26 Formulas and Theories
26.1 Split-Prediction Methodology
26.2 Normally Distributed Response Binomial Predictor
26.2.1 Univariate Case
26.2.2 Multivariate Case
26.3 Normally Distributed Response Continuous-Ordinal Predictor
26.4 Normally Distributed Response Categorical Predictor
26.5 Linear Regression From a Tree Node
26.6 Haplotype Trend Regression (HTR) with Continuous Response
26.7 Composite Haplotype Method (CHM)
26.7.1 Technical details
26.7.2 Haplotype Trend Regression (HTR)
26.8 Haplotype Trend Regression (HTR) with Continuous Response and Covariates (Optional Module)
26.9 Stepwise Regression (Optional Module)
26.10 Categorical Covariates and Interaction Terms (Optional Module)
26.11 Results from Linear Regression (Optional Module)
26.11.1 P-value Plot
26.11.2 Residual Spreadsheet
26.11.3 Linear Regression Statistical Output Viewer
26.11.4 Overall Statistics
26.11.5 Regressor Statistics
26.11.6 Left-Out Regressors
26.11.7 Table of Haplotypes
26.11.8 Parameters
26.12 Binomially Distributed Response Binary Predictor
26.12.1 Univariate Case
26.12.2 Multivariate Case
26.13 Binomially Distributed Response Continuous/Ordinal Predictor
26.14 Binomially Distributed Response Categorical Predictor
26.15 Logistic Regression From a Tree Node
26.16 Haplotype Trend Regression (HTR) with Binomial Response
26.17 Haplotype Trend Regression (HTR) with Binomial Response and Covariates (Optional Module)
26.18 Results from Logistic Regression (Optional Module)
26.18.1 P-value Plot
26.18.2 Residual Spreadsheet
26.18.3 Logistic Regression Statistical Output Viewer
26.18.4 Overall Statistics
26.18.5 Regressor Statistics
26.18.6 Left-Out Regressors
26.18.7 Table of Haplotypes
26.18.8 Parameters
26.18.9 Caveats
26.19 Categorical Response
26.20 The False Discovery Rate and the Simes Method
26.20.1 The False Discovery Rate
26.20.2 Simes’ Method
26.21 Permutation Test Methodology
26.21.1 Single Value Permutations
26.21.2 Full Scan Permutations
26.22 Methods for the Genetic Association Tests
26.22.1 Correlation/Trend Test
26.22.2 Armitage Trend Test
26.22.3 Exact Form of Armitage Test
26.22.4 (Pearson) Chi-Squared Test
26.22.5 Fisher’s Exact Test
26.22.6 Odds Ratio with Confidence Limits
26.22.7 Analysis of Deviance
26.22.8 The F-Test
26.22.9 The T-Test
26.23 Formulas for Principal Components Analysis
26.23.1 Motivation
26.23.2 Technique
26.23.3 Applying the PCA Corrections
26.23.4 Formulas for PCA Normalization
26.24 Methods for Obtaining General Marker Statistics
26.24.1 Fisher’s Exact Test for HWE P-Value
26.24.2 Signed HWE R
26.2 Normally Distributed Response Binomial Predictor
26.2.1 Univariate Case
26.2.2 Multivariate Case
26.3 Normally Distributed Response Continuous-Ordinal Predictor
26.4 Normally Distributed Response Categorical Predictor
26.5 Linear Regression From a Tree Node
26.6 Haplotype Trend Regression (HTR) with Continuous Response
26.7 Composite Haplotype Method (CHM)
26.7.1 Technical details
26.7.2 Haplotype Trend Regression (HTR)
26.8 Haplotype Trend Regression (HTR) with Continuous Response and Covariates (Optional Module)
26.9 Stepwise Regression (Optional Module)
26.10 Categorical Covariates and Interaction Terms (Optional Module)
26.11 Results from Linear Regression (Optional Module)
26.11.1 P-value Plot
26.11.2 Residual Spreadsheet
26.11.3 Linear Regression Statistical Output Viewer
26.11.4 Overall Statistics
26.11.5 Regressor Statistics
26.11.6 Left-Out Regressors
26.11.7 Table of Haplotypes
26.11.8 Parameters
26.12 Binomially Distributed Response Binary Predictor
26.12.1 Univariate Case
26.12.2 Multivariate Case
26.13 Binomially Distributed Response Continuous/Ordinal Predictor
26.14 Binomially Distributed Response Categorical Predictor
26.15 Logistic Regression From a Tree Node
26.16 Haplotype Trend Regression (HTR) with Binomial Response
26.17 Haplotype Trend Regression (HTR) with Binomial Response and Covariates (Optional Module)
26.18 Results from Logistic Regression (Optional Module)
26.18.1 P-value Plot
26.18.2 Residual Spreadsheet
26.18.3 Logistic Regression Statistical Output Viewer
26.18.4 Overall Statistics
26.18.5 Regressor Statistics
26.18.6 Left-Out Regressors
26.18.7 Table of Haplotypes
26.18.8 Parameters
26.18.9 Caveats
26.19 Categorical Response
26.20 The False Discovery Rate and the Simes Method
26.20.1 The False Discovery Rate
26.20.2 Simes’ Method
26.21 Permutation Test Methodology
26.21.1 Single Value Permutations
26.21.2 Full Scan Permutations
26.22 Methods for the Genetic Association Tests
26.22.1 Correlation/Trend Test
26.22.2 Armitage Trend Test
26.22.3 Exact Form of Armitage Test
26.22.4 (Pearson) Chi-Squared Test
26.22.5 Fisher’s Exact Test
26.22.6 Odds Ratio with Confidence Limits
26.22.7 Analysis of Deviance
26.22.8 The F-Test
26.22.9 The T-Test
26.23 Formulas for Principal Components Analysis
26.23.1 Motivation
26.23.2 Technique
26.23.3 Applying the PCA Corrections
26.23.4 Formulas for PCA Normalization
26.24 Methods for Obtaining General Marker Statistics
26.24.1 Fisher’s Exact Test for HWE P-Value
26.24.2 Signed HWE R