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Marginal analysis of multivariate failure time data with a surviving fraction based on semiparametric transformation cure models

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  • Chen, Chyong-Mei
  • Lu, Tai-Fang C.

Abstract

In biomedical, genetic and social studies, there may exist a fraction of individuals not experiencing the event of interest such that the survival curves eventually level off to nonzero proportions. These people are referred to as “cured” or “nonsusceptible” individuals. Models that have been developed to address this issue are known as cured models. The mixture model, which consists of a model for the binary cure status and a survival model for the event times of the noncured individuals, is one of the widely used cure models. In this paper, we propose a class of semiparametric transformation cure models for multivariate survival data with a surviving fraction by fitting a logistic regression model to the cure status and a semiparametric transformation model to the event time of the noncured individual. Both models allow incorporating covariates and do not require any assumption of the association structure. The statistical inference is based on the marginal approach by constructing a system of estimating equations. The asymptotic properties of the proposed estimators are proved, and the performance of the estimation is demonstrated via simulations. In addition, the approach is illustrated by analyzing the smoking cessation data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:645-655
    DOI: 10.1016/j.csda.2011.09.013
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    References listed on IDEAS

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    1. Chen, Ming-Hui & Ibrahim, Joseph G. & Sinha, Debajyoti, 2002. "Bayesian Inference for Multivariate Survival Data with a Cure Fraction," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 101-126, January.
    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. Sudipto Banerjee & Bradley P. Carlin, 2004. "Parametric Spatial Cure Rate Models for Interval-Censored Time-to-Relapse Data," Biometrics, The International Biometric Society, vol. 60(1), pages 268-275, March.
    5. 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.
    6. 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.
    7. Peng, Yingwei, 2003. "Fitting semiparametric cure models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 481-490, January.
    8. Tsodikov A.D. & Ibrahim J.G. & Yakovlev A.Y., 2003. "Estimating Cure Rates From Survival Data: An Alternative to Two-Component Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1063-1078, January.
    9. Yu, Binbing & Peng, Yingwei, 2008. "Mixture cure models for multivariate survival data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1524-1532, January.
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    Cited by:

    1. 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.
    2. 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.
    3. Niu, Yi & Peng, Yingwei, 2014. "Marginal regression analysis of clustered failure time data with a cure fraction," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 129-142.

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