Statistical Methods in Human Genetics (Indian Statistical Institute Series)

✍ Scribed by Indranil Mukhopadhyay, Partha Pratim Majumder

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 281
• Category: Library

✦ Synopsis

This book provides an overview of statistical concepts and basic methodology for the study of genetics of human traits and diseases. It attempts to provide a step-by-step description of problem identification, study design, methodology of data collection, data exploration, data summarization and visualization, and more advanced analytical methods for inferring genetic underpinnings of human phenotypes. The book provides codes in R programming language for implementation of most of the statistical methods described, which will enable practitioners to perform analysis of data on their own, without having to mold the data to fit the requirements of commercial statistical packages. Useful to anyone engaged in studies to understand and manage good health, the book is a useful guide for sustainable development of humankind. Primarily intended for practicing biologists especially those who carry out quantitative biological research, in particular, human geneticists, the book is also helpful in classroom teaching.

✦ Table of Contents

Preface
Contents
About the Authors
1 Introduction to Analysis of Human Genetic Data
1.1 Need for Genetic Data Analysis
1.2 Nature of Analysis
1.3 R: A Versatile Tool for Genetic Data Analysis
1.4 Some Remarks
2 Basic Understanding of Single Gene Expression Data
2.1 Generating Questions
2.2 Visualising Data
2.2.1 Frequency Data
2.2.2 Histogram
2.2.3 Ogive
2.2.4 Boxplot
2.3 Summary Measures
2.3.1 Measures of Central Tendency
2.3.2 Measures of Dispersion
2.4 Points to Remember
References
3 Basic Probability Theory and Inference
3.1 Random Experiment
3.2 Event
3.3 Idea and Definition of Probability
3.4 Some Facts
3.5 Random Variable
3.6 Conditional Probability
3.6.1 Breaking a Probability Down by Conditioning
3.6.2 Bayes' Theorem
3.7 Independence
3.8 Discrete Probability Distributions
3.9 Expectation and Variance
3.9.1 Expectation
3.9.2 Variance
3.9.3 A Few More Discrete Distributions
3.10 Continuous Probability Distributions
3.10.1 Normal Distribution
3.10.2 Few Other Distributions
3.10.3 Important Results Related to Probability Distributions
4 Analysis of Single Gene Expression Data
4.1 Q-Q Plot
4.2 Transformation of Variables
4.3 A Few Testing Problems
4.3.1 Basics of Testing of Hypothesis
4.3.2 Interpretation of p-value
4.3.3 Test for Mean: Single Sample Problem
4.3.4 Wilcoxon Single Sample Test
4.3.5 Test for Variance: Single Sample Problem
4.3.6 Test for Equality of Two Means
4.3.7 Test for Equality of Two Variances
4.3.8 Wilcoxon Two-Sample Test for Locations
4.3.9 Test for Normality
4.4 Points to Remember
References
5 Analysis of Gene Expression Data in a Dependent Set-up
5.1 Understanding the Data
5.2 Generating Questions
5.3 Visually Inspecting the Data
5.3.1 Histogram and Boxplot
5.3.2 Finding Relationship Between Genes
5.3.3 Regression
5.4 Some Diagnostic Testing Problems for Paired Data
5.4.1 Test for Normal Distribution
5.4.2 Are Genes Correlated?
5.4.3 Test of Independence
5.5 Some Standard Paired Sample Testing Problems
5.5.1 Are Two Means Equal?
5.5.2 Test for Locations for Non-Normal Distribution
5.5.3 Regression-Based Testing
5.6 Points to Remember
References
6 Tying Genomes with Disease
6.1 Characteristics of Genomic Data
6.2 Representing Mathematically
6.3 Generating Questions
6.4 Relation Between Allele Frequency and Genotype Frequency
6.4.1 Hardy-Weinberg Equilibrium for an Autosomal Locus
6.4.2 HWE for X-linked Locus
6.4.3 Estimation of Allele Frequency
6.4.4 Mean and Variance of Allele Frequency Estimator
6.4.5 Test for HWE
6.4.6 Study Design
6.5 Genetic Association
6.5.1 Genetic Association for Qualitative Phenotype
6.5.2 Genetic Association in Presence of Covariates
6.5.3 Odds Ratio
6.5.4 Statistical Test Relating to Odds Ratio
6.5.5 Genetic Association for Quantitative Phenotype
6.6 Problems in Association Testing
6.6.1 Multiple Testing
6.6.2 Population Stratification
6.6.3 Polygenic Risk Score
6.7 Some Advanced Association Testing Methods
6.7.1 Kernel-Based Association Test (KBAT)
6.7.2 Sequence Kernel Association Test (SKAT)
6.8 Points to Remember
References
7 Some Extensions of Genetic Association Study
7.1 Generating Questions
7.2 Haplotype Association
7.2.1 Linkage Disequilibrium
7.2.2 Estimation of LD and Other Parameters from Genotype Counts
7.2.3 Haplotype Block
7.2.4 Haplotype Determination
7.2.5 Haplpotype Phasing
7.2.6 Haplotype Association
7.3 Studying Levels of Gene Expression at Various Stages of Cancer
7.3.1 Testing Means of Multiple Samples
7.3.2 Kruskal-Wallis Test
7.4 Covariate Adjustment in a Genetic Association Study
7.4.1 Example Data Set with Covariates
7.4.2 Covariate Adjustment for Quantitative Phenotype
7.4.3 Covariate Adjustment for Qualitative Phenotype
7.4.4 A Few Issues on Covariate Adjustment
7.5 Points to Remember
References
8 Exploring Multivariate Data
8.1 Generating Questions
8.2 A Multivariate Data Set
8.3 Multiple Regression
8.4 Multiple Correlation Coefficient
8.5 Partial Correlation Coefficient
8.6 Principal Component Analysis
8.7 Cluster Analysis
8.7.1 Hierarchical Clustering
8.7.2 k-means Clustering
8.7.3 Tight Clustering
8.8 Association with Multivariate Phenotypes
8.8.1 Linear Mixed Effects Model
8.8.2 Variable Reduction Method Using PCA
8.8.3 O'Brien's Method of Combining Univariate Test Statistics
8.8.4 Methods with Heterogeneous Genetic Effects
References
Appendix Appendix A
Appendix Appendix B
Appendix Appendix C
Appendix Appendix D