Medical applications of finite mixture models:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis/Dissertation Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
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| Series: | Statistics for biology and health
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| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018763063&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Literaturverz. S. 219 - 235 |
| Physical Description: | X, 246 S. graph. Darst. 25 cm |
| ISBN: | 9783540686507 |
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Titel: Medical applications of finite mixture models
Autor: Schlattmann, Peter
Jahr: 2009
Contents
1 Overview of the Book I
2 Introduction: Heterogeneity in Medicine 7
2.1 Example: Plasma Concentration of Beta-Carotene 11
2.1.1 Identification of a Latent Structure 11
2.1.2 Including Covariates 13
2.2 Computation 15
2.3 Example: Analysis of Heterogeneity in Drug Development 18
2.3.1 Basic Pharmacokinetic Concepts 18
2.3.2 Pharmacokinetic Parameters 19
2.3.3 First-Order Compartment Models 20
2.3.4 Population Pharmacokinetics 21
2.3.5 Theophylline Pharmacokinetics 22
2.4 A Note of Caution 28
3 Modeling Count Data 29
3.1 Example: Morbidity in Northeast Thailand 29
3.2 Parametric Mixture Models 30
3.3 Finite Mixture Models 33
3.3.1 Diagnostic Plots for Finite Mixture Models 34
3.3.2 A Finite Mixture Model for the Illness Spell Data 34
3.3.3 Estimating the Number of Components 36
3.4 Computation 39
3.4.1 Combination of VEM and EM Algorithms 39
3.4.2 Using the EM Algorithm 41
3.4.3 Estimating the Number of Components 42
3.5 Including Covariates 43
3.5.1 The Ames Test 43
3.5.2 Poisson and Negative Binomial Regression Models 47
3.5.3 Covariate-Adjusted Mixture Model for the Ames
Test Data 49
vii
viii Contents
3.6 Computation 51
3.6.1 Fitting Poisson and Negative Binomial Regression Models
with SAS 51
3.6.2 Fitting Poisson and Negative Binomial Regression Models
with R 52
3.6.3 Fitting Finite Mixture Models with the Package CAMAN . 53
4 Theory and Algorithms 55
4.1 The Likelihood of Finite Mixture Models 55
4.2 Convex Geometry and Optimization 56
4.2.1 Derivatives and Directional Derivatives of Convex
Functions 61
4.3 Application to the Flexible Support Size Case 64
4.3.1 Geometric Characterization 64
4.3.2 Algorithms for Flexible Support Size 69
4.3.3 VEM Algorithm: Computation 70
4.4 The Fixed Support Size Case 72
4.4.1 Fixed Support Size: The Newton-Raphson Algorithm 72
4.4.2 A General Description of the EM Algorithm 73
4.4.3 The EM Algorithm for Finite Mixture Models 74
4.4.4 EM Algorithm: Computation 77
4.4.5 A Hybrid Mixture Algorithm 79
4.4.6 The EM Algorithm with Gradient Update 80
4.5 Estimating the Number of Components 82
4.5.1 Graphical Techniques 82
4.5.2 Testing for the Number of Components 83
4.5.3 The Bootstrap Approach 84
4.6 Adjusting for Covariates 87
4.6.1 Generalized Linear Models 87
4.6.2 The EM Algorithm for Covariate-Adjusted Mixture
Models 91
4.6.3 Computation: Vitamin A Supplementation Revisited 93
4.6.4 An Extension of the EM Algorithm with Gradient Update
for Covariate-Adjusted Mixture Models 95
4.7 Case Study: EM Algorithm with Gradient Update for Nonlinear
Finite Mixture Models 97
4.7.1 Introduction 97
4.7.2 Example: Dipyrone Pharmacokinetics 98
4.7.3 First-Order Compartment Models 98
4.7.4 Finite Mixture Model Analysis 102
5 Disease Mapping and Cluster Investigations 107
5.1 Introduction 107
5.2 Investigation of General Clustering 109
5.2.1 Traditional Approaches 110
5.2.2 The Empirical Bayes Approach 112
Contents jx
5.3 Computation 117
5.4 A Note on Autocorrelation Versus Heterogeneity 119
5.4.1 Heterogeneity 119
5.4.2 Autocorrelation 121
5.5 Focused Clustering 124
5.5.1 The Score Test for Focused Clustering 124
5.5.2 The Score Test Adjusted for Heterogeneity 128
5.5.3 The Score Test Based on the Negative Binomial
Distribution 129
5.5.4 Estimation of a and v 130
5.6 Case Study: Leukemia in Adults in the Vicinity of Kriimmel 132
5.6.1 Background 133
5.6.2 The Retrospective Incidence Study Elbmarsch 134
5.6.3 Focused Analysis 135
5.6.4 Disease Mapping and Model-Based Methods 136
5.7 Mathematical Details of the Score Test 138
5.7.1 Expectation and Variance of the Score 138
5.7.2 The Score Test 139
6 Modeling Heterogeneity in Psychophysiology 143
6.1 The Electroencephalogram 143
6.1.1 Digitization 143
6.2 Modeling Spatial Heterogeneity Using Generalized Linear Mixed
Models 144
6.2.1 The Periodogram and its Distributional Properties 144
6.3 Connection to Generalized Linear Models 148
6.3.1 Covariate-Adjusted Finite Mixture Models
for the EEG Data 149
7 Investigating and Analyzing Heterogeneity in Meta-analysis 153
7.1 Introduction 153
7.1.1 Different Types of Overviews 154
7.2 Basic Statistical Analysis 155
7.2.1 Single Study Results 155
7.2.2 Publication Bias 157
7.2.3 Estimation of a Summary Effect 160
7.3 Analysis of Heterogeneity 162
7.3.1 The DerSimonian-Laird Approach 164
7.3.2 Maximum Likelihood Estimation of the Heterogeneity
Variance T2 166
7.3.3 Another Estimator of T2: The Simple Heterogeneity
Variance Estimator 168
7.3.4 A Comment on Summary Estimates Under Heterogeneity . 169
7.3.5 The Finite Mixture Model Approach 169
7.4 A Simulation Study Comparing Four Estimators of r2 171
7.4.1 Design of the Simulation Study 171
x Contents
7.4.2 Simulation Results 173
7.4.3 Discussion 173
7.5 Metaregression 176
7.5.1 Finite Mixture Models Adjusted for Covariates 177
7.6 Interpretation of the Results of Meta-analysis of Observational
Studies 180
7.6.1 Bias 181
7.6.2 Confounding 181
7.6.3 Heterogeneity 182
7.7 Case Study. Aspirin Use and Breast Cancer Risk - A Meta-
analysis and Metaregression of Observational Studies from 2001
to 2007 183
7.7.1 Introduction 183
7.7.2 Literature Search and Data Extraction 184
7.7.3 Study Characteristics 184
7.7.4 Publication Bias 185
7.7.5 Results 186
7.7.6 Results of a Metaregression 186
7.7.7 Modeling Dose Response 187
7.7.8 A Metaregression Model for Dose-Response Analysis 190
7.7.9 Discussion 191
7.8 Computation 192
7.8.1 "Standard Meta-analysis" 192
7.8.2 Meta-analysis with SAS 194
7.8.3 Finite Mixture Models 196
7.8.4 Metaregression 197
8 Analysis of Gene Expression Data 201
8.1 DNA Microarrays 201
8.2 The Analysis of Differential Gene Expression 202
8.2.1 Analysis Based on Simultaneous Hypothesis Testing 202
8.2.2 A Mixture Model Approach 206
8.2.3 Computation 209
8.3 A Change of Perspective: Applying Methods from Meta-analysis .210
8.4 Case Study: Identification of a Gene Signature for Breast Cancer
Prognosis 213
8.4.1 Introduction 213
8.4.2 Application of the Meta-analytic Mixture Model
to the Breast Cancer Data 214
8.4.3 Validation of Results 215
References 219
Subject Index 237
Author Index 243 |
| any_adam_object | 1 |
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| ctrlnum | (OCoLC)319207898 (DE-599)DNB988424908 |
| dewey-full | 610.727 |
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| dewey-ones | 610 - Medicine and health |
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| discipline | Mathematik Medizin |
| format | Thesis Book |
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| spelling | Schlattmann, Peter 1962- Verfasser (DE-588)138812187 aut Medical applications of finite mixture models Peter Schlattmann Berlin [u.a.] Springer 2009 X, 246 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Statistics for biology and health Literaturverz. S. 219 - 235 Zugl.: Berlin, Univ.-Medizin, Habil.-Schr., 2008 Statistiques médicales ram Biometry Data Interpretation, Statistical Medical statistics Meta-Analysis as Topic Models, Statistical Medizinische Statistik (DE-588)4127563-9 gnd rswk-swf Zusammengesetzte Verteilung (DE-588)4191153-2 gnd rswk-swf Statistisches Modell (DE-588)4121722-6 gnd rswk-swf Heterogenität (DE-588)4201275-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Medizinische Statistik (DE-588)4127563-9 s Heterogenität (DE-588)4201275-2 s Statistisches Modell (DE-588)4121722-6 s Zusammengesetzte Verteilung (DE-588)4191153-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018763063&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schlattmann, Peter 1962- Medical applications of finite mixture models Statistiques médicales ram Biometry Data Interpretation, Statistical Medical statistics Meta-Analysis as Topic Models, Statistical Medizinische Statistik (DE-588)4127563-9 gnd Zusammengesetzte Verteilung (DE-588)4191153-2 gnd Statistisches Modell (DE-588)4121722-6 gnd Heterogenität (DE-588)4201275-2 gnd |
| subject_GND | (DE-588)4127563-9 (DE-588)4191153-2 (DE-588)4121722-6 (DE-588)4201275-2 (DE-588)4113937-9 |
| title | Medical applications of finite mixture models |
| title_auth | Medical applications of finite mixture models |
| title_exact_search | Medical applications of finite mixture models |
| title_full | Medical applications of finite mixture models Peter Schlattmann |
| title_fullStr | Medical applications of finite mixture models Peter Schlattmann |
| title_full_unstemmed | Medical applications of finite mixture models Peter Schlattmann |
| title_short | Medical applications of finite mixture models |
| title_sort | medical applications of finite mixture models |
| topic | Statistiques médicales ram Biometry Data Interpretation, Statistical Medical statistics Meta-Analysis as Topic Models, Statistical Medizinische Statistik (DE-588)4127563-9 gnd Zusammengesetzte Verteilung (DE-588)4191153-2 gnd Statistisches Modell (DE-588)4121722-6 gnd Heterogenität (DE-588)4201275-2 gnd |
| topic_facet | Statistiques médicales Biometry Data Interpretation, Statistical Medical statistics Meta-Analysis as Topic Models, Statistical Medizinische Statistik Zusammengesetzte Verteilung Statistisches Modell Heterogenität Hochschulschrift |
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