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Random effects in promotion time cure rate models

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  • Carvalho Lopes, Celia Mendes
  • Bolfarine, Heleno

Abstract

In this paper, a survival model with long-term survivors and random effects, based on the promotion time cure rate model formulation for models with a surviving fraction is investigated. We present Bayesian and classical estimation approaches. The Bayesian approach is implemented using a Markov chain Monte Carlo (MCMC) based on the Metropolis-Hastings algorithms. For the second one, we use restricted maximum likelihood (REML) estimators. A simulation study is performed to evaluate the accuracy of the applied techniques for the estimates and their standard deviations. An example on an oropharynx cancer study is used to illustrate the model and the estimation approaches considered in the study.

Suggested Citation

  • Carvalho Lopes, Celia Mendes & Bolfarine, Heleno, 2012. "Random effects in promotion time cure rate models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 75-87, January.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:1:p:75-87
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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.
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    4. Joseph G. Ibrahim & Ming-Hui Chen & Debajyoti Sinha, 2001. "Bayesian Semiparametric Models for Survival Data with a Cure Fraction," Biometrics, The International Biometric Society, vol. 57(2), pages 383-388, June.
    5. Guosheng Yin, 2005. "Bayesian Cure Rate Frailty Models with Application to a Root Canal Therapy Study," Biometrics, The International Biometric Society, vol. 61(2), pages 552-558, June.
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    9. Tsodikov, Alexander, 1998. "Asymptotic efficiency of a proportional hazards model with cure," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 237-244, August.
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    Cited by:

    1. Aurelie Bertrand & Catherine Legrand & Raymond J. Carroll & Christophe de Meester & Ingrid Van Keilegom, 2017. "Inference in a survival cure model with mismeasured covariates using a simulation-extrapolation approach," Biometrika, Biometrika Trust, vol. 104(1), pages 31-50.
    2. Gallardo, Diego I. & Bolfarine, Heleno & Pedroso-de-Lima, Antonio Carlos, 2016. "Destructive weighted Poisson cure rate models with bivariate random effects: Classical and Bayesian approaches," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 31-45.
    3. Gressani, Oswaldo & Lambert, Philippe, 2016. "Fast Bayesian inference in semi-parametric P-spline cure survival models using Laplace approximations," LIDAM Discussion Papers ISBA 2016041, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Bremhorst, Vincent & Kreyenfeld, Michaela & Lambert, Philippe, 2017. "Nonparametric double additive cure survival models: an application to the estimation of the nonlinear effect of age at first parenthood on fertility progression," LIDAM Discussion Papers ISBA 2017004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Gressani, Oswaldo & Lambert, Philippe, 2018. "Fast Bayesian inference using Laplace approximations in a flexible promotion time cure model based on P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 151-167.
    6. Durga H. Kutal & Lianfen Qian, 2018. "A Non-Mixture Cure Model for Right-Censored Data with Fréchet Distribution," Stats, MDPI, vol. 1(1), pages 1-13, November.
    7. Philippe Lambert & Vincent Bremhorst, 2020. "Inclusion of time‐varying covariates in cure survival models with an application in fertility studies," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 333-354, January.
    8. Han, Bo & Wang, Xiaoguang, 2020. "Semiparametric estimation for the non-mixture cure model in case-cohort and nested case-control studies," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).

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