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Semiparametric generalized exponential frailty model for clustered survival data

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  • Wagner Barreto-Souza

    (Universidade Federal de Minas Gerais)

  • Vinícius Diniz Mayrink

    (Universidade Federal de Minas Gerais)

Abstract

In this paper, we propose a novel and mathematically tractable frailty model for clustered survival data by assuming a generalized exponential (GE) distribution for the latent frailty effect. Both parametric and semiparametric versions of the GE frailty model are studied with main focus for the semiparametric case, where an EM-algorithm is proposed. Our EM-based estimation for the GE frailty model is simpler, faster and immune to a flat likelihood issue affecting, for example, the semiparametric gamma model, as illustrated in this paper through simulated and real data. We also show that the GE model is at least competitive with respect to the gamma frailty model under misspecification. A broad analysis is developed, with simulation results explored via Monte Carlo replications, to evaluate and compare models. A real application using a clustered kidney catheter data is considered to demonstrate the potential for practice of the GE frailty model.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:3:d:10.1007_s10463-018-0658-9
    DOI: 10.1007/s10463-018-0658-9
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    References listed on IDEAS

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    1. Cetinyurek, Aysun & Lambert, Philippe, 2016. "Semi-parametric frailty model for clustered interval-censored data," LIDAM Reprints ISBA 2016032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Yu, Binbing, 2006. "Estimation of shared Gamma frailty models by a modified EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 463-474, January.
    3. Munda, Marco & Rotolo, Federico & Legrand, Catherine, 2012. "parfm: Parametric Frailty Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i11).
    4. Nadarajah, Saralees & Kotz, Samuel, 2006. "The beta exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 689-697.
    5. Munda, Marco & Rotolo, Federico & Legrand, Catherine, 2012. "parfm: Parametric Frailty Models in R," LIDAM Discussion Papers ISBA 2012005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. 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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    Cited by:

    1. Ingvild M. Helgøy & Hans J. Skaug, 2022. "The Sibling Distribution for Multivariate Life Time Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 340-363, May.
    2. 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.

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