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Bayesian semiparametric models for survival data with a cure fraction. (English) Zbl 1209.62036
Summary: 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
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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)
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