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The Aalen additive gamma frailty hazards model

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  • Torben Martinussen
  • Thomas H. Scheike
  • David M. Zucker

Abstract

In this paper, we consider clustered right-censored time-to-event data. Such data can be analysed either using a marginal model if one is interested in population effects or using so-called frailty models if one is interested in covariate effects on the individual level and in estimation of correlation. The Cox frailty model has been studied extensively in the last decade or so and estimation techniques and large sample results are now available. It is, however, difficult to deal with time-changing covariate effects when using the Cox model. An appealing alternative model is the Aalen additive hazards model, in which it is easy to work with time dynamics. In this paper, we describe an innovative approach to estimation in the Aalen additive gamma frailty hazards model. We give the large sample properties of the estimators and investigate their small sample properties by Monte Carlo simulation. A real example is provided for illustration. Copyright 2011, Oxford University Press.

Suggested Citation

  • Torben Martinussen & Thomas H. Scheike & David M. Zucker, 2011. "The Aalen additive gamma frailty hazards model," Biometrika, Biometrika Trust, vol. 98(4), pages 831-843.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:4:p:831-843
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    File URL: http://hdl.handle.net/10.1093/biomet/asr049
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    Cited by:

    1. He, W., 2014. "Analysis of multivariate survival data with Clayton regression models under conditional and marginal formulations," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 52-63.
    2. Frank Eriksson & Jianing Li & Thomas Scheike & Mei‐Jie Zhang, 2015. "The proportional odds cumulative incidence model for competing risks," Biometrics, The International Biometric Society, vol. 71(3), pages 687-695, September.
    3. Frank Eriksson & Thomas Scheike, 2015. "Additive gamma frailty models with applications to competing risks in related individuals," Biometrics, The International Biometric Society, vol. 71(3), pages 677-686, September.
    4. Ying Hung & Li‐Hsiang Lin & C. F. Jeff Wu, 2022. "Varying coefficient frailty models with applications in single molecular experiments," Biometrics, The International Biometric Society, vol. 78(2), pages 474-486, June.
    5. Yuxue Jin & Tze Leung Lai, 2017. "A new approach to regression analysis of censored competing-risks data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(4), pages 605-625, October.
    6. Zhongwen Zhang & Xiaoguang Wang & Yingwei Peng, 2022. "An additive hazards frailty model with semi-varying coefficients," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(1), pages 116-138, January.
    7. Ramesh Gupta, 2016. "Properties of additive frailty model in survival analysis," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 1-17, January.

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