Applied Statistical Genetics with R: For Population-based Association Studies Book

Preface VII

List of Tables XVII

List of Figures XIX

Acronyms XXI

1 Genetic Association Studies 1

1.1 Overview of population-based investigations 2

1.1.1 Types of investigations 2

1.1.2 Genotype versus gene expression 4

1.1.3 Population-versus family-based investigations 6

1.1.4 Assocation versus population genetics 7

1.2 Data components and terminology 7

1.2.1 Genetic information 8

1.2.2 Traits 11

1.2.3 Covariates 12

1.3 Data examples 12

1.3.1 Complex disease association studies 13

1.3.2 HIV genotype association studies 16

1.3.3 Publicly available data used throughout the text 18

Problems 27

2 Elementary Statistical Principles 29

2.1 Background 30

2.1.1 Notation and basic probability concepts 30

2.1.2 Important epidemiological concepts 33

2.2 Measures and tests of association 37

2.2.1 Contingency table analysis for a binary trait 38

2.2.2 M-sample tests for a quantitative trait 44

2.2.3 Generalized linear model 48

2.3 Analytic challenges 55

2.3.1 Multiplicity and high dimensionality 55

2.3.2 Missing and unobservable data considerations 58

2.3.3 Race and ethnicity 60

2.3.4 Genetic models and models of association 61

Problems 62

3 Genetic Data Concepts and Tests 65

3.1 Linkage disequilibrium (LD) 65

3.1.1 Measures of LD: D' and r2 66

3.1.2 LD blocks and SNP tagging 74

3.1.3 LD and population stratification 76

3.2 Hardy-Weinberg equilibrium (HWE) 78

3.2.1 Pearson's X2-test and Fisher's exact test 78

3.2.2 HWE and population substructure 82

3.3 Quality control and preprocessing 86

3.3.1 SNP chips 86

3.3.2 Genotyping errors 88

3.3.3 Identifying population substructure 89

3.3.4 Relatedness 92

3.3.5Accounting for unobservable substructure 94

Problems 95

4 Multiple Comparison Procedures 97

4.1 Measures of error 97

4.1.1 Family-wise error rate 98

4.1.2 False discovery rate 100

4.2 Single-step and step-down adjustments 101

4.2.1 Bonferroni adjustment 102

4.2.2 Tukey and Scheffe tests 105

4.2.3 False discovery rate control 109

4.2.4 The q-value 112

4.3 Resampling-based methods 114

4.3.1 Free step-down resampling 114

4.3.2 Null unrestricted bootstrap 120

4.4 Alternative paradigms 123

4.4.1 Effective number of tests 123

4.4.2 Global tests 125

Problems 127

5 Methods for Unobservable Phase 129

5.1 Haplotype estimation 130

5.1.1 An expectation-maximization algorithm 130

5.1.2 Bayesian haplotype reconstruction 137

5.2 Estimating and testing for haplotype-trait association 140

5.2.1 Two-stage approaches 140

5.2.2 A fully likelihood-based approach 145

Problems 149

Supplemental notes 150

Supplemental R scripts 155

6 Classification and Regression Trees 157

6.1 Building a tree 157

6.1.1 Recursive partitioning 157

6.1.2 Splitting rules 158

6.1.3 Defining inputs 167

6.2 Optimal trees 173

6.2.1 Honest estimates 174

6.2.2 Cost-complexity pruning 174

Problems 179

7 Additional Topics in High-Dimensional Data Analysis 181

7.1 Random forests 182

7.1.1 Variable importance 183

7.1.2 Missing data methods 187

7.1.3 Covariates 198

7.2 Logic regression 198

7.3 Multivariate adaptive regression splines 205

7.4 Bayesian variable selection 209

7.5 Further readings 211

Problems 212

Appendix R Basics 213

A.1 Getting started 213

A.2 Types of data objects 216

A.3 Importing data 220

A.4 Managing data 221

A.5 Installing packages 224

A.6 Additional help 225

References 227

Glossary of Terms 237

Glossary of Select R Packages 243

Subject Index 247

Index of R Functions and Packages 251