frailty models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(4), pages 673-696, September.
    9. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
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