Ibrahim, Joseph G.; Chen, Ming-Hui; Sinha, Debajyoti Bayesian semiparametric models for survival data with a cure fraction. (English) Zbl 1209.62036 Biometrics 57, No. 2, 383-388 (2001). 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. Cited in 29 Documents 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 PDFBibTeX XMLCite \textit{J. G. Ibrahim} et al., Biometrics 57, No. 2, 383--388 (2001; Zbl 1209.62036) Full Text: DOI 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 · doi:10.2307/2670006 [2] Ibrahim, Power distributions for regression models, Statistical Science 15 pp 46– (2000) · doi:10.1214/ss/1009212673 [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 · doi:10.1142/9789812831798 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.