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Estimation of the accelerated failure time frailty model under generalized gamma frailty

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  • Chen, Pengcheng
  • Zhang, Jiajia
  • Zhang, Riquan

Abstract

The frailty model is one of the most popular models used to analyze clustered failure time data, where the frailty term is used to assess an association within each cluster. The frailty model based on the semiparametric accelerated failure time model attracts less attention than the one based on the proportional hazards model due to its computational difficulties. In this paper, we relax the frailty distribution to the generalized gamma distribution, which can accommodate most of the popular frailty assumptions. The estimation procedure is based on the EM-like algorithm by employing the MCMC algorithm in the E-step and the profile likelihood estimation method in the M-step. We conduct an extensive simulation study and find that there is a significant gain in the proposed method with respect to the estimation of the frailty variance with a slight loss of accuracy in the parameter estimates. For illustration, we apply the proposed model and method to a data set of sublingual nitroglycerin and oral isosorbide dinitrate on angina pectoris of coronary heart disease patients.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:62:y:2013:i:c:p:171-180
    DOI: 10.1016/j.csda.2013.01.016
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    References listed on IDEAS

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    1. Xu, Linzhi & Zhang, Jiajia, 2010. "An EM-like algorithm for the semiparametric accelerated failure time gamma frailty model," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1467-1474, June.
    2. Peng, Yingwei & Zhang, Jiajia, 2008. "Identifiability of a mixture cure frailty model," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2604-2608, November.
    3. Zeng, Donglin & Lin, D.Y., 2007. "Efficient Estimation for the Accelerated Failure Time Model," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1387-1396, December.
    4. Zhang, Jiajia & Peng, Yingwei, 2007. "An alternative estimation method for the accelerated failure time frailty model," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4413-4423, May.
    5. Z. Jin & D. Y. Lin & Z. Ying, 2006. "Rank Regression Analysis of Multivariate Failure Time Data Based on Marginal Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 1-23, March.
    6. 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.
    7. 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.
    8. Zhezhen Jin & D. Y. Lin & Zhiliang Ying, 2006. "On least-squares regression with censored data," Biometrika, Biometrika Trust, vol. 93(1), pages 147-161, March.
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    Cited by:

    1. Sukhmani Sidhu & Kanchan Jain & Suresh Kumar Sharma, 2018. "Bayesian estimation of generalized gamma shared frailty model," Computational Statistics, Springer, vol. 33(1), pages 277-297, March.
    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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