Bayesian semiparametric models for survival data with a cure fraction.

*(English)*Zbl 1209.62036Summary: We propose methods for Bayesian inference for a new class of semiparametric survival models with a cure fraction. Specifically, we propose a semiparametric cure rate model with a smoothing parameter that controls the degree of parametricity in the right tail of the survival distribution. We show that such a parameter is crucial for these kinds of models and can have an impact on the posterior estimates. Several novel properties of the proposed model are derived. In addition, we propose a class of improper noninformative priors based on this model and examine the properties of the implied posterior. Also, a class of informative priors based on historical data is proposed and its theoretical properties are investigated. A case study involving a melanoma clinical trial is discussed in detail to demonstrate the proposed methodology.

##### MSC:

62F15 | Bayesian inference |

62N02 | Estimation in survival analysis and censored data |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

##### Keywords:

cure rate model; Gibbs sampling; historical data; latent variables; piecewise exponential; posterior distribution; semiparametric model; smoothing parameter
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\textit{J. G. Ibrahim} et al., Biometrics 57, No. 2, 383--388 (2001; Zbl 1209.62036)

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##### References:

[1] | Chen, A new Bayesian model for survival data with a surviving fraction, Journal of the American Statistical Association 94 pp 909– (1999) · Zbl 0996.62019 |

[2] | Ibrahim, Power distributions for regression models, Statistical Science 15 pp 46– (2000) |

[3] | Ibrahim, Bayesian semi-parametric models for survival data with a cure fraction (1999) |

[4] | Yakovlev, Stochastic Models of Tumor Latency and Their Biostatistical Applications (1996) · Zbl 0919.92024 |

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