The Statistics of Gene Mapping (Statistics for Biology and Health)

Contents......Page 12
Preface......Page 7
List of Notations and Terminology......Page 17
Part I: Background and Preparations......Page 18
1. Background in Statistics......Page 19
1.1 Introduction to R......Page 20
1.2 The Binomial, Poisson, and Normal Models......Page 23
1.3 Testing Hypothesis......Page 25
1.4 Limit Theorems......Page 29
1.5 Testing Equality of Two Binomial Parameters......Page 32
1.6 Statistical Power......Page 33
1.7 Correlation and Regression......Page 40
1.8 Stochastic Processes......Page 44
1.9 Likelihood-Based Inference......Page 45
1.10 Properties of Expectations and Variances......Page 48
Problems......Page 49
2. Introduction to Experimental Genetics......Page 51
2.1 The Mouse Model......Page 52
2.2 Segregation of the Trait in Crosses......Page 58
2.3 Molecular Genetic Markers......Page 64
Problems......Page 66
3.1 Inbreeding......Page 68
3.2 The Recombination Fraction......Page 77
3.3 Random Mating......Page 83
3.4 Inbreeding in Infinite Populations and Identity by Descent......Page 85
Problems......Page 86
Part II: Experimental Genetics......Page 89
4.1 Tests for the Presence of a QTL......Page 90
4.2 The Effect of Recombination......Page 101
4.3 Intercross and Other Designs......Page 107
Problems......Page 109
5. Whole Genome Scans: The Significance Level......Page 112
5.1 The Multi-Marker Process......Page 113
5.2 Multiple Testing and the Significance Level......Page 118
5.3 Mathematical Approximations of the Significance Level......Page 122
5.4 Other Methods......Page 127
5.5 P-values......Page 129
5.7 Bibliographical Comments......Page 130
Problems......Page 131
6. Statistical Power and Confidence Regions......Page 133
6.1 The Power to Detect a QTL......Page 134
6.2 An Analytic Approximation of the Power......Page 140
6.3 Designing an Experiment......Page 144
6.4 Confidence Sets......Page 147
6.5 Confidence Bounds for the Genetic Effect of a QTL......Page 150
6.6 Bibliographical Remarks......Page 152
Problems......Page 153
7. Missing Data and Interval Mapping......Page 155
7.1 Missing Marker Genotypes......Page 156
7.2 Interval Mapping......Page 163
Problems......Page 179
8.1 Multivariate Phenotypes, Gene-Environment Interaction, and Longitudinal Studies......Page 180
8.2 Multiple Gene Models and Gene-Gene Interaction......Page 184
8.3 Selective Genotyping......Page 188
8.4 Advanced Intercross Lines and Fine Mapping......Page 189
8.5 Bibliographical Comments......Page 190
Problems......Page 191
Part III: Human Genetics......Page 193
9. Mapping Qualitative Traits in Humans Using Affected Sib Pairs......Page 194
9.1 Genetic Models......Page 195
9.2 IBD Probabilities at the Candidate Trait Locus......Page 198
9.3 A Test for Linkage at a Single Marker Based on a Normal Approximation......Page 200
9.4 Genome Scans......Page 202
9.5 Parametric Methods......Page 206
9.6 Estimating the Number of Alleles Shared IBD......Page 209
Problems......Page 231
10. Admixture Mapping......Page 235
10.1 Testing for the Presence of a QTL......Page 237
10.2 Inferring Population Origin from Molecular Markers......Page 243
10.3 Estimating Parameters of the HMM......Page 253
Problems......Page 261
11.1 Model and Covariances......Page 264
11.2 Statistics to Detect Linkage......Page 266
11.3 A Two Degree of Freedom Statistic......Page 270
11.4 [sup(∗)]Sibships and Larger Pedigrees......Page 271
11.5 [sup(∗)]Multiple Gene Models and Gene-Gene Interaction......Page 273
11.6 Using Pedigrees to Map Disease Genes......Page 275
11.7 Discussion......Page 281
11.8 Bibliographical Comments......Page 282
Problems......Page 283
12. Association Studies......Page 286
12.1 Statistical Models and Statistical Tests......Page 287
12.2 Population Substructure and Inbreeding......Page 298
12.3 The Transmission Disequilibrium Test......Page 308
Problems......Page 311
13. Inferring Haplotypes from Genotypes and Testing Association......Page 313
13.1 Determining the Phase Between Two Loci......Page 314
13.2 The Expectation-Maximization Algorithm......Page 318
13.3 Testing Association with Haplotypes......Page 324
Problems......Page 328
References......Page 329
H......Page 334
P......Page 335
V......Page 336
Index of R Functions......Page 337