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A Likelihood Based Estimating Equation for the Clayton–Oakes Model with Marginal Proportional Hazards

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  • Christian Bressen Pipper
  • Torben Martinussen

Abstract

Multivariate failure time data arise when data consist of clusters in which the failure times may be dependent. A popular approach to such data is the marginal proportional hazards model with estimation under the working independence assumption. In this paper, we consider the Clayton–Oakes model with marginal proportional hazards and use the full model structure to improve on efficiency compared with the independence analysis. We derive a likelihood based estimating equation for the regression parameters as well as for the correlation parameter of the model. We give the large sample properties of the estimators arising from this estimating equation. Finally, we investigate the small sample properties of the estimators through Monte Carlo simulations.

Suggested Citation

  • Christian Bressen Pipper & Torben Martinussen, 2003. "A Likelihood Based Estimating Equation for the Clayton–Oakes Model with Marginal Proportional Hazards," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 509-521, September.
    • Handle: RePEc:bla:scjsta:v:30:y:2003:i:3:p:509-521
    DOI: 10.1111/1467-9469.00345
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    Cited by:

    1. Frank Eriksson & Torben Martinussen & Thomas H. Scheike, 2015. "Clustered Survival Data with Left-truncation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1149-1166, December.
    2. Dandan Liu & John D. Kalbfleisch & Douglas E. Schaubel, 2011. "A Positive Stable Frailty Model for Clustered Failure Time Data with Covariate-Dependent Frailty," Biometrics, The International Biometric Society, vol. 67(1), pages 8-17, March.
    3. 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.
    4. Ross L. Prentice, 2022. "On the targets of inference with multivariate failure time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(4), pages 546-559, October.

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