Partitioning Heritability using GWAS Summary Statistics with LD Score Regression
- 1. Partitioning heritability by functional annotation using summary statistics Hilary Finucane MIT Department of Mathematics HSPH Department of Epidemiology October 21, 2014
- 2. Acknowledgements • Brendan Bulik- Sullivan • Alkes Price • Ben Neale • Alexander Gusev • Nick Patterson • Po-Ru Loh • Gosia Trynka • Han Xu • Verneri Anttila • Yakir Reshef • Chongzhi Zang • Stephan Ripke • Schizophrenia Working Group of the PGC • Shaun Purcell • Mark Daly • Eli Stahl • Soumya Raychaudhuri • Sara Lindstrom
- 3. Partitioning heritability by functional annotation is an important goal • Learn about genetic architecture of disease – Where does the heritability lie? • Learn about disease biology – What are the relevant cell types? • Learn about the functional annotations – Which functional annotations show the highest enrichments? • Downstream applications – Fine mapping – Risk prediction – GWAS priors Maurano et al. 2012 Science Trynka et al. 2013 Nat Genet Pickrell 2014 AJHG
- 4. What is partitioned heritability? • Our model is Where • Y is an individual’s phenotype, • Xj is an individual’s genotype at the j-th SNP (normalized to mean 0 and variance 1), • βj is the effect of SNP j, and • ε is noise and random environmental effects.
- 5. What is partitioned heritability? • Our model is • We define heritability as
- 6. What is partitioned heritability? • Our model is • We define heritability as and the heritability of a category as
- 7. Partitioning heritability using variance components has yielded many insights • 31% of schizophrenia SNP-heritability lies in CNS+ gene regions spanning 20% of the genome1. • 28% of Tourette syndrome SNP-heritability and 29% of OCD SNP-heritability lies in parietal lobe eQTLs spanning 5% of the genome2. • 79% of SNP-heritability, averaged across WTCCC and WTCCC2 traits, lies in DHS regions spanning 16% of the genome3. 1 Lee et al. 2012 Nat Genet 2 Davis et al. 2013 PLoS Genet 3 Gusev et al. in press AJHG
- 8. A method for partitioning heritability from summary statistics is needed • Variance components methods are intractable at very large sample sizes. • There is lots of information in large meta-analyses. • Lots of publicly available summary statistics allow us to compare many phenotypes and many annotations to get a big picture.
- 9. Our method partitions heritability from summary statistics • Input: – Sample size and p-value for every SNP tested in a large GWAS of a quantitative or case-control trait – LD information from a reference panel like 1000G – Genome annotation of interest – Other genome annotations to include in the model.
- 10. Our method partitions heritability from summary statistics • Input: – Sample size and p-value for every SNP tested in a large GWAS of a quantitative or case-control trait – LD information from a reference panel like 1000G – Genome annotation of interest – Other genome annotations to include in the model. • Output: – Estimated proportion of heritability that falls within the annotation of interest. – Enrichment = (% of heritability) / (% of SNPs)
- 11. Outline • Description of method • Validation on simulated data • Results on real data
- 12. Outline • Description of method • Validation on simulated data • Results on real data
- 13. LD is important for summary statistics-based methods • Some SNPs have a lot of LD to other SNPs in the same category. • Some SNPs have a lot of LD to SNPs in other categories. • Some SNPs do not have a lot of LD to other SNPs.
- 14. LD is important for summary statistics-based methods • Some SNPs have a lot of LD to other SNPs in the same category. • Some SNPs have a lot of LD to SNPs in other categories. • Some SNPs do not have a lot of LD to other SNPs. Our solution: LD Score Regression. See Bulik-Sullivan et al. biorxiv (under revision, Nat Genet) and ASHG 2014 poster 1787T Bulik-Sullivan
- 15. LD Score Regression: basic intuition High LD region Low LD region Chi-square • Polygenicity causes more chi-square statistic inflation in high LD regions than in low LD regions Mean chi-square for high LD region: high Mean chi-square for low LD region: low
- 16. Multivariate LD Score Regression: basic intuition High chi-square Low chi-square Enriched category BIG difference between lots of LD vs little LD to the category Low chi-square Low chi-square Depleted category SMALL difference between lots of LD vs little LD to the category
- 17. Multivariate LD Score regression allows us to partition SNP heritability • Multivariate LD Score: the sum over all SNPs in a category of r^2 with that SNP.
- 18. Multivariate LD Score regression allows us to partition SNP heritability • Multivariate LD Score: the sum over all SNPs in a category of r^2 with that SNP. • Derivations based on a polygenic model give:
- 19. Multivariate LD Score regression allows us to partition SNP heritability • Multivariate LD Score: the sum over all SNPs in a category of r^2 with that SNP. • Derivations based on a polygenic model give: • Easily extends to overlapping categories.
- 20. Multivariate LD Score regression allows us to partition SNP heritability To estimate partitioned heritability: • Estimate LD Scores from a reference panel. • Regress chi-square statistics on LD Scores. • The slopes give the partitioned heritability. • For best results, use many categories!
- 21. Outline • Description of method • Validation on simulated data • Results on real data
- 22. Multivariate LD Score regression works in simulations Null simulations DHS 3x enriched True h2(DHS) 0.092 REML (2 cat) 0.089 (0.006) LD Score (27 cat) 0.086 (0.012) True h2(DHS) 0.276 REML (2 cat) 0.281 (0.006) LD Score (27 cat) 0.278 (0.013) • Standard errors are over 100 simulations. • Simulated quantitative phenotype with h2 = 0.5. • M = 110,444, N = 2,713
- 23. Multivariate LD Score regression works in simulations Null simulations DHS 3x enriched True h2(DHS) 0.092 REML (2 cat) 0.089 (0.006) LD Score (27 cat) 0.086 (0.012) True h2(DHS) 0.276 REML (2 cat) 0.281 (0.006) LD Score (27 cat) 0.278 (0.013) FANTOM5 Enhancer* causal True h2(DHS) 0.379 REML (2 cat) 0.531 (0.007) LD Score (27 cat) 0.361 (0.015) • Standard errors are over 100 simulations. • Simulated quantitative phenotype with h2 = 0.5. • M = 110,444, N = 2,713 * Andersson et al. 2014 Nature
- 24. Multivariate LD Score regression works in simulations Null simulations DHS 3x enriched True h2(DHS) 0.092 REML (2 cat) 0.089 (0.006) LD Score (27 cat) 0.086 (0.012) True h2(DHS) 0.276 REML (2 cat) 0.281 (0.006) LD Score (27 cat) 0.278 (0.013) FANTOM5 Enhancer* causal True h2(DHS) 0.379 REML (2 cat) 0.531 (0.007) LD Score (27 cat) 0.361 (0.015) FANTOM5 Enhancer* causal, Excluded from the model True h2(DHS) 0.379 REML (2 cat) 0.531 (0.007) LD Score (26 cat) 0.318 (0.014) • Standard errors are over 100 simulations. • Simulated quantitative phenotype with h2 = 0.5. • M = 110,444, N = 2,713 * Andersson et al. 2014 Nature
- 25. Outline • Description of method • Validation on simulated data • Results on real data
- 26. Datasets analyzed Phenotype Citation Sample size Schizophrenia SCZ working grp of the PGC, 2014 Nature 70,100 Bipolar Disorder Bip working grp of the PGC, 2011 Nat Genet 16,731 Rheumatoid Arthritis* Okada et al., 2014 Nature 38,242 Crohn’s Disease* Jostins et al., 2012 Nature 20,883 Ulcerative Colitis* Jostins et al., 2012 Nature 27,432 Height Wood et al., 2014 Nature Genetics 253,280 BMI Speliotes et al., 2010 Nature Genetics 123,865 Coronary Artery Disease Schunkert et al., 2011 Nature Genetics 86,995 College (yes/no) Rietveld et al., Science 2013 126,559 Type 2 Diabetes Morris et al., 2012 Nature Genetics 69,033 *HLA locus excluded from all analyses for autoimmune traits
- 27. Annotations used Mark Source/reference Coding, 3’ UTR, 5’ UTR, Promoter, Intron UCSC; Gusev et al., in press AJHG Digital Genomic Footprint, TFBS ENCODE; Gusev et al., in press AJHG CTCF binding site, Promoter Flanking, Repressed, Transcribed, TSS, Enhancer, Weak Enhancer ENCODE; Hoffman et al., 2012 Nucleic Acids Research DHS, fetal DHS, H3K4me1, H3K4me3, H3K9ac Trynka et al., 2013 Nature Genetics.* Conserved Lindblad-Toh et al., 2011 Nature FANTOM5 Enhancer Andersson et al., 2014 Nature lincRNAs Cabili et al., 2011 Genes Dev DHS and DHS promoter Maurano et al., 2012 Science H3K27ac Roadmap; PGC2 2014 Nature *Post-processed from ENCODE and Roadmap data by S. Raychaudhuri and X. Liu labs
- 28. Coding, Intergenic, Enhancer, H3K4me3, and DHS enrichments in six phenotypes (Bars indicate 95% confidence intervals)
- 29. Coding, Intergenic, Enhancer, H3K4me3, DHS, and Conserved enrichments in six phenotypes (Bars indicate 95% confidence intervals) *Lindblad-Toh et al., 2011 Nature
- 30. Coding, Intergenic, Enhancer, H3K4me3, DHS, and FANTOM5 Enhancer enrichments in six phenotypes (Bars indicate 95% confidence intervals) *Andersson et al., 2014 Nature
- 31. Cell-type specific H3K27ac enrichments inform trait biology • We group 56 cell types into 7 basic categories. • For each trait (10 traits) – For each category (7 categories) • We asses the significance of improvement to the model from adding that category.
- 33. Conclusions • Many annotations are enriched in many phenotypes. • Conserved regions, 2.6% of SNPs, are estimated to explain 30% of heritability on average. • FANTOM5 Enhancers are extremely enriched in auto-immune traits. • H3K27ac cell-type enrichment matches and extends our understanding of disease biology.
- 34. Acknowledgements • Brendan Bulik- Sullivan • Alkes Price • Ben Neale • Alexander Gusev • Nick Patterson • Po-Ru Loh • Gosia Trynka • Han Xu • Verneri Anttila • Yakir Reshef • Chongzhi Zang • Stephan Ripke • Schizophrenia Working Group of the PGC • Shaun Purcell • Mark Daly • Eli Stahl • Soumya Raychaudhuri • Sara Lindstrom
Editor's Notes
- #4: For a GWAS of a common complex trait, most of the heritability—and so most of the information--lies in the majority of SNPs that do not reach statistical significance. Partitioning heritability is a way to leverage all of the SNPs, instead of just the statistically significant SNPs, to answer questions about genetic architecture, about the biology of disease, and about functional annotations.
- #7: Note: this extends to case-control traits under a liability threshold model. Note: equivalent to other definitions under certain assumptions.
- #8: Partitioning heritability is traditionally done with a variance components method such as REML implemented in GCTA, and has yielded many insights in the past. I’d like to highlight this recent result of Gusev et al that non-coding DHS regions comprising 16% of the genome explain an estimated 79% of heritability on average across 11 traits.
- #9: We need a method for partitioning heritability from summary statistics not just because many of our largest datasets are meta-analyses for which no one has the genotype data required for a variance components approach, but also because even when we do have all of the genotypes, variance components methods are intractable, especially for more than a very few components. As an added benefit of computational ease, we can look at a lot of phenotypes and a lot of annotations to look at higher level patterns.