Bayesian Disease Mapping : Hierarchical Modeling in Spatial Epidemiology, Third Edition

Description

Focusing on data commonly found in public health databases and clinical settings,Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiologyprovides an overview of the main areas of Bayesian hierarchical modeling and its application to the geographical analysis of disease. The book explores a range of topics in Bayesian inference and modeling, including Markov chain Monte Carlo methods, Gibbs sampling, the Metropolis-Hastings algorithm, goodness-of-fit measures, and residual diagnostics. It also focuses on special topics, such as cluster detection; space-time modeling; and multivariate, survival, and longitudinal analyses. The author explains how to apply these methods to disease mapping using numerous real-world data sets pertaining to cancer, asthma, epilepsy, foot and mouth disease, influenza, and other diseases. In the appendices, he shows how R and WinBUGS can be useful tools in data manipulation and simulation. Applying Bayesian methods to the modeling of georeferenced health data,Bayesian Disease Mappingproves that the application of these approaches to biostatistical problems can yield important insights into data. Content: Intro Halftitle Page Title Page Copyright Table of Contents List of Tables Preface to Third Edition Preface to Second Edition Preface to First Edition I Background 1 Introduction 1.1 Data Sets 2 Bayesian Inference and Modeling 2.1 Likelihood Models 2.1.1 Spatial Correlation 2.1.1.1 Conditional Independence 2.1.1.2 Joint Densities with Correlations 2.1.1.3 Pseudolikelihood Approximation 2.2 Prior Distributions 2.2.1 Propriety 2.2.2 Non-Informative Priors 2.3 Posterior Distributions 2.3.1 Conjugacy 2.3.2 Prior Choice 2.3.2.1 Regression Parameters 2.3.2.2 Variance or Precision Parameters2.3.2.3 Correlation Parameters 2.3.2.4 Probabilities 2.3.2.5 Correlated Parameters 2.4 Predictive Distributions 2.4.1 Poisson-Gamma Example 2.5 Bayesian Hierarchical Modeling 2.6 Hierarchical Models 2.7 Posterior Inference 2.7.1 Bernoulli and Binomial Examples 2.8 Exercises 3 Computational Issues 3.1 Posterior Sampling 3.2 Markov Chain Monte Carlo (MCMC) Methods 3.3 Metropolis and Metropolis-Hastings Algorithms 3.3.1 Metropolis Updates 3.3.2 Metropolis-Hastings Updates 3.3.3 Gibbs Updates 3.3.4 Metropolis-Hastings (M-H) versus Gibbs Algorithms3.3.5 Special Methods 3.3.6 Convergence 3.3.6.1 Single-Chain Methods 3.3.6.2 Multi-Chain Methods 3.3.7 Subsampling and Thinning 3.3.7.1 Monitoring Metropolis-Like Samplers 3.4 Perfect Sampling 3.5 Posterior and Likelihood Approximations 3.5.1 Pseudolikelihood and Other Forms 3.5.2 Asymptotic Approximations 3.5.2.1 Asymptotic Quadratic Form 3.5.2.2 Laplace Integral Approximation 3.5.2.3 INLA and R-INLA 3.6 Alternative Computational Aproaches 3.6.1 Maximum A Posteriori Estimation (MAP) 3.6.2 Iterated Conditional Modes (ICMs) 3.6.3 MC3 and Parallel Tempering3.6.4 Variational Bayes 3.6.5 Sequential Monte Carlo 3.7 Approximate Bayesian Computation (ABC) 3.8 Exercises 4 Residuals and Goodness-of-Fit 4.1 Model GOF Measures 4.1.1 Deviance Information Criterion 4.1.2 Posterior Predictive Loss 4.2 General Residuals 4.3 Bayesian Residuals 4.4 Predictive Residuals and Bootstrap 4.4.1 Conditional Predictive Ordinates (CPOs.) 4.5 Interpretation of Residuals in a Bayesian Setting 4.6 Pseudo-Bayes Factors and Marginal Predictive Likelihood 4.7 Other Diagnostics 4.8 Exceedance Probabilities 4.9 Exercises II Themes5 Disease Map Reconstruction and Relative Risk Estimation 5.1 Introduction to Case Event and Count Likelihoods 5.1.1 Poisson Process Model 5.1.2 Conditional Logistic Model 5.1.3 Binomial Model for Count Data 5.1.4 Poisson Model for Count Data 5.1.4.1 Standardisation 5.1.4.2 Relative Risk 5.2 Specification of Predictor in Case Event and Count Models 5.2.1 Bayesian Linear Model 5.3 Simple Case and Count Data Models with Uncorrelated Random Effects 5.3.1 Gamma and Beta Models 5.3.1.1 Gamma Models 5.3.1.1.1 Hyperprior Distributions 5.3.1.1.2 Linear Parameterization