Page 14 - Applied Probability

4 Hypothesis Testing and Categorical Data
59
4.1
4.2
59
Hypotheses About Genotype Frequencies . . . . . . . . . .
Other Multinomial Problems in Genetics . . . . . . . . . . .
4.3
62
The Z max Test ... .. .. ... .. .. ... .. ... .. .
63
4.4
The W d Statistic . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
65
4.6 Exact Tests of Independence . . . . . . . . . . . . . . . . . 67
4.7 Case-Control Association Tests . . . . . . . . . . . . . . . . 69
4.8 The Transmission/Disequilibrium Test . . . . . . . . . . . . 70
4.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5 Genetic Identity Coefficients 81
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2 Kinship and Inbreeding Coefficients . . . . . . . . . . . . . . 81
5.3 Condensed Identity Coefficients . . . . . . . . . . . . . . . . 84
5.4 Generalized Kinship Coefficients . . . . . . . . . . . . . . . 86
5.5 From Kinship to Identity Coefficients . . . . . . . . . . . . . 86
5.6 Calculation of Generalized Kinship Coefficients . . . . . . . 88
5.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6 Applications of Identity Coefficients 97
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2 Genotype Prediction . . . . . . . . . . . . . . . . . . . . . . 97
6.3 Covariances for a Quantitative Trait . . . . . . . . . . . . . 99
6.4 Risk Ratios and Genetic Model Discrimination . . . . . . . 102
6.5 An Affecteds-Only Method of Linkage Analysis . . . . . . . 106
6.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

7 Computation of Mendelian Likelihoods 115
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
7.2 Mendelian Models . . . . . . . . . . . . . . . . . . . . . . . 115
7.3 Genotype Elimination and Allele Consolidation . . . . . . . 118
7.4 Array Transformations and Iterated Sums . . . . . . . . . . 120
7.5 Array Factoring . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.6 Examples of Pedigree Analysis . . . . . . . . . . . . . . . . 124
7.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
8 The Polygenic Model 141
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8.2 Maximum Likelihood Estimation by Scoring . . . . . . . . . 142
8.3 Application to Gc Measured Genotype Data . . . . . . . . . 146