Spatial Data Analysis Using Bayesian AFT Model

In recent years,with the availability of large cancer registries and the importance for research,flexible combination of both geographical patterning and risk effects in cancer survival models becomes more and more popular.Most spatial survival models randomly get survival curves from different subpopulations.However,in epidemiological cancer studies,it is common for survival curves to cross in two subpopulations,so interpretable standard survival models can not be used without modification.Usually the solution is including time-varying regression effects in the proportional hazards model or fully non-parametric model,but either of the two models will destroy interpretability in fitted model.To solve this problem,Zhou et al develop a generalized accelerated failure time model,it allows stratification on continuous or categorical covariates,meanwhile it provides per-variable tests for whether stratification is necessary with novel approximate Bayes factors.This model has many advantages,such as it can be used for arbitrarily censored data,can be interprected easily and capture crossing survival curves when spatial correlation exists.For posterior inference,they develop a detailed Markov chain Monte Carlo algorithm,which can be implemented with fraltyGAFT function in the R package spBayesSurv.In this paper,first,we illustrate work done by some scholars in recent years.Second,we make a brief introduction to related concepts and methods.Next,we make a series of studies in simulation to ensure the applicability and stability.Then we analyze some real data and make some conclusions.Finally,we summarize the work in this paper and make further discussions.