GLIDE: GPU-based LInear Detection of Epistasis

Transcription

1 GLIDE: GPU-based LInear Detection of Epistasis Chloé-Agathe Azencott with Tony Kam-Thong, Lawrence Cayton, and Karsten Borgwardt Machine Learning and Computational Biology Research Group Max Planck Institute for Developmental Biology & Max Planck Institute for Intelligent Systems Tübingen, Germany May 16, 2012 C.-A. Azencott GLIDE May 16,

2 GWAS: Genome-Wide Association Studies...ATTACGTACGAT......ATTA GGTACGAT......ATTACGTACGAT......ATTACGTACGAT......ATTACGTACGAT SNPs subjects Which SNPs explain the phenotype? C.-A. Azencott GLIDE May 16,

3 GWAS Variables Phenotype and genotype can be binary, discrete or continuous Phenotype SNPs values Binary Sick / Not sick Homozygous SNPs Discrete Eye color {0, 1, 2} encoding Continuous Height Imputed values {0, 1, 2} allele count encoding Alleles A A A a a a Encoding { 1, 1, 1} dominance encoding Alleles A A A a a a Encoding C.-A. Azencott GLIDE May 16,

4 Missing Heritability and Epistasis Single-locus GWAS fail to explain all the heritability of most complex traits rare variants, undetected SNPs with small effect size... interactions between SNPs [Manolio et al. 2010, Zuk et al. 2012] Known synergetic effects between genes Enhance/suppress cancer mutations [Ashworth et al. 2011] Loss of VHL (tumor supressor) causes cellular senescense, unless Retinoblastoma (another tumor supressor) is also inactivated Working memory related brain activation [Tan et al. 2007] GRM3 adverse effect on prefrontal engagement only in presence of one variant of COMT Map pairs of SNPs to the phenotype C.-A. Azencott GLIDE May 16,

5 State of the Art SNP pairs Computational burden Statistical issues IC 1101 the biggest known galaxy Reduce the search space Two-stage approaches Only consider SNPs from single-locus GWAS [Zhang et al. 2007] relevant pathways underlying PPI [Emily et al. 2009] C.-A. Azencott GLIDE May 16,

6 State of the Art Reduce the search space Space-pruning techniques FastANOVA: branch-and-bound on SNPs [Zhang et al. 2008] TEAM: efficient updates of contigency tables [Zhang et al. 2010] Sampling approaches BEAM [Zhang et al. 2007] MCMC sampling Random forests [Lunetta et al. 2004] Lightbulb [Achlioptas et al. 2011] all limited to binary or discrete phenotypes/genotypes C.-A. Azencott GLIDE May 16,

7 State of the Art Use Graphics Processing Units (GPUs) Build images fast for display Highly parallelizable, simple functions SHEsisEpi [Hu et al., 2010], EPIBLASTER [Kam-Thong et al., 2011], EPIGPUHSIC [Kam-Thong et al., 2011], GBOOST [Young et al., 2011], EpiGPU [Hemani et al., 2011] Drawbacks: Limited to binary or discrete phenotypes/genotypes Neglect main effects Reduced interpretability C.-A. Azencott GLIDE May 16,

8 GLIDE GPU-based linear regression for the detection of epistasis Phenotype = α SNP 1 + β SNP 2 + γ SNP 1 SNP 2 + δ Is γ signficantly different from 0? t-test Both phenotype and genotype can be continuous Main effects are accounted for C.-A. Azencott GLIDE May 16,

9 GPU Implementation m n subject-snp matrix X, Phenotype y R m Each SNP is a column x i R m Each thread looks at one SNP pair (x i, x j) define: X ij = 1 x i x j x i x j solve: X ij α ij y by α ij = ( X ij X ij) 1 X ij y C.-A. Azencott GLIDE May 16,

10 GPU Implementation Threads are grouped in blocks that use a subset of columns of X Each block k, l of size B B looks at the interactions between SNPs from {x kb+1, x kb+2,..., x kb+b } and {x lb+1, x lb+2,..., x lb+b } Phase I compute A k,l = x kb+1... x kb+b x lb+1... x lb+b x 2 kb+1... x2 kb+b x2 lb+1... x2 lb+b 1 y store T k,l = A k,l A k,l in shared memory C.-A. Azencott GLIDE May 16,

11 GPU Implementation Phase II recover X ij X ij as X ij X ij = m x i 1 x j 1 (x i x j) 1 x i 1 x i x i x i x j x i (x i x j) x j 1 x j x i x j x j x j (x i x j) (x i x j) 1 (x i x j) x i (x i x j) x j (x i x j) (x i x j) invert X ij X ij of dimension 4 4 analytically estimate the regression coefficients as (X ij X ij ) 1 X ij y compute the estimated phenotype, residual, t-scores C.-A. Azencott GLIDE May 16,

12 Statistical Significance Multiple Hypothesis Testing correction Bonferroni correction overly conservative (linked markers) Permutation testing computationally intractable [Becker et al. 2011] MC-simulations correction factor: 0.4 m m = n(n 1)/2 SNP pairs C.-A. Azencott GLIDE May 16,

13 Runtime Performance Synthetic data 1, 000 subjects, 5, 000 SNPs GPUs: NVIDIA GTX 580 ( $450) GLIDE Speed Performance Speed vs. Number of Subjects Method Runtime GLIDE speedup PLINK s FastEpistasis / node s 280 GLIDE / GPU 5 s GLIDE FastEpistasis PLINK 1000 '000 Interactions/sec # of Subjects C.-A. Azencott GLIDE May 16,

14 Hippocampus Volume Epistasis Detection I Hippocampus I involved in many cognitive processes (e.g. formation of new memories) I volume reduction Alzheimer s disease, schizophrenia, recurrent depression I volume known to be inheritable I GWAS study: 567 genotyped subjects, about 106 SNPs C.-A. Azencott GLIDE May 16,

15 Hippocampus Volume Epistasis Detection Single-locus GWAS 20 SNPs with significant main effects 14 associated with hippocampal morphology and brain maturation explain 18% of the variance Two-locus GWAS Runtime 3 days on a single GPU 20 pairs with lowest p-values ( ) No significant main effects 8 independent pairs, explain 40% of the variance Together explain 50% of the variance Low MAF potentially driven by small number of outliers C.-A. Azencott GLIDE May 16,

16 Hippocampus Volume Epistasis Detection SNPs close to genes linked to: ICOS, CTLA4: neurogenesis and neural plasticity Q-Q Plot ZEB2: hippocampal development regulation ZPLD1: cerebral malformations TRPM6: cation channels, expressed in the brain PCDH8: cell adhesion in the central nervous system C.-A. Azencott GLIDE May 16,

17 Future Work additive & dominance effects y = α 1x 1 + β 1z 1 + α 2x 2 + β 2z 2+ γ aax 1x 2 + γ ad x 1z 2 + γ da z 1x 2 + γ dd z 1z 2 + δ Assessment of significance: permutation tests on GPU Population structure correction for epistasis on GPU Eigenstrat approach: add large eigenvectors of the kinship matrix as covariates Linear Mixed Models (EMMA, FaST-LMM) y N (Xβ; σ 2 gk + σ 2 ei) Hippocampal volume: per cytoarchitectonic subregion C.-A. Azencott GLIDE May 16,

18 Other Ongoing Projects Learning from data with missing information Long-range SNP correlation & genetic interactions Disease gene prediction from gene networks Analysis of clinical data (mood disorders and immunology) C.-A. Azencott GLIDE May 16,

19 Acknowledgements Karsten Borgwardt, Bernhard Schölkopf, Betram Müller-Myhsok, Detlef Weigel Tony Kam-Thong Lawrence Cayton Philipp Sämann Benno Pütz, André Altmann Theofanis Karaletsos Alexander von Humboldt Stiftung T. Kam-Thong, C.-A. Azencott, L. Cayton, B. Pütz, A. Altmann, P. Sämann, B. Schölkopf, B. Müller-Myhsok and K. Borgwardt. GLIDE: GPU-based linear regression for detection of epistasis, submitted GLIDE is available at C.-A. Azencott GLIDE May 16,