A general class of Bayesian survival models with zero and nonzero cure fractions.
We propose a new class of survival models which naturally links a family of proper and improper population survival functions. The models resulting in improper survival functions are often referred to as cure rate models. This class of regression models is formulated through the Box-Cox transformation on the population hazard function and a proper density function. By adding an extra transformation parameter into the cure rate model, we are able to generate models with a zero cure rate, thus leading to a proper population survival function. A graphical illustration of the behavior and the influence of the transformation parameter on the regression model is provided. We consider a Bayesian approach which is motivated by the complexity of the model. Prior specification needs to accommodate parameter constraints due to the non-negativity of the survival function. Moreover, the likelihood function involves a complicated integral on the survival function, which may not have an analytical closed form, and thus makes the implementation of Gibbs sampling more difficult. We propose an efficient Markov chain Monte Carlo computational scheme based on Gaussian quadrature. The proposed method is illustrated with an example involving a melanoma clinical trial.
Yin
Guosheng
G
Department of Biostatistics and Applied Mathematics, M. D. Anderson Cancer Center, The University of Texas, Houston, Texas 77030, USA. gyin@odin.mdacc.tmc.edu
Ibrahim
Joseph G
JG
D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D000465:Algorithms; D000704:Analysis of Variance; D001499:Bayes Theorem; D001699:Biometry / Q000379:methods*; D019496:Cancer Vaccines / Q000627:therapeutic use; D002986:Clinical Trials as Topic; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D000077190:Interferon alpha-2; D016898:Interferon-alpha / Q000627:therapeutic use; D016013:Likelihood Functions; D008297:Male; D008390:Markov Chains; D008545:Melanoma / Q000401:mortality / Q000628:therapy; D008875:Middle Aged; D015233:Models, Statistical; D009010:Monte Carlo Method; D016016:Proportional Hazards Models; D011994:Recombinant Proteins; D012044:Regression Analysis; D012107:Research Design; D016019:Survival Analysis
D019496:Cancer Vaccines; D000077190:Interferon alpha-2; D016898:Interferon-alpha; D011994:Recombinant Proteins