Genome-Wide Association Studies Caitlin Collins , Thibaut Jombart - PowerPoint PPT Presentation

Genome-Wide Association Studies Caitlin Collins , Thibaut Jombart MRC Centre for Outbreak Analysis and Modelling Imperial College London Genetic data analysis using 30-10-2014

Outline • Introduction to GWAS • Study design o GWAS design o Issues and considerations in GWAS • Testing for association o Univariate methods o Multivariate methods • Penalized regression methods • Factorial methods 2

Genomics & GWAS 3

The genomics revolution Sequencing technology • o 1977 – Sanger o 1995 – 1 st bacterial genomes • < 10,000 bases per day per machine o 2003 – 1 st human genome • > 10,000,000,000,000 bases per day per machine GWAS publications • o 2005 – 1 st GWAS o Age-related macular degeneration o 2014 – 1,991 publications o 14,342 associations Genomics & GWAS 4

A few GWAS discoveries… Genomics & GWAS 5

So what is GWAS? • Genome Wide Association Study o Looking for SNPs… associated with a phenotype. • Purpose: o Explain • Understanding • Mechanisms • Therapeutics o Predict • Intervention • Prevention • Understanding not required Genomics & GWAS 6

Association p SNPs • Definition Controls o Any relationship between two measured quantities Cases that renders them statistically dependent. n • Heritability individuals o The proportion of variance explained by genetics o P = G + E + G*E • Heritability > 0 Genomics & GWAS 7

Genomics & GWAS 8

Why? • Environment, Gene-Environment interactions • Complex traits, small effects, rare variants • Gene expression levels • GWAS methodology? Genomics & GWAS 9

Study Design 10

GWAS design • Case-Control o Well- defined “case” o Known heritability • Variations o Quantitative phenotypic data • Eg. Height, biomarker concentrations o Explicit models • Eg. Dominant or recessive Study Design 11

Issues & Considerations • Data quality o 1% rule • Controlling for confounding o Sex, age, health profile o Correlation with other variables * • Population stratification* * • Linkage disequilibrium* Study Design 12

Population stratification • Definition o “Population stratification” = population structure o Systematic difference in allele frequencies btw. sub- populations … • … possibly due to different ancestry • Problem o Violates assumed population homogeneity, independent observations •  Confounding, spurious associations o Case population more likely to be related than Control population •  Over-estimation of significance of associations Study Design 13

Population stratification II • Solutions o Visualise • Phylogenetics • PCA o Correct • Genomic Control • Regression on Principal Components of PCA Study Design 14

Linkage disequilibrium (LD) • Definition o Alleles at separate loci are NOT independent of each other • Problem? o Too much LD is a problem •  noise >> signal o Some (predictable) LD can be beneficial •  enables use of “marker” SNPs Study Design 15

Testing for Association 16

Methods for association testing • Standard GWAS o Univariate methods • Incorporating interactions o Multivariate methods • Penalized regression methods (LASSO) • Factorial methods (DAPC-based FS) Testing for Association 17

Univariate methods p SNPs • Approach o Individual test statistics Controls o Correction for multiple testing Cases • Variations n individuals o Testing • Fisher’s exact test, Cochran -Armitage trend test, Chi- squared test, ANOVA • Gold Standard — Fischer’s exact test o Correcting • Bonferroni • Gold Standard — FDR Testing for Association 18

Univariate – Strengths & weaknesses Strengths Weaknesses Straightforward Multivariate system, • • univariate framework Computationally fast • Effect size of individual • Conservative • SNPs may be too small Easy to interpret • Marginal effects of • individual SNPs ≠ combined effects Testing for Association 19

What about interactions? Testing for Association 20

Interactions • Epistasis o “Deviation from linearity under a general linear model” 𝑍 𝑗 = 𝑥 0 + 𝑥 1 𝐵 𝑗 + 𝑥 2 𝐶 𝑗 +𝒙 𝟒 𝑩 𝒋 𝑪 𝒋 With p predictors, there are: • 𝑞 𝑙 • 𝑞 𝑙! k-way interactions 𝑙 = • p = 10,000,000  5 x 10 11 o That’s 500 BILLION possible pair-wise interactions! Need some way to limit the number of pairwise • interactions considered… Testing for Association 21

Multivariate methods Neural Networks Penalized Regression Genetic programming Parametric LASSO penalized regression optimized neural decreasing method networks The elastic net Ridge regression Logic Trees Logic feature selection Monte Carlo Bayesian Approaches Logic regression Logic Regression Bayesian partitioning Modified Logic Bayesian Logistic Bayesian Epistasis Regression-Gene Regression with Association Mapping Expression Programming Stochastic Search Genetic Programming for Set association Variable Selection Association Studies approach Factorial Methods Non-parametric Methods Multi-factor Sparse-PCA Random forests dimensionality reduction Restricted Supervised-PCA method partitioning method DAPC-based FS Combinatorial (snpzip) Odds-ratio- partitioning method based MDR Testing for Association 22

Multivariate methods (ii) • Penalized regression methods o LASSO penalized regression • Factorial methods o DAPC-based feature selection Testing for Association 23

Penalized regression methods • Approach o Regression models multivariate association o Shrinkage estimation  feature selection • Variations o LASSO, Ridge, Elastic net, Logic regression • Gold Standard — LASSO penalized regression Testing for Association 24

LASSO penalized regression • Regression o Generalized linear model (“ glm ”) • Penalization o L1 norm o Coefficients  0 o Feature selection! Testing for Association 25

LASSO – Strengths & weaknesses Strengths Weaknesses Multicollinearity • • Stability Not designed for high-p • • Interpretability Computationally intensive • • Likely to accurately Calibration of penalty • select the most parameters influential predictors User-defined  variability o Sparsity • • Sparsity NO p-values! • Testing for Association 26

Factorial methods • Approach o Place all variables (SNPs) in a multivariate space o Identify discriminant axis  best separation o Select variables with the highest contributions to that axis • Variations o Supervised-PCA, Sparse-PCA, DA, DAPC-based FS o Our focus — DAPC with feature selection (snpzip) Testing for Association 27

DAPC-based feature selection a b e Alleles d c Individuals Diseased (“cases”) Healthy (“controls”) Discriminant Axis Discriminant Axis Density of individuals Density of individuals 0.5 0.4 0.3 Contribution to 0.2 Discriminant Axis 0.1 0 a b c d e Testing for Association 28 Discriminant axis Discriminant axis

DAPC-based feature selection • Where should we draw the line? o  Hierarchical clustering 0.4 0.35 Density of individuals 0.3 0.25 0.2 Contribution to Discriminant Axis ? 0.15 0.1 0.05 0 Discriminant axis a b c d e

Hierarchical clustering (FS) 0.5 0.4 0.3 Contribution to 0.2 Discriminant Axis 0.1 0 a b c d e Hooray! Testing for Association 30

DAPC – Strengths & weaknesses Strengths Weaknesses • More likely to catch all • Sensitive to n.pca relevant SNPs (signal) • N.snps.selected varies • Computationally quick • No “p - value” • Good exploratory tool • Redundancy > sparsity • Redundancy > sparsity Testing for Association 31

Conclusions • Study design o GWAS design o Issues and considerations in GWAS • Testing for association o Univariate methods o Multivariate methods • Penalized regression methods • Factorial methods 32

Thanks for listening! 33

Questions? 34