title: A transformation class for spatio-temporal survival data with a cure fraction.
abstract: We propose a hierarchical Bayesian methodology to model spatially or spatio-temporal clustered survival data with possibility of cure. A flexible continuous transformation class of survival curves indexed by a single parameter is used. This transformation model is a larger class of models containing two special cases of the well-known existing models: the proportional hazard and the proportional odds models. The survival curve is modeled as a function of a baseline cumulative distribution function, cure rates, and spatio-temporal frailties. The cure rates are modeled through a covariate link specification and the spatial frailties are specified using a conditionally autoregressive model with time-varying parameters resulting in a spatio-temporal formulation. The likelihood function is formulated assuming that the single parameter controlling the transformation is unknown and full conditional distributions are derived. A model with a non-parametric baseline cumulative distribution function is implemented and a Markov chain Monte Carlo algorithm is specified to obtain the usual posterior estimates, smoothed by regional level maps of spatio-temporal frailties and cure rates. Finally, we apply our methodology to melanoma cancer survival times for patients diagnosed in the state of New Jersey between 2000 and 2007, and with follow-up time until 2007.
authors.affiliation: Division of Biostatistics and Epidemiology, Department of Public Health, Weill Medical College of Cornell University, New York, USA sah2024@med.cornell.edu.
authors.forename: Sandra M
authors.initials: SM
authors.lastname: Hurtado Rúa
authors.affiliation: Department of Statistics, University of Connecticut, Storrs, USA.
authors.forename: Dipak K
authors.initials: DK
authors.lastname: Dey
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D056808:Biostatistics; D006801:Humans; D016013:Likelihood Functions; D008390:Markov Chains; D008545:Melanoma / Q000401:mortality; D015233:Models, Statistical; D009010:Monte Carlo Method; D016017:Odds Ratio; D016016:Proportional Hazards Models; D016019:Survival Analysis