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A general transformation class of semiparametric cure rate frailty models

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  • Guoqing Diao
  • Guosheng Yin

Abstract

We consider a class of cure rate frailty models for multivariate failure time data with a survival fraction. This class is formulated through a transformation on the unknown population survival function. It incorporates random effects to account for the underlying correlation, and includes the mixture cure model and the proportional hazards cure model as two special cases. We develop efficient likelihood-based estimation and inference procedures. We show that the nonparametric maximum likelihood estimators for the parameters of these models are consistent and asymptotically normal, and that the limiting variances achieve the semiparametric efficiency bounds. Simulation studies demonstrate that the proposed methods perform well in finite samples. We provide an application of the proposed methods to the data of the age at onset of alcohol dependence, from the Collaborative Study on the Genetics of Alcoholism. Copyright The Institute of Statistical Mathematics, Tokyo 2012

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  • Guoqing Diao & Guosheng Yin, 2012. "A general transformation class of semiparametric cure rate frailty models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 959-989, October.
    • Handle: RePEc:spr:aistmt:v:64:y:2012:i:5:p:959-989
    DOI: 10.1007/s10463-012-0354-0
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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. 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.
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    5. 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.
    6. Zeng, Donglin & Yin, Guosheng & Ibrahim, Joseph G., 2006. "Semiparametric Transformation Models for Survival Data With a Cure Fraction," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 670-684, June.
    7. David V. Glidden, 2007. "Pairwise dependence diagnostics for clustered failure-time data," Biometrika, Biometrika Trust, vol. 94(2), pages 371-385.
    8. Cooner, Freda & Banerjee, Sudipto & Carlin, Bradley P. & Sinha, Debajyoti, 2007. "Flexible Cure Rate Modeling Under Latent Activation Schemes," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 560-572, June.
    9. Rebecca A. Betensky & David A. Schoenfeld, 2001. "Nonparametric Estimation in a Cure Model with Random Cure Times," Biometrics, The International Biometric Society, vol. 57(1), pages 282-286, March.
    10. Yu, Binbing & Peng, Yingwei, 2008. "Mixture cure models for multivariate survival data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1524-1532, January.
    11. D. Zeng & D. Y. Lin, 2007. "Maximum likelihood estimation in semiparametric regression models with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 507-564, September.
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    Cited by:

    1. Yuan Mengdie & Diao Guoqing, 2014. "Semiparametric Odds Rate Model for Modeling Short-Term and Long-Term Effects with Application to a Breast Cancer Genetic Study," The International Journal of Biostatistics, De Gruyter, vol. 10(2), pages 231-249, November.
    2. Guoqing Diao & Donglin Zeng & Song Yang, 2013. "Efficient Semiparametric Estimation of Short-Term and Long-Term Hazard Ratios with Right-Censored Data," Biometrics, The International Biometric Society, vol. 69(4), pages 840-849, December.
    3. Weibin Zhong & Guoqing Diao, 2023. "Semiparametric Density Ratio Model for Survival Data with a Cure Fraction," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 217-241, April.

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