One of the most popular models in survival analysis is the Cox proportional hazards model. This model has been widely used because of its simplicity. Despite its simplicity, the basic problem of the Cox model is its inability to enter unknown risk factors into the model. Some risk factors may affect the survival of a trial unit, but due to time and cost constraints, there is no possibility to measure all of these factors in the form of explanatory variables in the model. In many cases, measuring risk factors is not possible. For entering unknown risk factors into the model, a positive random variable, representative of unknown risk factors, is multiplied in the model. Then a new class of survival models, namely frailty models, is introduced. When survival data are spatially correlated, frailty models do not have good performance for analyzing the data. In these cases, a Gaussian random field would be used as frailty variable such that the spatial correlation of the data can be included in the model. But in some applications, the Gaussian assumption of spatial effects is not realistic. In this paper, we use a spatial survival model with Gaussian and non-Gaussian random effects. Considering the complexity of likelihood function for spatial survival models and the lack of closed form, the frequency approach is very time-consuming for estimation of the model parameters. We use the Bayesian approach and MCMC algorithms for estimating the model parameters. Next, the application of the model is shown in an analysis of a real dataset.
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S. Banerjee, B. P. Carlin, and A. Gelfand, Hierarchical Modeling and Analysis for Spatial Data, Chapman and Hall, New York (2004).zbMATHGoogle Scholar
S. Banerjee, M. W. Melanie, and P.C. Bradley, “Frailty modeling for spatially correlated survival data, with application to infant mortality in Minnesota,” Biostatistics, 4, No. 1, 123–142 (2003).CrossRefzbMATHGoogle Scholar
J. Besag, “Spatial interaction and the statistical analysis of lattice systems,” J. R. Stat. Soc. Ser. B., 36, No. 2, 192–236 (1974).MathSciNetzbMATHGoogle Scholar
V. Bhatt and N. Tiwari, “A spatial scan statistic for survival data based on Weibull distribution,” Stat. Med., 33, 1867–1876 (2014).MathSciNetCrossRefGoogle Scholar
D. Brook, “On the distinction between the conditional probability and the joint probability approaches in the specification of nearest-neighbour systems,” Biometrika, 51, No. 3, 481–483 (1964).MathSciNetCrossRefzbMATHGoogle Scholar
B. P. Carlin and S. Banerjee, Hierarchical Multivariate CAR Models for Spatio-Temporally Correlated Survival Data, Oxford University Press, Oxford (2003).Google Scholar