Medical Applications of Finite... | Buy

The book shows how to model heterogeneity in medical research with covariate adjusted finite mixture models. The areas of application include epidemiology, gene expression data, disease mapping, meta-analysis, neurophysiology and pharmacology. After an informal introduction the book provides and summarizes the mathematical background necessary to understand the algorithms. The emphasis of the book is on a variety of medical applications such as gene expression data, meta-analysis and population pharmacokinetics. These applications are discussed in detail using real data from the medical literature. The book offers an R package which enables the reader to use the methods for his/her needs.

Peter Schlattmann is Associate Professor (Priv. - Doz.) in the Department of Biostatistics and Clinical Epidemiology at the Charite (mit Accent) Universitatsmedizin Berlin. He is actively involved in medical consulting and the author of many papers in medical and statistical journals.

Overview of the Book	p. 1
Introduction: Heterogeneity in Medicine	p. 7
Example: Plasma Concentration of Beta-Carotene	p. 11
Identification of a Latent Structure	p. 11
Including Covariates	p. 13
Computation	p. 15
Example: Analysis of Heterogeneity in Drug Development	p. 18
Basic Pharmacokinetic Concepts	p. 18
Pharmacokinetic Parameters	p. 19
First-Order Compartment Models	p. 20
Population Pharmacokinetics	p. 21
Theophylline Pharmacokinetics	p. 22
A Note of Caution	p. 28
Modeling Count Data	p. 29
Example: Morbidity in Northeast Thailand	p. 29
Parametric Mixture Models	p. 30
Finite Mixture Models	p. 33
Diagnostic Plots for Finite Mixture Models	p. 34
A Finite Mixture Model for the Illness Spell Data	p. 34
Estimating the Number of Components	p. 36
Computation	p. 39
Combination of VEM and EM Algorithms	p. 39
Using the EM Algorithm	p. 41
Estimating the Number of Components	p. 42
Including Covariates	p. 43
The Ames Test	p. 43
Poisson and Negative Binomial Regression Models	p. 47
Covariate-Adjusted Mixture Model for the Ames Test Data	p. 49
Computation	p. 51
Fitting Poisson and Negative Binomial Regression Models with SAS	p. 51
Fitting Poisson and Negative Binomial Regression Models with R	p. 52
Fitting Finite Mixture Models with the Package Caman	p. 53
Theory and Algorithms	p. 55
The Likelihood of Finite Mixture Models	p. 55
Convex Geometry and Optimization	p. 56
Derivatives and Directional Derivatives of Convex Functions	p. 61
Application to the Flexible Support Size Case	p. 64
Geometric Characterization	p. 64
Algorithms for Flexible Support Size	p. 69
Vem Algorithm: Computation	p. 70
The Fixed Support Size Case	p. 72
Fixed Support Size: The Newton-Raphson Algorithm	p. 72
A General Description of the EM Algorithm	p. 73
The EM Algorithm for Finite Mixture Models	p. 74
EM Algorithm: Computation	p. 77
A Hybrid Mixture Algorithm	p. 79
The EM Algorithm with Gradient Update	p. 80
Estimating the Number of Components	p. 82
Graphical Techniques	p. 82
Testing for the Number of Components	p. 83
The Bootstrap Approach	p. 84
Adjusting for Covariates	p. 87
Generalized Linear Models	p. 87
The EM Algorithm for Covariate-Adjusted Mixture Models	p. 91
Computation: Vitamin A Supplementation Revisited	p. 93
An Extension of the EM Algorithm with Gradient Update for Covariate-Adjusted Mixture Models	p. 95
Case Study: EM Algorithm with Gradient Update for Nonlinear Finite Mixture Models	p. 97
Introduction	p. 97
Example: Dipyrone Pharmacokinetics	p. 98
First-Order Compartment Models	p. 98
Finite Mixture Model Analysis	p. 102
Disease Mapping and Cluster Investigations	p. 107
Introduction	p. 107
Investigation of General Clustering	p. 109
Traditional Approaches	p. 110
The Empirical Bayes Approach	p. 112
Computation	p. 117
A Note on Autocorrelation Versus Herterogeneity	p. 119
Heterogeneity	p. 119
Autocorrelation	p. 121
Focused Clustering	p. 124
The Score Test for Focused Clustering	p. 124
The Score Test Adjusted for Heterogeneity	p. 128
The Score Test Based on the Negative Binomial Distribution	p. 129
Estimation of ¿ and ¿	p. 130
Case Study: Leukemia in Adults in the Vicinity of Krümmel	p. 132
Background	p. 133
The Retrospective Incidence Study Elbmarsch	p. 134
Focused Analysis	p. 135
Disease Mapping and Model-Based Methods	p. 136
Mathematical Details of the Score Test	p. 138
Expectation and Variance of the Score	p. 138
The Score Test	p. 139
Modeling Heterogeneity in Psychophysiology	p. 143
The Electroencephalogram	p. 143
Digitization	p. 143
Modeling Spatial Heterogeneity Using Generalized Linear Mixed Models	p. 144
The Periodogram and its Distributional Properties	p. 144
Connection to Generalized Linear Models	p. 148
Covariate-Adjusted Finite Mixture Models for the EEG Data	p. 149
Investigating and Analyzing Heterogeneity in Meta-analysis	p. 153
Introduction	p. 153
Different Types of Overviews	p. 154
Basic Statistical Analysis	p. 155
Single Study Results	p. 155
Publication Bias	p. 157
Estimation of a Summary Effect	p. 160
Analysis of Heterogeneity	p. 162
The DerSimonian-Laird Approach	p. 164
Maximum Likelihood Estimation of the Heterogeneity Variance ¿²	p. 166
Another Estimator of ¿²: The Simple Heterogeneity Variance Estimator	p. 168
A Comment on Summary Estimates Under Heterogeneity	p. 169
The Finite Mixture Model Approach	p. 169
Simulation Study Comparing Four Estimators of ¿²	p. 171
Desing of the Simulation Study	p. 171
Simulation Results	p. 173
Discussion	p. 173
Metaregression	p. 176
Interpretation of the Results of Meta-analysis of Observational Studies	p. 180
Bias	p. 181
Confounding	p. 181
Heterogeneity	p. 182
Case Study: Aspirin Use and Breast Cancer Risk - A Meta-analysis and Metaregression of Observational Studies from 2001 to 2007	p. 183
Introduction	p. 183
Literature Search and Data Extraction	p. 184
Study Characteristics	p. 184
Publication Bias	p. 185
Results	p. 186
Results of a Metaregression	p. 187
Modeling Dose Response	p. 187
A Metaregression Model for Dose-Response Analysis	p. 190
Discussion	p. 191
Computation	p. 192
"Standard Meta-analysis"	p. 192
Meta-analysis with SAS	p. 194
Finite Mixture Models	p. 196
Metaregression	p. 197
Analysis of Gene Expression Data	p. 201
DNA Microarrays	p. 201
The Analysis of Differential Gene Expression	p. 202
Analysis Based on Simultaneous Hypothesis Testing	p. 202
A Mixture Model Approach	p. 206
Computation	p. 209
A Change of Perspective: Applying Methods from Meta-analysis	p. 210
Case Study: Identification of a Gene Signature for Breast Cancer Prognosis	p. 213
Introduction	p. 213
Application of the Meta-analytic Mixture Model to the Breast Cancer Data	p. 214
Validation of Results	p. 215
References	p. 219
Subject Index	p. 237
Author Index	p. 243
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