title: Bayesian random threshold estimation in a Cox proportional hazards cure model.
abstract: In this paper, we develop a Bayesian approach to estimate a Cox proportional hazards model that allows a threshold in the regression coefficient, when some fraction of subjects are not susceptible to the event of interest. A data augmentation scheme with latent binary cure indicators is adopted to simplify the Markov chain Monte Carlo implementation. Given the binary cure indicators, the Cox cure model reduces to a standard Cox model and a logistic regression model. Furthermore, the threshold detection problem reverts to a threshold problem in a regular Cox model. The baseline cumulative hazard for the Cox model is formulated non-parametrically using counting processes with a gamma process prior. Simulation studies demonstrate that the method provides accurate point and interval estimates. Application to a data set of oropharynx cancer patients suggests a significant threshold in age at diagnosis such that the effect of gender on disease-specific survival changes after the threshold.
authors.affiliation: Department of Biostatistics, University of Michigan, Ann Arbor, MI, U.S.A.
authors.forename: Lili
authors.initials: L
authors.lastname: Zhao
authors.forename: Dai
authors.initials: D
authors.lastname: Feng
authors.forename: Emily L
authors.initials: EL
authors.lastname: Bellile
authors.forename: Jeremy M G
authors.initials: JM
authors.lastname: Taylor
mesh_terms: D000328:Adult; D000367:Age Factors; D000368:Aged; D000369:Aged, 80 and over; D001499:Bayes Theorem; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D053208:Kaplan-Meier Estimate; D008297:Male; D008390:Markov Chains; D008875:Middle Aged; D009010:Monte Carlo Method; D009959:Oropharyngeal Neoplasms / Q000453:epidemiology; D016016:Proportional Hazards Models; D012737:Sex Factors
keywords: Cox model; Markov chain Monte Carlo; cure model; mixture model; threshold