Spatially-dependent Bayesian model selection for disease mapping

In disease mapping where predictor effects are to be modeled, it is often the case that sets of predictors are fixed, and the aim is to choose between fixed model sets. Model selection methods, both Bayesian model selection and Bayesian model averaging, are approaches within the Bayesian paradigm for achieving this aim. In the spatial context, model selection could have a spatial component in the sense that some models may be more appropriate for certain areas of a study region than others. In this work, we examine the use of spatially referenced Bayesian model averaging and Bayesian model selection via a large-scale simulation study accompanied by a small-scale case study. Our results suggest that BMS performs well when a strong regression signature is found.

[1]  David Madigan,et al.  Bayesian Variable and Transformation Selection in Linear Regression , 2002 .

[2]  H. Bondell,et al.  Joint Variable Selection for Fixed and Random Effects in Linear Mixed‐Effects Models , 2010, Biometrics.

[3]  Neal Alexander,et al.  Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiology , 2011 .

[4]  Han Lin Shang,et al.  The BUGS book: a practical introduction to Bayesian analysis , 2013 .

[5]  Merlise A. Clyde,et al.  Bayesian Model Averaging in the M-Open Framework , 2013 .

[6]  Kevin A. Henry,et al.  Associations of Census-Tract Poverty with Subsite-Specific Colorectal Cancer Incidence Rates and Stage of Disease at Diagnosis in the United States , 2014, Journal of cancer epidemiology.

[7]  E. George,et al.  Negotiating multicollinearity with spike-and-slab priors , 2014, Metron.

[8]  David C. Wheeler,et al.  Assessing local model adequacy in Bayesian hierarchical models using the partitioned deviance information criterion , 2010, Comput. Stat. Data Anal..

[9]  Ida Scheel,et al.  A Bayesian hierarchical model with spatial variable selection: the effect of weather on insurance claims , 2013, Journal of the Royal Statistical Society. Series C, Applied statistics.

[10]  P. Diggle,et al.  Model‐based geostatistics , 2007 .

[11]  B. Carlin,et al.  Identifiability and convergence issues for Markov chain Monte Carlo fitting of spatial models. , 2000, Statistics in medicine.

[12]  J M Klaase,et al.  Spatial variation in stage distribution in colorectal cancer in the Netherlands. , 2012, European journal of cancer.

[13]  Adrian E. Raftery,et al.  Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors , 1999 .

[14]  Andrew B. Lawson,et al.  Bayesian Biostatistics: Lesaffre/Bayesian Biostatistics , 2012 .

[15]  Adrian E. Raftery,et al.  Bayesian Model Averaging: A Tutorial , 2016 .

[16]  Hongtu Zhu,et al.  VARIABLE SELECTION FOR REGRESSION MODELS WITH MISSING DATA. , 2010, Statistica Sinica.

[17]  Guifang Fu,et al.  The Bayesian lasso for genome-wide association studies , 2011, Bioinform..

[18]  M. Clyde,et al.  Model Uncertainty , 2003 .

[19]  S. Richardson,et al.  Variable selection and Bayesian model averaging in case‐control studies , 2001, Statistics in medicine.

[20]  Chris Hans,et al.  Model uncertainty and variable selection in Bayesian lasso regression , 2010, Stat. Comput..

[21]  T. Sheehan,et al.  Spatial analysis of colorectal cancer incidence and proportion of late-stage in Massachusetts residents: 1995–1998 , 2007, International journal of health geographics.