Structured Association Advanced Topics in Computa8onal Genomics

Transcription

1 Structured Association Advanced Topics in Computa8onal Genomics

2 Structured Association Lasso ACGTTTTACTGTACAATT Gflasso (Kim & Xing, 2009) ACGTTTTACTGTACAATT Greater power Fewer false posi2ves Phenome associa2ons

3 Structured Association Lasso ACGTTTTACTGTACAATT Network- constrained regulariza8on (Li & Li, 2008) ACGTTTTACTGTACAATT

4 Regression with Regularization Fused lasso (Tibshirani et al., 2004)

5 Standard regression Regression with Regularization (Fused Lasso) lasso Fusion penalty only Fused lasso Black line: true values Red line: es8mated values

6 Lasso for Reducing False Positives (Tibshirani, 1996) Trait Genotype Associa8on Strength 2.1 = T G A A C C A T G A A G T A x Lasso Penalty for sparsity argmin (y Xβ) (y Xβ) β + β j Many zero associa8ons (sparse results), but what if there are mul8ple related traits?

7 Multivariate Regression for Multiple-Trait Association Analysis Trait Genotype Associa8on Strength (3.4, 1.5, 2.1, 0.9, 1.8) Allergy Lung physiology = T G A A C C A T G A A G T A x Associa8on strength between SNP j and Trait k: β jk argmin (y Xβ) (y Xβ) β + β j + We introduce graph- guided fusion penalty

8 Multiple-trait Association: Graph-Constrained Fused Lasso Step 1: Thresholded correla8on graph of phenotypes Step 2: Graph- constrained fused lasso ACGTTTTACTGTACAATT Fusion Lasso Penalty Graph- constrained fusion penalty

9 Fusion Penalty SNP j ACGTTTTACTGTACAATT Associa8on strength between SNP j and Trait k: β jk Associa8on strength between SNP j and Trait m: β jm Trait m Trait k Fusion Penalty: β jk - β jm For two correlated traits (connected in the network), the association strengths may have similar values.

10 Graph-Constrained Fused Lasso Overall effect ACGTTTTACTGTACAATT Fusion effect propagates to the entire network Association between SNPs and subnetworks of traits

11 Multiple-trait Association: Graph-Weighted Fused Lasso Overall effect ACGTTTTACTGTACAATT Subnetwork structure is embedded as a densely connected nodes with large edge weights Edges with small weights are effectively ignored

12 Estimating Parameters Quadratic programming formulation Graph-constrained fused lasso Graph-weighted fused lasso Many publicly available software packages for solving convex optimization problems can be used

13 Improving Scalability Original problem Equivalently Using a varia8onal formula8on Itera8ve op8miza8on Update β k Update d jk s, d jml s

14 Simula2on Results 50 SNPs taken from HapMap chromosome 7, CEU population 10 traits SNPs Trait Correla8on Matrix Phenotypes Thresholded Trait Correla8on Network High associa8on No associa8on True Regression Coefficients Single SNP- Single Trait Test Significant at α = 0.01 Lasso Graph- guided Fused Lasso

15 Asthma Trait Network Subnetwork for Asthma symptoms Phenotype Correla8on Network Subnetwork for lung physiology Subnetwork for quality of life

16 Results from Single-SNP/Trait Test Phenotypes Phenotypes Trait Network Lung physiology- related traits I Baseline FEV1 predicted value: MPVLung Pre FEF predicted value Average nitric oxide value: online Body Mass Index Postbronchodila8on FEV1, liters: Spirometry Baseline FEV1 % predicted: Spirometry Baseline predrug FEV1, % predicted Baseline predrug FEV1, % predicted Q551R SNP Codes for amino- acid changes in the intracellular signaling por8on of the receptor Exon 11 SNPs High associa8on No associa8on Single- Marker Single- Trait Test Permuta8on test α = 0.05 Permuta8on test α = 0.01

17 Comparison of Gflasso with Others Phenotypes Phenotypes Trait Network Lung physiology- related traits I Baseline FEV1 predicted value: MPVLung Pre FEF predicted value Average nitric oxide value: online Body Mass Index Postbronchodila8on FEV1, liters: Spirometry Baseline FEV1 % predicted: Spirometry Baseline predrug FEV1, % predicted Baseline predrug FEV1, % predicted Q551R SNP Codes for amino- acid changes in the intracellular signaling por8on of the receptor Exon 11 SNPs? High associa8on No associa8on Single- Marker Single- Trait Test Lasso Graph- guided Fused Lasso

18 Simulation Results

19 Linkage Disequilibrium Structure in IL-4R gene SNP rs SNP rs SNP Q551R r 2 =0.64 r 2 =0.07

20 Bias and Variance Tradeoff The penalty func8on introduces bias to the es8ma8on process, but can reduce the variance The amount of the bias is controlled by selec8ng the appropriate regulariza8on parameter

21 Network-Constrained Regularization for Leveraging Pathway Information (Li and Li, 2008) Pathway databases as prior biological knowledge KEGG, Reactome, BioCarta, BioCyc Leverage the pathway informa8on to detect genes in pathway relevant to the given outcome

22 Graph Laplacian Graph Laplacian: L = D- W Weighted adjacency matrix W: w ij =w ji, w ij =0 if no edges between nodes i and j Degree matrix D: diagonal matrix with diagonal entries Normalized graph Laplacian: Symmetric and posi8ve definite

23 Network-Constrained Regularized Regression Network- constrained regulariza8on criterion Equivalently, If L=I, it becomes elas8c net

24 Optimization Cast it as a lasso op8miza8on problem where

25 Simulation Studies Model: 200 transcrip8on factors, each regula8ng 10 genes four transcrip8on factors and their target genes are relevant to the given response

26 Results from Simulation Study Comparison of lasso, elas8c net, and network- constrained regularized regression

27 Analysis of Glioblastoma Dataset Response: Cancer survival/death Predictors: 1533 genes on 33 KEGG pathways

28 Gene Graph Components Relevant to Cancer Survival