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An EM-like algorithm for the semiparametric accelerated failure time gamma frailty model

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  • Xu, Linzhi
  • Zhang, Jiajia

Abstract

The frailty model is one of the most popular models used to analyze clustered failure time data, and the frailty term in the model is used to assess associations in 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 develop a new estimation method for the semiparametric accelerated failure time gamma frailty model based on the EM-like algorithm and the rank-like estimation method. The proposed method is compared with the existing EM algorithm, which incorporates the M-estimator in the M-step. From simulation studies, we show that the rank-like estimation method in the M-like step simplifies the estimation procedure and reduces the computational time by the linear programming approach. With respect to the accuracy of estimates and length of computational time, the proposed method outperforms the existing estimation methods. For illustration, we apply the proposed method to the data set of sublingual nitroglycerin and oral isosorbide dinitrate on angina pectoris of coronary heart disease patients.

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  • 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.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:6:p:1467-1474
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    References listed on IDEAS

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    1. 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.
    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. Zhezhen Jin, 2003. "Rank-based inference for the accelerated failure time model," Biometrika, Biometrika Trust, vol. 90(2), pages 341-353, June.
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    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. 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.
    7. 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. 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.
    2. Lea Kats & Malka Gorfine, 2023. "An accelerated failure time regression model for illness–death data: A frailty approach," Biometrics, The International Biometric Society, vol. 79(4), pages 3066-3081, December.

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