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

392 Pages·2013·18.56 MB·\392

by  Andrew B. Lawson (Author)

Bayesian Disease Mapping
Hierarchical Modeling
in Spatial Epidemiology
Second Edition
CHAPMAN & HALL/CRC
Interdisciplinar y Statistics Series
Series editors: N. Keiding, B.J.T. Morgan, C.K. Wikle, P. van der Heijden
Published titles
AN INVARIANT APPROACH TO S. Lele and J. Richtsmeier
STATISTICAL ANALYSIS OF SHAPES
ASTROSTATISTICS G. Babu and E. Feigelson
BAYESIAN ANALYSIS FOR Ruth King, Byron J. T. Morgan,
POPULATION ECOLOGY Olivier Gimenez, and
Stephen P. Brooks

BAYESIAN DISEASE MAPPING: Andrew B. Lawson
HIERARCHICAL MODELING IN SPATIAL
EPIDEMIOLOGY, SECOND EDITION
BIOEQUIVALENCE AND S. Patterson and
STATISTICS IN CLINICAL B. Jones
PHARMACOLOGY
CLINICAL TRIALS IN ONCOLOGY, S. Green, J. Benedetti,
THIRD EDITION A. Smith, and J. Crowley

CLUSTER RANDOMISED TRIALS R.J. Hayes and L.H. Moulton
CORRESPONDENCE ANALYSIS M. Greenacre
IN PRACTICE, SECOND EDITION
DESIGN AND ANALYSIS OF D.L. Fairclough
QUALITY OF LIFE STUDIES
IN CLINICAL TRIALS, SECOND EDITION
DYNAMICAL SEARCH L. Pronzato, H. Wynn,
and A. Zhigljavsky
FLEXIBLE IMPUTATION OF MISSING DATA S. van Buuren
GENERALIZED LATENT VARIABLE A. Skrondal and
MODELING: MULTILEVEL, S. Rabe-Hesketh
LONGITUDINAL, AND STRUCTURAL
EQUATION MODELS
GRAPHICAL ANALYSIS OF K. Basford and J. Tukey
MULTI-RESPONSE DATA
MARKOV CHAIN MONTE CARLO W. Gilks, S. Richardson,
IN PRACTICE and D. Spiegelhalter
Published titles
INTRODUCTION TO M. Waterman
COMPUTATIONAL BIOLOGY:
MAPS, SEQUENCES, AND GENOMES
MEASUREMENT ERROR AND P. Gustafson
MISCLASSIFICATION IN STATISTICS
AND EPIDEMIOLOGY: IMPACTS AND
BAYESIAN ADJUSTMENTS
MEASUREMENT ERROR: J. P. Buonaccorsi
MODELS, METHODS, AND APPLICATIONS
META-ANALYSIS OF BINARY DATA D. Böhning, R. Kuhnert,
USING PROFILE LIKELIHOOD and S. Rattanasiri
STATISTICAL ANALYSIS OF GENE T. Speed
EXPRESSION MICROARRAY DATA
STATISTICAL AND COMPUTATIONAL R. Wu and M. Lin
PHARMACOGENOMICS
STATISTICS IN MUSICOLOGY J. Beran
STATISTICS OF MEDICAL IMAGING T. Lei
STATISTICAL CONCEPTS J. Aitchison, J.W. Kay,
AND APPLICATIONS IN and I.J. Lauder
CLINICAL MEDICINE
STATISTICAL AND PROBABILISTIC P.J. Boland
METHODS IN ACTUARIAL SCIENCE
STATISTICAL DETECTION AND P. Rogerson and I. Yamada
SURVEILLANCE OF GEOGRAPHIC
CLUSTERS
STATISTICS FOR ENVIRONMENTAL A. Bailer and W. Piegorsch
BIOLOGY AND TOXICOLOGY
STATISTICS FOR FISSION R.F. Galbraith
TRACK ANALYSIS
VISUALIZING DATA PATTERNS D.B. Carr and L.W. Pickle
WITH MICROMAPS
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
Chapman & Hall/CRC
Interdisciplinary Statistics Series
Bayesian Disease Mapping
Hierarchical Modeling
in Spatial Epidemiology
Second Edition
Andrew B. Lawson
Division of Biostatistics and Epidemiology
Medical University of South Carolina (MUSC)
Charleston, South Carolina, USA
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Contents
List of Tables xiii
Preface xv
Preface to Second Edition xvii
I Background 1
1 Introduction 3
1.1 Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Bayesian Inference and Modeling 19
2.1 Likelihood Models . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.1 Spatial Correlation . . . . . . . . . . . . . . . . . . . . 20
2.2 Prior Distributions . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.1 Propriety . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.2 Non-informative Priors . . . . . . . . . . . . . . . . . . 22
2.3 Posterior Distributions . . . . . . . . . . . . . . . . . . . . . . 23
2.3.1 Conjugacy . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.2 Prior Choice. . . . . . . . . . . . . . . . . . . . . . . . 25
2.4 Predictive Distributions . . . . . . . . . . . . . . . . . . . . . 25
2.4.1 Poisson-Gamma Example . . . . . . . . . . . . . . . . 26
2.5 Bayesian Hierarchical Modeling . . . . . . . . . . . . . . . . . 26
2.6 Hierarchical Models . . . . . . . . . . . . . . . . . . . . . . . . 26
2.7 Posterior Inference . . . . . . . . . . . . . . . . . . . . . . . . 28
2.7.1 A Bernoulli and Binomial Example . . . . . . . . . . . 29
2.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 Computational Issues 35
3.1 Posterior Sampling . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Markov Chain Monte Carlo Methods . . . . . . . . . . . . . . 36
3.3 Metropolis and Metropolis-Hastings Algorithms . . . . . . . . 37
3.3.1 Metropolis Updates. . . . . . . . . . . . . . . . . . . . 37
3.3.2 Metropolis-Hastings Updates . . . . . . . . . . . . . . 37
3.3.3 Gibbs Updates . . . . . . . . . . . . . . . . . . . . . . 38
3.3.4 M-H versus Gibbs Algorithms . . . . . . . . . . . . . . 38
3.3.5 Special Methods . . . . . . . . . . . . . . . . . . . . . 39
vii
viii Contents
3.3.6 Convergence. . . . . . . . . . . . . . . . . . . . . . . . 39
3.3.7 Subsampling and Thinning . . . . . . . . . . . . . . . 44
3.4 Perfect Sampling . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.5 Posterior and Likelihood Approximations . . . . . . . . . . . 47
3.5.1 Pseudo-likelihood and Other Forms . . . . . . . . . . . 47
3.5.2 Asymptotic Approximations . . . . . . . . . . . . . . . 48
3.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4 Residuals and Goodness-of-Fit 53
4.1 Model GOF Measures . . . . . . . . . . . . . . . . . . . . . . 53
4.1.1 The Deviance Information Criterion . . . . . . . . . . 54
4.1.2 Posterior Predictive Loss. . . . . . . . . . . . . . . . . 55
4.2 General Residuals . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3 Bayesian Residuals . . . . . . . . . . . . . . . . . . . . . . . . 58
4.4 Predictive Residuals and the Bootstrap . . . . . . . . . . . . . 59
4.4.1 Conditional Predictive Ordinates . . . . . . . . . . . . 60
4.5 Interpretation of Residuals in a Bayesian Setting . . . . . . . 61
4.6 Pseudo Bayes Factors and Marginal Predictive Likelihood . . 62
4.7 Other Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.8 Exceedence Probabilities . . . . . . . . . . . . . . . . . . . . . 64
4.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
II Themes 69
5 Disease Map Reconstruction and Relative Risk Estimation 71
5.1 An Introduction to Case Event and Count Likelihoods . . . . 71
5.1.1 The Poisson Process Model . . . . . . . . . . . . . . . 71
5.1.2 The Conditional Logistic Model . . . . . . . . . . . . . 72
5.1.3 The Binomial Model for Count Data . . . . . . . . . . 73
5.1.4 The Poisson Model for Count Data . . . . . . . . . . . 74
5.2 Specification of the Predictor in Case Event and Count Models 75
5.2.1 The Bayesian Linear Model . . . . . . . . . . . . . . . 76
5.3 Simple Case and Count Data Models with Uncorrelated Ran-
dom Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.3.1 Gamma and Beta Models . . . . . . . . . . . . . . . . 78
5.3.2 Log-normal/Logistic-normal Models . . . . . . . . . . 80
5.4 Correlated Heterogeneity Models . . . . . . . . . . . . . . . . 81
5.4.1 Conditional Autoregressive (CAR) Models . . . . . . . 83
5.4.2 Fully-specified Covariance Models. . . . . . . . . . . . 86
5.5 Convolution Models . . . . . . . . . . . . . . . . . . . . . . . 87
5.6 Model Comparison and Goodness-of-Fit Diagnostics . . . . . 88
5.6.1 Residual Spatial Autocorrelation . . . . . . . . . . . . 90
5.7 Alternative Risk Models . . . . . . . . . . . . . . . . . . . . . 92
5.7.1 Autologistic Models . . . . . . . . . . . . . . . . . . . 93
5.7.2 Spline-based Models . . . . . . . . . . . . . . . . . . . 96
Contents ix
5.7.3 Zip Regression Models . . . . . . . . . . . . . . . . . . 99
5.7.4 Ordered and Unordered Multi-Category Data . . . . . 102
5.7.5 Latent Structure Models . . . . . . . . . . . . . . . . . 102
5.8 Edge Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.8.1 Edge Weighting Schemes and McMC Methods . . . . 107
5.8.2 Discussion and Extension to Space-Time . . . . . . . . 108
5.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.9.1 Maximum Likelihood . . . . . . . . . . . . . . . . . . . 109
5.9.2 Poisson-Gamma Model: Posterior and Predictive In-
ference . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.9.3 Poisson-Gamma Model: Empirical Bayes . . . . . . . . 111
6 Disease Cluster Detection 113
6.1 Cluster Definitions . . . . . . . . . . . . . . . . . . . . . . . . 113
6.1.1 Hot Spot Clustering . . . . . . . . . . . . . . . . . . . 115
6.1.2 Clusters as Objects or Groupings . . . . . . . . . . . . 115
6.1.3 Clusters Defined as Residuals . . . . . . . . . . . . . . 115
6.2 Cluster Detection using Residuals . . . . . . . . . . . . . . . . 116
6.2.1 Case Event Data . . . . . . . . . . . . . . . . . . . . . 116
6.2.2 Count Data . . . . . . . . . . . . . . . . . . . . . . . . 120
6.3 Cluster Detection using Posterior Measures . . . . . . . . . . 122
6.4 Cluster Models . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.4.1 Case Event Data . . . . . . . . . . . . . . . . . . . . . 125
6.4.2 Count Data . . . . . . . . . . . . . . . . . . . . . . . . 133
6.4.3 Markov Connected Component Field (MCCF) Models 137
6.5 Edge Detection and Wombling . . . . . . . . . . . . . . . . . 139
7 Regression and Ecological Analysis 141
7.1 Basic Regression Modeling . . . . . . . . . . . . . . . . . . . . 141
7.1.1 Linear Predictor Choice . . . . . . . . . . . . . . . . . 141
7.1.2 Covariate Centering . . . . . . . . . . . . . . . . . . . 142
7.1.3 Initial Model Fitting . . . . . . . . . . . . . . . . . . . 142
7.1.4 Contextual Effects . . . . . . . . . . . . . . . . . . . . 145
7.2 Missing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
7.2.1 Missing Outcomes . . . . . . . . . . . . . . . . . . . . 146
7.2.2 Missing Covariates . . . . . . . . . . . . . . . . . . . . 151
7.3 Non-Linear Predictors . . . . . . . . . . . . . . . . . . . . . . 151
7.4 Confounding and Multi-colinearity . . . . . . . . . . . . . . . 152
7.5 Geographically Dependent Regression . . . . . . . . . . . . . 155
7.6 Variable Selection . . . . . . . . . . . . . . . . . . . . . . . . . 157
7.7 Ecological Analysis: The General Case of Regression . . . . . 159
7.8 Biases and Misclassification Error . . . . . . . . . . . . . . . . 165
7.8.1 Ecological Biases . . . . . . . . . . . . . . . . . . . . . 165