Big Data in Omics and Imaging: Association Analysis

Content: Mathematical FoundationSparsity-Inducing Norms, Dual Norms and Fenchel ConjugateSubdifferentialDefinition of SubgradientSubgradients of differentiable functionsCalculus of subgradientsProximal MethodsIntroductionBasics of Proximate MethodsProperties of the Proximal OperatorProximal AlgorithmsComputing the Proximal OperatorMatrix CalculusDerivative of a Function with Respect to a VectorDerivative of a Function with Respect to a MatrixDerivative of a Matrix with Respect to a ScalarDerivative of a Matrix with Respect to a Matrix or a VectorDerivative of a Vector Function of a VectorChain RulesWidely Used FormulaeFunctional Principal Component Analysis (FPCA)Principal Component Analysis (PCA)Basic Mathematical Tools for Functional Principal Component AnalysisUnsmoothed Functional Principal Component AnalysisSmoothed Principal Component AnalysisComputations for the Principal Component Function and the Principal Component ScoreCanonical Correlation AnalysisExercisesAppendix Linkage DisequilibriumConcepts of Linkage DisequilibriumMeasures of Two-locus Linkage DisequilibriumLinkage Disequilibrium Coefficient DNormalized Measure of Linkage DisequilibriumCorrelation Coefficient rComposite Measure of Linkage DisequilibriumThe Relationship Between the Measure of LD and Physical DistanceHaplotype ReconstructionClark\'s AlgorithmEM algorithmBayesian and Coalescence-based MethodsMulti-locus Measures of Linkage DisequilibriumMutual Information Measure of LDMulti-Information and Multi-locus Measure of LDJoint Mutual Information and a Measure of LD between a Marker and a Haplotype Block or Between Two Haplotype BlocksInteraction InformationConditional Interaction InformationNormalized Multi-InformationDistribution of Estimated Mutual Information, Multi-information and Interaction InformationCanonical Correlation Analysis Measure for LD between Two Genomic RegionsAssociation Measure between Two Genomic Regions Based on CCARelationship between Canonical Correlation and Joint InformationSoftware PackageBibliographical NotesAppendicesExercisesAssociation Studies for Qualitative TraitsPopulation-based Association Analysis for Common VariantsIntroductionThe Hardy-Weinberg EquilibriumGenetic ModelsOdds RatioSingle Marker Association AnalysisMulti-marker Association AnalysisPopulation-based Multivariate Association Analysis for Next-generation SequencingMultivariate Group TestsScore Tests and Logistic RegressionApplication of Score Tests for Association of Rare VariantsVariance-component Score Statistics and Logistic Mixed Effects ModelsPopulation-based Functional Association Analysis for Next-generation SequencingIntroductionFunctional Principal Component Analysis for Association TestSmoothed Functional Principal Component Analysis for Association TestSoftware PackageAppendicesExercisesAssociation Studies for Quantitative TraitsFixed Effect Model for a Single TraitIntroductionGenetic EffectsLinear Regression for a Quantitative TraitMultiple Linear Regression for a Quantitative TraitGene-based Quantitative Trait AnalysisFunctional Linear Model for a Quantitative TraitCanonical Correlation Analysis for Gene-based Quantitative Trait AnalysisKernel Approach to Gene-based Quantitative Trait AnalysisKernel and RKHSCovariance Operator and Dependence MeasureSimulations and Real Data AnalysisPower EvaluationApplication to Real Data ExamplesSoftware PackageAppendicesExercisesMultiple Phenotype Association StudiesPleiotropic Additive and Dominance EffectsMultivariate Marginal RegressionModelsEstimation of Genetic EffectsTest StatisticsLinear Models for Multiple Phenotypes and Multiple MarkersMultivariate Multiple Linear Regression ModelsMultivariate Functional Linear Models for Gene-based Genetic Analysis of Multiple PhenotypesCanonical Correlation Analysis for Gene-based Genetic Pleiotropic AnalysisMultivariate Canonical Correlation Analysis (CCA)Kernel CCAFunctional CCAQuadratically Regularized Functional CCADependence Measure and Association Tests of Multiple TraitsPrincipal Component for Phenotype Dimension ReductionPrincipal Component AnalysisKernel Principal Component AnalysisQuadratically Regularized PCA or Kernel PCAOther Statistics for Pleiotropic Genetics AnalysisSum of Squared Score TestUnified Score-based Association Test (USAT)Combining Marginal TestsFPCA-based Kernel Measure Test of IndependenceConnection between StatisticsSimulations and Real Data AnalysisType Error Rate and Power EvaluationApplication to Real Data ExampleSoftware PackageAppendices ExercisesFamily-based Association AnalysisGenetic Similarity and Kinship CoefficientsKinship CoefficientsIdentity CoefficientsRelation between identity coefficients and kinship coefficientEstimation of Genetic Relations from the DataGenetic Covariance between RelativesAssumptions and Genetic ModelsAnalysis for Genetic Covariance between RelativesMixed Linear Model for a Single TraitGenetic Random EffectMixed Linear Model for Quantitative Trait Association AnalysisEstimating Variance ComponentsHypothesis Test in Mixed Linear ModelsMixed Linear Models for Quantitative Trait Analysis with Sequencing DataMixed Functional Linear Models for Sequence-based Quantitative Trait AnalysisMixed Functional Linear Models (Type )Mixed Functional Linear Models (Type : Functional Variance Component Models)Multivariate Mixed Linear Model for Multiple TraitsMultivariate Mixed Linear ModelMaximum Likelihood Estimate of Variance ComponentsREML Estimate of Variance ComponentsHeritabilityHeritability Estimation for a Single TraitHeritability Estimation for Multiple TraitsFamily-based Association Analysis for Qualitative TraitThe Generalized T Test with Families and Additional Population StructuresCollapsing MethodCMC with FamiliesThe Functional Principal Component Analysis and Smooth Functional Principal Component Analysis with FamiliesSoftware PackageExerciseInteraction AnalysisMeasures of Gene-gene and Gene-environment Interaction for Qualitative TraitBinary Measure of Gene-gene and Gene-environment InteractionDisequilibrium Measure of Gene-gene and Gene-environment InteractionInformation Measure of Gene-gene and Gene-environment InteractionMeasure of Interaction between Gene and Continuous EnvironmentStatistics for Testing Gene-gene and Gene-Environment Interaction for Qualitative Trait with Common VariantsRelative Risk and Odds-ration-based Statistics for Testing Interaction between Gene and Discrete EnvironmentDisequilibrium-based Statistics for Testing Gene-gene InteractionInformation-based Statistics for Testing Gene-Gene InteractionHaplotype-Odds Ratio and Tests for Gene-Gene InteractionMultiplicative Measure-based Statistics for Testing Interaction between Gene and Continuous EnvironmentInformation Measure-based Statistics for Testing Interaction between Gene and Continuous EnvironmentReal ExampleStatistics for Testing Gene-gene and Gene-Environment Interaction for Qualitative Trait with Next-generation Sequencing DataMultiple Logistic Regression Model for Gene-Gene Interaction AnalysisFunctional logistic regression model for gene-gene interaction analysisStatistics for Testing Interaction between Two Genomic RegionsStatistics for Testing Gene-gene and Gene-Environment Interaction for Quantitative TraitsGenetic Models for Epistasis Effects of Quantitative TraitsRegression Model for Interaction Analysis with Quantitative TraitsFunctional Regression Model for Interaction Analysis with a Quantitative TraitFunctional Regression Model for Interaction Analysis with Multiple Quantitative TraitsMultivariate and Functional Canonical Correlation as a Unified Framework for Testing Gen-Gene and Gene-Environment Interaction for both Qualitative and Quantitative TraitsData Structure of CCA for Interaction AnalysisCCA and Functional CCAKernel CCASoftware PackageAppendicesExerciseMachine Learning, Low Rank Models and Their Application to Disease Risk Prediction and Precision MedicineLogistic RegressionTwo Class Logistic RegressionMulticlass Logistic RegressionParameter EstimationTest StatisticsNetwork Penalized Two-class Logistic RegressionNetwork Penalized Multiclass Logistic RegressionFisher\'s Linear Discriminant AnalysisFisher\'s Linear Discriminant Analysis for Two ClassesMulti-class Fisher\'s Linear Discriminant AnalysisConnections between Linear Discriminant Analysis, Optimal Scoring and Canonical Correlation Analysis (CCA)Support Vector MachineIntroductionLinear Support Vector MachinesNonlinear SVMPenalized SVMsLow Rank ApproximationQuadratically Regularized PCAGeneralized RegularizationGeneralized Canonical Correlation Analysis (CCA)Quadratically Regularized Canonical Correlation AnalysisSparse Canonical Correlation AnalysisSparse Canonical Correlation Analysis via a Penalized Matrix DecompositionInverse Regression (IR) and Sufficient Dimension ReductionSufficient Dimension Reduction (SDR) and Sliced Inverse Regression (SIR)Sparse SDRSoftware PackageAppendicesExercises ã  ã  ã  ã  ã