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Association estimation for clustered failure time data with a cure fraction

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  • Chen, Chyong-Mei
  • Lu, Tai-Fang C.
  • Hsu, Chao-Min

Abstract

Substantial research has been devoted to developing methodology for inferring the association of clustered failure time data. However, in the study of familial disease, there may be a proportion of patients cured or nonsusceptible to the disease. Thus, it is necessary to simultaneously consider two types of association, i.e., the association of the susceptibility of the individuals, and that of the ages at onset between the susceptible individuals. In this paper, we consider the pairwise association in both types of association to reduce the mathematical intractability and the difficulty in specifying the full correlation structure. The former association is measured by the pairwise odds ratio of the binary cure statuses, and the latter by the bivariate Clayton copula with a semiparametric marginal regression model for any pair of correlated failure times. For the marginal model, it is formulated as a fairly general semiparametric regression cure model. A two-stage estimation procedure is adopted for the association estimation. We establish the consistency and asymptotic normality of the estimators for these two types of association. Simulation studies are conducted to assess finite sample properties, and the proposed method is illustrated by a subset of the data in the Australian Twins Study.

Suggested Citation

  • Chen, Chyong-Mei & Lu, Tai-Fang C. & Hsu, Chao-Min, 2013. "Association estimation for clustered failure time data with a cure fraction," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 210-222.
    • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:210-222
    DOI: 10.1016/j.csda.2012.06.016
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    References listed on IDEAS

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    1. Anthony Y. C. Kuk, 2007. "A Hybrid Pairwise Likelihood Method," Biometrika, Biometrika Trust, vol. 94(4), pages 939-952.
    2. Nilanjan Chatterjee & Joanna Shih, 2001. "A Bivariate Cure-Mixture Approach for Modeling Familial Association in Diseases," Biometrics, The International Biometric Society, vol. 57(3), pages 779-786, September.
    3. Wenbin Lu, 2004. "On semiparametric transformation cure models," Biometrika, Biometrika Trust, vol. 91(2), pages 331-343, June.
    4. Yingwei Peng & Keith B. G. Dear, 2000. "A Nonparametric Mixture Model for Cure Rate Estimation," Biometrics, The International Biometric Society, vol. 56(1), pages 237-243, March.
    5. Judy P. Sy & Jeremy M. G. Taylor, 2000. "Estimation in a Cox Proportional Hazards Cure Model," Biometrics, The International Biometric Society, vol. 56(1), pages 227-236, March.
    6. Chen, Chyong-Mei & Lu, Tai-Fang C., 2012. "Marginal analysis of multivariate failure time data with a surviving fraction based on semiparametric transformation cure models," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 645-655.
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    Cited by:

    1. Jie Huang & Haiming Zhou & Nader Ebrahimi, 2022. "Bayesian Bivariate Cure Rate Models Using Copula Functions," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(3), pages 1-9, May.
    2. Man-Hua Chen & Xingwei Tong, 2020. "Varying coefficient transformation cure models for failure time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(3), pages 518-544, July.
    3. Lajmi Lakhal-Chaieb & Thierry Duchesne, 2017. "Association measures for bivariate failure times in the presence of a cure fraction," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(4), pages 517-532, October.

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