zbMATH — the first resource for mathematics

Cure rate models: a unified approach. (English) Zbl 1098.62127
Summary: The authors propose a novel class of cure rate models for right-censored failure time data. The class is formulated through a transformation on the unknown population survival function. It includes the mixture cure model and the promotion time cure model as two special cases. The authors propose a general form of the covariate structure which automatically satisfies an inherent parameter constraint and includes the corresponding binomial and exponential covariate structures in the two main formulations of cure models.
The proposed class provides a natural link between the mixture and the promotion time cure models, and it offers a wide variety of new modelling structures as well. Within the Bayesian paradigm, a Markov chain Monte Carlo computational scheme is implemented for sampling from the full conditional distributions of the parameters. Model selection is based on the conditional predictive ordinate criterion. The use of the new class of models is illustrated with a set of real data involving a melanoma clinical trial.

62N02 Estimation in survival analysis and censored data
62F15 Bayesian inference
62P10 Applications of statistics to biology and medical sciences; meta analysis
65C40 Numerical analysis or methods applied to Markov chains
Full Text: DOI
[1] Aranda-Ordaz, An extension of the proportional-hazards model for grouped data, Biometrics 39 pp 109– (1983) · Zbl 0521.62089
[2] Arjas, Nonparametric Bayesian inference from right censored survival data, using the Gibbs sampler, Statistica Sinica 4 pp 505– (1994) · Zbl 0823.62030
[3] Barlow, General relative risk models in stratified epidemiologic studies, Applied Statistics 34 pp 246– (1985) · Zbl 0584.62180
[4] Berkson, Survival curve for cancer patients following treatment, Journal of the American Statistical Association 47 pp 501– (1952)
[5] Betensky, Nonparametric estimation in a cure model with random cure times, Biometrics 57 pp 282– (2001) · Zbl 1209.62257
[6] Box, An analysis of transformations (with discussion), Journal of the Royal Statistical Society Series B 26 pp 211– (1964) · Zbl 0156.40104
[7] Breslow, General relative risk functions for case-control studies, American Journal of Epidemiology 122 pp 149– (1985)
[8] 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
[9] Chen, Monte Carlo methods for Bayesian analysis of constrained parameter problems, Biometrika 85 pp 73– (1998) · Zbl 0904.62035
[10] Chen, Monte Carlo Methods in Bayesian Computation. (2000) · Zbl 0949.65005 · doi:10.1007/978-1-4612-1276-8
[11] Cowles, Markov chain Monte Carlo convergence diagnostics: A comparative review, Journal of the American Statistical Association 91 pp 883– (1996) · Zbl 0869.62066
[12] Cox, Regression models and life-tables (with discussion), Journal of the Royal Statistical Society Series B 34 pp 187– (1972) · Zbl 0243.62041
[13] Dey, Bayesian approach for nonlinear random effects models, Biometrics 53 pp 1239– (1997) · Zbl 0911.62024
[14] Geisser, Predictive Inference: an Introduction. (1993) · doi:10.1007/978-1-4899-4467-2
[15] Gelfand, Model determination using predictive distributions with implementation via sampling-based methods pp 147– (1992)
[16] Gelfand, Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling, Journal of the American Statistical Association 87 pp 523– (1992)
[17] Gilks, Adaptive rejection metropolis sampling within Gibbs sampling, Applied Statistics 44 pp 455– (1995) · Zbl 0893.62110
[18] Gray, A linear rank test for use when the main interest is in differences in cure rates, Biometrics 45 pp 899– (1989) · Zbl 0715.62226
[19] Ibrahim, Power prior distributions for regression models, Statistical Science 15 pp 46– (2000)
[20] Ibrahim, Bayesian Survival Analysis. (2001) · Zbl 0978.62091 · doi:10.1007/978-1-4757-3447-8
[21] Ibrahim, Bayesian semiparametric models for survival data with a cure fraction, Biometrics 57 pp 383– (2001) · Zbl 1209.62036
[22] Kirkwood, High- and low-Dose interferon Alfa-2b in high-risk melanoma: first analysis of intergroup trial E1690/S9111/C9190, Journal of Clinical Oncology 18 pp 2444– (2000)
[23] Kuk, A mixture model combining logistic regression with proportional hazards regression, Biometrika 79 pp 531– (1992) · Zbl 0775.62300
[24] Maller, Survival Analysis with Long-Term Survivors. (1996) · Zbl 1151.62350
[25] Peng, A nonparametric mixture model for cure rate estimation, Biometrics 56 pp 237– (2000)
[26] Sy, Estimation in a Cox proportional hazards cure model, Biometrics 56 pp 227– (2000) · Zbl 1060.62670
[27] Taylor, Semi-parametric estimation in failure time mixture models, Biometrics 51 pp 899– (1995) · Zbl 0875.62493
[28] Tsodikov, A proportional hazards model taking account of long-term survivors, Biometrics 54 pp 1508– (1998) · Zbl 1058.62663
[29] Yu. Yakovlev, Biométrie et Analyse de Données Spatio-Temporelles: 12 pp 66– (1993)
[30] Yakovlev, Stochastic Models of Tumor Latency and Their Biostatistical Applications. (1996) · Zbl 0919.92024
[31] Yin, A general class of Bayesian survival models with zero and non-zero cure fractions, Biometrics 61 pp 403– (2005) · Zbl 1077.62087
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.