1. Alkes Price Harvard School of Public Health April 23 & April 25, 2019
EPI 511, Advanced Population and Medical Genetics
Week 12:
• Functional interpretation of genetic associations
Alkes Price Harvard School of Public Health April 23 & April 25, 2019

2. EPI511, Advanced Population and Medical Genetics
Week 12:
• Functional interpretation of genetic associations
Final project: due date is officially May 17 at 5pm, but anytime before May 20 at 6am is ok.
Every registered student is encouraged to schedule a 15min meeting with Alkes May 1-10 to discuss the final project (
Apr 30 guest lecture: Alexander (Sasha) Gusev,
Assistant Professor, DFCI/Harvard Medical School 2

3. Outline 1. Introduction to functional annotation data
2. Functional architectures of diseases and complex traits
3. LD-dependent architectures of diseases and complex traits
4. Improving association and fine-mapping using functional data

4. Outline 1. Introduction to functional annotation data
2. Functional architectures of diseases and complex traits
3. LD-dependent architectures of diseases and complex traits
4. Improving association and fine-mapping using functional data

5. Functional annotations can provide an interpretation of genetic associations
—Nat Genet editorial, July 2012

6. Functional annotation of the human genome
“Here, we assign biochemical functions for 80% of the genome”
—ENCODE Consortium 2012 Nature

7. Functional annotation of the human genome
“Here, we assign biochemical functions for 80% of the genome”
—ENCODE Consortium 2012 Nature
“Here, we detail the many transgressions involved in assigning
functionality to almost every nucleotide in the human genome”
—Graur et al Genome Biol Evol

8. What does “functional annotation” mean?
• Coding regions: DNA that codes for proteins (~1% of genome)
Untranslated regions (UTR): flanking coding regions (~1%)
Promoter: RNA polymerase binding => transcription (~2%)

9. What does “functional annotation” mean?
• Coding regions: DNA that codes for proteins (~1% of genome)
Untranslated regions (UTR): flanking coding regions (~1%)
Promoter: RNA polymerase binding => transcription (~2%)
• Cis-regulatory regions (up to 1,000,000bp away from genes)
Enhancer: region where transcription factors bind to
activate transcription.
Pennacchio et al. al Nat Rev Genet
Shlyueva et al. al Nat Rev Genet

10. What does “functional annotation” mean?
• Coding regions: DNA that codes for proteins (~1% of genome)
Untranslated regions (UTR): flanking coding regions (~1%)
Promoter: RNA polymerase binding => transcription (~2%)
• Cis-regulatory regions (up to 1,000,000bp away from genes)
Enhancer: region where transcription factors bind to
activate transcription.
Enhancer activity can vary by tissue or cell type! ≠

11. Enhancer activity can vary by tissue or cell type!
Shlyueva et al. al Nat Rev Genet

12. Enhancer activity can vary by tissue or cell type!
Shlyueva et al. al Nat Rev Genet

13. Enhancer activity can vary by tissue or cell type!
Shlyueva et al. al Nat Rev Genet

14. How do we figure out where the enhancers are, for a given tissue or cell type?
i. Identify DNase I Hypersensitivity Sites (DHS) via DNase-seq.
ii. Identify histone marks via ChIP-Seq.
iii. Other experimental assays.
iv. Use gene expression data to perform eQTL mapping.
v. Binding sites of known transcription factors.
vi. Identify promoter-enhancer interactions using Hi-C.
The ENCODE Project Consortium 2012 Nature
Roadmap Epigenomics Consortium 2015 Nature
dsQTL: Degner et al Nature, ATAC-QTL: Gate et al Nat Genet
hQTL: Waszak et al Cell, Chen et al Cell, Ng et al Nat Neurosci
also see van de Geijn et al Nat Methods, Taudt et al Nat Rev Genet

15. How do we figure out where the enhancers are, for a given tissue or cell type?
i. Identify DNase I Hypersensitivity Sites (DHS) via DNase-seq.
• Closed chromatin => Transcription factors cannot bind.
Open chromatin => Transcription factors can bind.
• DNase I = enzyme that cuts DNA at regions of open chromatin.
DNase-seq = sequence regions cut by DNase I
to identify regions of open chromatin (DHS).
Transcription factors
Thurman et al Nature, Shlyueva et al. al Nat Rev Genet; also see
Buenrostro et al Nat Methods (ATAC-seq), Gate et al Nat Genet (ATAC-QTL)

16. How do we figure out where the enhancers are, for a given tissue or cell type?
ii. Identify histone marks via ChIP-Seq (Park et al Nat Rev Genet)
Histone mark
Barski et al Cell, Ernst et al Nature, Shlyueva et al Nat Rev Genet
also see Roadmap Epigenomics Consortium 2015 Nature, Lesch et al Nat Genet
hQTL: Waszak et al Cell, Chen et al Cell, Ng et al Nat Neurosci

17. How do we figure out where the enhancers are, for a given tissue or cell type?
ii. Identify histone marks via ChIP-Seq.
• Use chromHMM to define chromatin states from histone marks
Ernst et al Nature
Shlyueva et al. al Nat Rev Genet

18. How do we figure out where the enhancers are, for a given tissue or cell type?
ii. Identify histone marks via ChIP-Seq.
• Use chromHMM to define chromatin states from histone marks
• Cluster 2.3 million enhancer regions into 226 modules based on
coordinated activity patterns across 111 cell types.
Ernst et al Nature
Shlyueva et al. al Nat Rev Genet
Roadmap Epigenomics Consortium 2015 Nature

19. How do we figure out where the enhancers are, for a given tissue or cell type?
iii. Other experimental assays.
• FANTOM5 project: experimentally determined enhancers from
Cap Analysis of Gene Expression (CAGE)
Claim: Enhancer reporter assay shows higher specificity (70% vs %) vs. predicted enhancers from ENCODE
(The ENCODE Project Consortium 2012 Nature).
Andersson et al Nature
also see Core et al Nat Genet, Lara-Astiaso et al Science

20. How do we figure out where the enhancers are, for a given tissue or cell type?
iv. Use gene expression data to perform eQTL mapping.
Figure from Won et al Nature; also see
Cheung et al Nature, Stranger et al Nat Genet, Lappalainen et al.
2013 Nature, Wright et al Nat Genet, GTEx Consortium 2017 Nature

21. How do we figure out where the enhancers are, for a given tissue or cell type?
iv. Use gene expression data to perform eQTL mapping.
also see research connecting eQTL mapping to GWAS of diseases and complex traits:
Nicolae et al PLoS Genet, Gamazon et al Nat Genet, Gusev et al. 2016
Nat Genet, Zhu et al Nat Genet, Franzen et al Science, Gusev et al. 2018
Nat Genet, Hormozdiari et al Nat Genet, Gamazon et al Nat Genet

22. How do we figure out where the enhancers are, for a given tissue or cell type?
v. Binding sites of known transcription factors.
• In vivo approach: use ChIP-Seq (Park et al Nat Rev Genet)
to see where in the genome each transcription factor binds
(can combine with DNase-seq data; Moyerbrailean et al PLoS Genet).
• In vitro approach: measure binding of each transcription factor
to many short sequences, to predict binding genome-wide
(e.g. DeepBind; Alipanahi et al Nat Biotechnol)
… but sequence “motifs” at which transcription factors bind
are still poorly understood for most transcription factors.
reviewed in Levo & Segal 2014 Nat Rev Genet

23. How do we figure out where the enhancers are, for a given tissue or cell type?
vi. Identify promoter-enhancer interactions using Hi-C.
• Hi-C data can be combined with evidence from other sources
(Won et al Nature)
Dixon et al Nature, Rao et al Cell, Schmitt et al Cell Reports,
Won et al Nature; reviewed in Pombo & Dillon 2015 Nat Rev Mol Cell Biol

24. How do we figure out where the enhancers are, for a given tissue or cell type?
i. Identify DNase I Hypersensitivity Sites (DHS) via DNase-seq.
ii. Identify histone marks via ChIP-Seq.
iii. Other experimental assays.
iv. Use gene expression data to perform eQTL mapping.
v. Binding sites of known transcription factors.
vi. Identify promoter-enhancer interactions using Hi-C.
The ENCODE Project Consortium 2012 Nature
Roadmap Epigenomics Consortium 2015 Nature
dsQTL: Degner et al Nature, ATAC-QTL: Gate et al Nat Genet
hQTL: Waszak et al Cell, Chen et al Cell, Ng et al Nat Neurosci
also see van de Geijn et al Nat Methods, Taudt et al Nat Rev Genet

25. Limited role for protein-coding regions in GWAS associations
• 465 GWAS-associated SNPs (NHGRI GWAS catalogue),
based on 1 lead SNP per trait and genomic region.
• 11% of GWAS-associated SNPs lie in coding regions spanning
1% of the genome.
• 9% non-synonymous vs. 2% synonymous.
• 4-fold enrichment for non-synonymous SNPs when counting
all SNPs with P < 5 x 10-8 and SNPs in LD with those SNPs.
Hindorff et al PNAS

26. Major role for DNase I Hypersensitivity Sites
• 5,134 GWAS-associated SNPs (NHGRI GWAS catalogue)
57% of these SNPs lie in DHS spanning 42% of the genome
(from 349 cell/tissue types; ENCODE and Roadmap projects)
• Larger DHS enrichment for externally replicated GWAS SNPs.
Maurano et al Science
also see Thurman et al Nature, Trynka et al Am J Hum Genet

27. Linking enhancers to the genes they regulate
• Idea: Enhancers that regulate a gene will have similar patterns
of activation as the promoter of the regulated gene, leading to
enhancer-promoter correlation across cell types in DHS patterns.
• 419 GWAS-associated SNPs annotated as DHS in a subset of
cell types are strongly correlated (> 0.7) to a “nearby” promoter
in their DHS patterns.
Maurano et al Science
also see Thurman et al Nature, Trynka et al Am J Hum Genet

28. histone QTLs are enriched for GWAS hits
Enrichment of hQTL in
GWAS vs. random SNPs,
matched for MAF and
distance to nearest gene.
Waszak et al Cell
also see Chen et al Cell,
Ng et al Nat Neurosci

29. Linking enhancers to the genes they regulate
• Idea: Histone mark enhancers that regulate a gene will lead to
histone mark-gene expression correlation across individuals.
• 4,568 (22%) genes have expression correlated to a histone mark
at 0.1%. FDR.
Waszak et al Cell
also see Chen et al Cell, Ng et al Nat Neurosci

30. Identifying critical cell types for each disease
• Idea: for a given disease, histone marks (e.g. H3K4me3)
associated with promoter or enhancer activity may occur
specifically in critical cell types relevant to that disease,
in which the target gene is regulated.
• For a given disease (e.g. T2D) + histone mark (e.g. H3K4me3)
+ set of GWAS-associated (+ tag) SNPs for that disease, identify
cell types with excess of histone mark peaks near those SNPs.
Trynka et al Nat Genet
also see PGC-Schizophrenia Working Group 2014 Nature, Farh et al Nature

31. Identifying critical cell types for each disease
• Idea:
Trynka et al Nat Genet
also see PGC-Schizophrenia Working Group 2014 Nature, Farh et al Nature

32. Polygenic architectures motivate polygenic analyses of functional data
Boyle et al Cell; also see Wray et al Cell

33. Outline 1. Introduction to functional annotation data
2. Functional architectures of diseases and complex traits
3. LD-dependent architectures of diseases and complex traits
4. Improving association and fine-mapping using functional data

34. Defining hg2
Heritability explained by genotyped SNPs (hg2), a parameter which depends on the population studied + phenotype + set of genotyped SNPs, is defined as
the maximum proportion of phenotypic variance that can be explained by a linear combination of genotyped SNPs i.
This is defined in the entire population, not estimated in a
finite sample. No assumptions needed for this definition.
Yang et al Nat Genet

35. Defining hg2 across functional categories
Heritability explained by genotyped SNPs (hg2), a parameter defined in the entire population that depends on the phenotype + set of genotyped SNPs, is defined as
the maximum proportion of phenotypic variance that can be explained by a linear combination of genotyped SNPs i.
With multiple functional categories f, even if SNPs are linked this definition generalizes to the variances explained when jointly fitting weights wi for SNPs i in each category f.
Lee et al Nat Genet, Gusev et al Am J Hum Genet, Loh et al. 2015b Nat Genet

36. Assessing functional enrichment using raw genotype/phenotype data
• 72% of hg2 of height lies in genic regions spanning
49% of the genome (Yang, Manolio et al Nat Genet)
(from Week 8)
• 31% of hg2 of schizophrenia lies in CNS+ gene regions
spanning 20% of the genome (Lee et al Nat Genet)
• 38-79% of hg2 of 11 WTCCC diseases (6 autoimmune) lies in
16% of genome annotated as DHS (Gusev et al AJHG)
[38% using genotyped SNPs; 79% using imputed SNPs]

37. Assessing functional enrichment using raw genotype/phenotype data
• hg2 is enriched in regions with high GC content
N = 49,806 for schizophrenia
N = 54,734 for dyslipidemia
and hypertension
Loh, Bhatia et al Nat Genet

38. Functional enrichment can be assessed using summary statistics
—Nat Genet editorial, July 2012
Definition: Summary statistics consist of:
• GWAS association z-scores for each typed or imputed SNP
• Sample sizes on which z-scores were computed (may vary by SNP)
Note: Many applications also require LD information computed from a population reference panel, e.g Genomes (2015 Nature).
reviewed in Pasaniuc & Price 2017 Nat Rev Genet

39. Functional interpretation of hg2 using summary statistics
• Stratified LD score regression:
Regress χ2 association statistics on LD (from reference panel)
with different functional annotation categories.
Finucane et al Nat Genet

40. Average χ2 > 1 does not imply confounding
Linear Regression: E(χ2 statistic) = 1 + (hg2N/M)LDscore, where
M = #markers, N = #samples, LDscore(SNP m) =
Thus, average χ2 = 1 + (hg2N/M)LDscoreavg = 1 + hg2N/Meff
Inflation is not a bad thing! (see Yang et al Eur J Hum Genet)
CONFOUNDING 
(from Week 8)
also see Yang et al Nat Genet

41. LD score regression (schizophrenia example) X
λGC = 1.484
Average χ2 = 1.613
i = 1.066
LDscore(SNP m) =
Regress
χ2 = i + s*LDscore
Intercept i
= 1 if no confounding,
> 1 if confounding
(slide from Week 5)
Bulik-Sullivan, Loh et al Nat Genet; SCZ data from PGC-SCZ 2014 Nature

42. LD score regression: estimating hg2
LDscore(SNP m)
= (r2 from reference panel, e.g Genomes)
Linear Regression: regress χ2 statistics on LD
χ2 = i + s*LDscore
Intercept i = 1 if no confounding, > 1 if confounding
Slope s = hg2N/M, can be used to estimate hg2 (of all reference SNPs)
(from Week 8)
Bulik-Sullivan, Loh et al Nat Genet

43. Stratified LD score regression: estimating hg2 for disjoint functional categories
LDscoref (SNP m) for functional category f
= (r2 from reference panel, e.g Genomes)
Multi-linear Regression: regress χ2 statistics on LD with each category
χ2 statistic = 1 + Σf (Nhg2(f)/M(f))LDscoref
Define enrichment(f) = (% hg2) / (% SNPs) = (hg2(f)/hg2) / (M(f)/M)
Finucane et al Nat Genet

44. Stratified LD score regression: estimating hg2 for overlapping functional categories
LDscoref (SNP m) for functional category f
= (r2 from reference panel, e.g Genomes)
Multi-linear Regression: regress χ2 statistics on LD with each category
χ2 statistic = 1 + Σf (Nτf)LDscoref
Define enrichment(f) = (% hg2) / (% SNPs) = (hg2(f)/hg2) / (M(f)/M)
Finucane et al Nat Genet

45. Functional annotations analyzed
Mark
Source/reference
Coding, 3’ UTR, 5’ UTR, Promoter, Intron
UCSC; Gusev et al AJHG
Digital Genomic Footprint, TFBS
ENCODE; Gusev et al AJHG
CTCF binding site, Promoter Flanking, Repressed, Transcribed, TSS, Enhancer, Weak Enhancer
ENCODE; Hoffman et al Nucleic Acids Res
DHS, H3K4me1, H3K4me3, H3K9ac
Trynka et al Nat Genet*
Conserved
Ward & Kellis 2012 Science
FANTOM5 Enhancer
Andersson et al Nature
lincRNAs
Cabili et al Genes Dev
DHS and DHS promoter
Maurano et al Science
H3K27ac
Roadmap; PGC Nature
*Post-processed from ENCODE and Roadmap data by S. Raychaudhuri and X. Liu labs
Note: 500bp windows around each category were also included as additional annotations.

46. Simulations: LD Score regression works well when the causal categories are in the model
• DHS (1x enr.) + non-DHS
• DHS (3x enr.) + non-DHS
• DHS only (5.5x enriched)
(DHS)

47. Simulations: LD Score regression works well when the causal categories are not in the model
• 200bp flanking DHS
• Coding
• FANTOM5 enhancer*
*Andersson et al Nature
(DHS)

48. Next steps on LD score regression
                             
Next steps on LD score regression
If you feel like Dancin’ …
-- Prince
If you feel like Data …
-- Alkes

49. 17 traits analyzed (summary statistics only)*
*HLA locus excluded from all analyses

50. Coding, Enhancer, Super-enhancer and H3K4me3 enrichments in a subset of phenotypes

51. Coding, Enhancer, Super-enhancer, H3K4me3 and Conserved enrichments in a subset of phenotypes

52. Coding, Enhancer, Super-enhancer, H3K4me3, Conserved, and FANTOM5 Enhancer enrichments

53. Cell-type specific histone mark enrichments
inform trait biology
• 4 histone marks: H3K27ac, H3K4me1, H3K4me3, H3K9ac
• Up to 118 cell types; group into 10 cell-type groups
• For each trait (17 total)
For each cell-type group (10 total)
Assess model fit when adding all cell-type specific
annotations in that group as a single new annotation
Results for Schizophrenia, Height, Rheumatoid Arthritis:

55. Cell-type-specific heritability enrichments of specifically expressed genes inform trait biology
• 2 gene expression data sets:
GTEx (RNA-seq, 53 cell types; GTEx Consortium 2015 Science)
Franke lab (expression array, 152 cell types; Fehrmann et al Nat Genet)
• For each trait (48 total) and each cell type (205 total):
Assess model fit when adding cell-type-specific annotation of
specifically expressed genes (±100kb) (Finucane et al Nat Genet)
Results for Schizophrenia, Height, Rheumatoid Arthritis:

57. Inferring low-frequency variant functional architectures by extending S-LDSC
Common variant enrichment (CVE) of an annotation
= prop. of hc2 / prop. of common SNPs
Low-frequency variant enrichment (LFVE) of an annotation
= prop. of hlf2 / prop. of low-frequency SNPs
• Separate annotations for common and low-frequency SNPs
• Also include binary annotations for 10 low-frequency MAF bins
• UK Biobank target samples + UK10K LD reference samples
• Simulations confirm robust results (not shown)
Gazal et al Nat Genet

58. LFVE is correlated to CVE LFVE > CVE when CVE is large
33 main annotations:
r(LFVE,CVE) = 0.79
Meta-analysis across
40 UK Biobank traits
(average N = 363K) assoc. method: BOLT-LMM
Loh et al. biorxiv /
in press Nat Genet
Low-frequency variant enrichment (LFVE)
Common variant enrichment (CVE)

59. LFVE is correlated to CVE LFVE > CVE when CVE is large
33 main annotations:
r(LFVE,CVE) = 0.79
Non-synonymous variants:
17.3% of hlf2 vs. 2.1% of hc2
(Even larger LFVE for n.s. variants
• predicted as damaging: PolyPhen-2
• in genes under strong selection: shet)
Low-frequency variant enrichment (LFVE)
Common variant enrichment (CVE)

60. LFVE is correlated to CVE LFVE > CVE when CVE is large
33 main annotations:
r(LFVE,CVE) = 0.79
Regions conserved in primates:
43.5% of hlf2 vs. 21.2% of hc2
Low-frequency variant enrichment (LFVE)
Common variant enrichment (CVE)

61. LFVE ≈ CVE for most regulatory annotations but LFVE > CVE for brain annotations
637 cell-type-specific (CTS)
annotation-trait pairs with significant CVE
(Finucane et al Nat Genet)
Low-frequency variant enrichment (LFVE)
55 brain annotation-trait pairs
with LFVE/CVE>2x
Common variant enrichment (CVE)

62. LFVE ≈ CVE for most regulatory annotations but LFVE > CVE for brain annotations
H3K4me3 in brain DPFC-Neuroticism:
56.9% of hlf2 vs. 11.7% of hc2 (P = )
Low-frequency variant enrichment (LFVE)
Common variant enrichment (CVE)

63. LFVE ≈ CVE for most regulatory annotations but LFVE > CVE for brain annotations
H3K4me3 in germinal matrix-Age first birth:
63.2% of hlf2 vs. 11.1% of hc2 (P = 0.001)
Low-frequency variant enrichment (LFVE)
Common variant enrichment (CVE)

64. CVE depends on both strength of selection and proportion of variants causal for trait
Forward simulations
(SLiM2 + τEyre-Walker)
sdn = avg selection coefficient
of deleterious de novo variants
π = probability of de novo variant
to be causal for trait
(π)

65. LFVE/CVE ratio depends primarily on strength of selection
Forward simulations
(SLiM2 + τEyre-Walker)
Non-synonymous variants:
LFVE/CVE=5x, sdn=‒0.003
55 brain annotation-trait pairs:
LFVE/CVE>2x, sdn<‒0.0006
(π)

66. Outline 1. Introduction to functional annotation data
2. Functional architectures of diseases and complex traits
3. LD-dependent architectures of diseases and complex traits
4. Improving association and fine-mapping using functional data

67. What does “LD-dependent architecture” mean?

68. What does “LD-dependent architecture” mean?
• SNPs with higher LD have higher average χ2 association statistics
due to increased tagging of causal variants.
Pritchard & Przeworski 2001 Am J Hum Genet

69. What does “LD-dependent architecture” mean?
• SNPs with higher LD have higher average χ2 association statistics
due to increased tagging of causal variants.
“LD-dependent architecture”: dependence of causal effect sizes
on the level of LD of a SNP.

70. What does “LD-dependent architecture” mean?
• Common SNPs have higher LD and higher causal variance than
rare SNPs => SNPs with higher LD have higher causal variance.
Zuk et al PNAS

71. What does “LD-dependent architecture” mean?
• Common SNPs have higher LD and higher causal variance than
rare SNPs => SNPs with higher LD have higher causal variance.
“LD-dependent architecture”: dependence of causal effect sizes
on the level of LD of a SNP, after conditioning on MAF.

72. LD-dependent architectures: why should we care?
LD-dependent architectures lead to bias in hg2 estimates
(from Week 8)
Gusev et al PLoS Genet
also see Speed et al AJHG, Yang et al Nat Genet, Speed et al Nat Genet

73. LD-dependent architectures: why should we care?
Understanding which regions of the genome contribute most to the genetics of complex traits and diseases can:
• Help us understand biology and evolution
• Increase association power
(Pickrell 2014 AJHG, Sveinbjornsson et al Nat Genet)
• Improve fine-mapping resolution
(Kichaev et al PLoS Genet)

74. Enriched heritability in regulatory regions, which have lower LD, higher recombination rate
Finucane et al Nat Genet; also see Gusev et al Am J Hum Genet

75. BUT, in coding regions: more disease variants in regions with lower recombination rate
Hussin et al Nat Genet

76. BUT, in coding regions: more disease variants in regions with lower recombination rate
Hussin et al Nat Genet

77. Stratified LD score regression: estimating hg2 for overlapping functional categories
LDscoref (SNP m) for functional category f
= (r2 from reference panel, e.g Genomes)
Multi-linear Regression: regress χ2 statistics on LD with each category
χ2 statistic = 1 + Σf (Nτf)LDscoref
Define enrichment(f) = (% hg2) / (% SNPs) = (hg2(f)/hg2) / (M(f)/M)
Finucane et al Nat Genet

78. Extending LD score regression: estimating hg2 for continuous functional annotations
LDscoreq (SNP m) for continuous annotation q =
Multi-linear Regression: regress χ2 statistics on annotation LD scores
χ2 statistic = 1 + Σq(Nτq)LDscoreq
= normalized effect size of annotation q
conditioned on effects of other annotations included in model
(proportionate change in trait h2 per 1 s.d. increase in annot. q)
Gazal et al Nat Genet

79. Extending LD score regression: estimating hg2 for continuous LD-related annotations
Level of LD ( LLD ): MAF-adjusted LD score
(MAF-stratified quantile normalization)
LDscoreLLD (SNP m) for continuous LLD annotation =
Multi-linear Regression: regress χ2 statistics on annotation LD scores
χ2 statistic = 1 + (NτLLD) LDscoreLLD + …
(also include MAF bins + functional annotations from Finucane et al Nat Genet)
Gazal et al Nat Genet

80. Simulations: LD score regression produces unbiased estimates of LD-dependent architectures
Simulations using real genotypes, simulated phenotypes (τLLD = 0),
inference via LD score regression using 1000G reference panel.

81. Next steps on LD-dependent architectures
                             
Next steps on LD-dependent architectures
If you feel like Dancin’ …
-- Prince
If you feel like Data …
-- Alkes

82. 56 traits analyzed (summary statistics only) Public + 23andMe + UK Biobank (avg N = 101,401)
Phenotype
Reference/consortium N
Age at menarche
Perry et al Nature
132,989
Age at menopause
Day et al Nat Genet
67,265
Anorexia
Boraska et al Mol Psych
17,767
Autism Spectrum
PGC Cross-Disorder Group 2013 Lancet
10,263
Bipolar Disorder
BIP Working Group of the PGC 2011 Nat Genet
16,731
BMI
Speliotes et al Nat Genet
123,912
Celiac Disease
Dubois et al Nat Genet
15,283
Coronary Artery Disease
Schunkert et al Nat Genet
86,995
Crohn’s Disease
Jostins et al Nature
20,883
Educational Attainment
Rietveld et al Science
101,069
Ever Smoked
TAG Consortium 2010 Nat Genet
74,035
Fasting Glucose
Manning et al Nat Genet
46,186
HDL
Teslovich et al Nature
99,900
Height
Lango Allen et al Nature
133,858
LDL
95,454
Primary Biliary Cirrhosis
Cordell et al Nat Commun
13,239
Rheumatoid Arthritis
Okada et al Nature
38,242
Schizophrenia
SCZ Working Group of the PGC 2014 Nature
70,100
Systemic Lupus Erythematosus
Bentham et al Nat Genet
14,267
Triglycerides
96,598
Type-2 Diabetes
Morris et al Nat Genet
69,033
Ulcerative Colitis
27,432

83. SNPs with lower MAF-adjusted level of LD (LLD) have larger causal effect sizes
Same sign of effect across all 56 traits investigated!

84. Many annotations correlated to LD could contribute to LD-dependent architectures
LD-related annotations
Predicted allele age (ARGweaver; Rasmussen et al PLoS Genet)
LLD in Africans (LLD-AFR)
Recombination rate (±10kb window; Hussin et al Nat Genet)
GC-content (±1Mb window; Loh et al. 2015b Nat Genet)
Replication timing (Koren et al Am J Hum Genet)
Background selection (1 − B statistic; McVicker et al PLoS Genet)
Nucleotide diversity (SNPs per kb; ±10kb window)
CpG content (±50kb window)
Functional annotations (“Baseline model”; Finucane et al Nat Genet)
Coding, DHS, histone marks, enhancers, conserved, etc.

85. Many annotations correlated to LD could contribute to LD-dependent architectures|
LD-related
annotations
Functional annotations from “baseline model”
(Finucane et al Nat Genet)

86. Many annotations correlated to LD could contribute to LD-dependent architectures|
LD-related
annotations
Functional annotations from “baseline model”
(Finucane et al Nat Genet)

87. Many annotations correlated to LD could contribute to LD-dependent architectures|
LD-related
annotations
Functional annotations from “baseline model”
(Finucane et al Nat Genet)

88. Many LD-related annotations impact causal effect sizes
+ MAF
Annotation
+ baseline model
+ MAF
Meta-analysis of 31 independent traits

89. Many LD-related annotations impact causal effect sizes
+ MAF
Annotation
+ baseline model
+ MAF
Recombination rate has discordant sign of effect (Hill & Robertson 1966 Genet Res)
Heritability is enriched in SNPs with low LLD in low recombination rate regions
r = −0.63
Meta-analysis of 31 independent traits

90. Many LD-related annotations impact causal effect sizes after conditioning on baseline model
+ MAF
Annotation
+ baseline model
+ MAF
Meta-analysis of 31 independent traits

91. Many LD-related annotations impact causal effect sizes after conditioning on baseline model
+ MAF
Annotation
+ baseline model
+ MAF
LLD effect is 0.37x smaller when including annotations from baseline model
Some, but not all, of LD-dependent architecture due to DHS, enhancers, etc.
0.37x
Meta-analysis of 31 independent traits

92. Many LD-related annotations impact causal effect sizes after conditioning on baseline model
+ MAF
Annotation
+ baseline model
+ MAF
LLD effect is 0.51x smaller after adding baseline model
Predicted allele age has largest effect.
Meta-analysis of 31 independent traits

93. SNPs with smaller (more recent) allele age have larger causal effect sizes
Same sign of effect across 55 of 56 traits investigated

94. Many LD-related annotations impact causal effect sizes in joint fit after conditioning on baseline model
Annotation
+ MAF
Annotation
+ baseline model
+ MAF
Joint-fit annotations
+ baseline model
+ MAF
Meta-analysis of 31 independent traits

95. Many LD-related annotations impact causal effect sizes in joint fit after conditioning on baseline model
Annotation
+ MAF
Annotation
+ baseline model
+ MAF
Joint-fit annotations
+ baseline model
+ MAF
LLD effect is 0.51x smaller af
6 significant annotations in joint fit
Meta-analysis of 31 independent traits

96. Many LD-related annotations impact causal effect sizes in joint fit after conditioning on baseline model
Annotation
+ MAF
Annotation
+ baseline model
+ MAF
Joint-fit annotations
+ baseline model
+ MAF
LLD effect is 0.51x smaller af
predicted allele age has largest effect
Meta-analysis of 31 independent traits

97. Quintiles illustrate large effects of LD-related annotations
40%
30%
Proportion of heritability
20%
10% 0%

98. Quintiles illustrate large effects of LD-related annotations
40%
30%
Proportion of heritability
20%
10% 0%
Youngest 20% explain 3.8x more heritability than oldest 20%
vs. 1.8x
for MAF

99. No overall effect for recombination rate
40%
30%
Proportion of heritability
20%
10% 0%
Competing effects of LLD-AFR and RR imply no overall effect for RR

100. LD-related annotations tag negative selection
+ MAF
Annotation
+ baseline model
+ MAF
Joint-fit annotations
+ baseline model
+ MAF
• Predicted allele age:
deleterious variants are younger
• LLD-AFR:
information on variant history?
• Recombination rate:
low RR => less efficient selection
(Hill & Robertson 1966 Genetics)
• Diversity / Background selection:
regions under selection: lower
diversity, biologically important
• CpG-Content:
unknown functional elements?
31 traits

101. X X Forward simulations confirm impact of many
LD-related annotations on selection coefficient s
Annotation
+ MAF
Annotation
+ baseline model
+ MAF
Joint-fit annotations
+ baseline model
+ MAF
Forward
Simulations:
impact on s
• Forward simulations using
SLiM (Messer 2013 Genetics) under
African-European demographic
model (Gravel et al PNAS)
• Recombination rate and
% of deleterious SNPs vary
across regions, selection coeff s
varies across deleterious SNPs
• Jointly regress selection coeff s
on 4 LD-related annotations and
minor allele frequency X X
31 traits Simulations

102. Outline 1. Introduction to functional annotation data
2. Functional architectures of diseases and complex traits
3. LD-dependent architectures of diseases and complex traits
4. Improving association and fine-mapping using functional data

103. Improving association power using functional data
Main idea:
• If certain regions of the genome are more likely to contain
true signal, then association methods should favor those regions
while controlling the overall false-positive rate.

104. Improving association power using functional data: sFDR approach
Stratified false discovery rate (sFDR) approach:
• Use P-value distributions to attain a target false discovery rate
(FDR; Benjamini & Hochberg 1995 JRSS, Storey et al PNAS)
separately for each functional category.
Schork et al PLoS Genet
also see Sun et al Genet Epidemiol, Wang et al PLoS Genet

105. Improving association power using functional data: sFDR approach
Stratified false discovery rate (sFDR) approach:
True Discovery Rate, Crohn’s disease.
Schork et al PLoS Genet

106. Improving association power using functional data: sFDR approach
Stratified false discovery rate (sFDR) approach:
Replication Rate (in independent data set), Crohn’s disease.
Schork et al PLoS Genet

107. Improving association power using functional data: sFDR approach
Stratified false discovery rate (sFDR) approach:
• 381 SNPs at FDR=0.05, 452 at sFDR=0.05 for Crohn’s disease:
+19% increase in power (+24% for height, +270% for SCZ).
Schork et al PLoS Genet

108. Improving association power using functional data: sFDR approach
Stratified false discovery rate (sFDR) approach:
• 381 SNPs at FDR=0.05, 452 at sFDR=0.05 for Crohn’s disease:
+19% increase in power (+24% for height, +270% for SCZ).
• Caveat: #SNPs does not quantify independent associations.
Definition of functional categories (LD score ≥1 to category;
membership in multiple functional categories is allowed) may
lead to more associations for non-independent high-LD SNPs.
Schork et al PLoS Genet

109. Improving association power using functional data: Bayesian approach
• Use Bayesian hierarchical model to jointly model
- the prior probability that a region is associated, as a function
of regional annotations of 2.5Mb regions (e.g. gene density)
- the prior probability that a SNP in an associated region is the
(unique) causal associated SNP in the region, as a function of
annotations of individual SNPs (e.g. DHS).
• Infer posterior probability of association (PPA) for each region.
Pickrell 2014 Am J Hum Genet
also see Wen et al Am J Hum Genet, Wen 2016 Ann Appl Stat

110. Improving association power using functional data: Bayesian approach
Inferred enrichments for HDL (data: Teslovich et al Nature)
Repressed, TSS annotations:
chromHMM chromatin states
(Hoffman et al NAR)
HepG2: liver cancer-derived
(95% CI)
Pickrell 2014 AJHG

111. Improving association power using functional data: Bayesian approach
Inferred enrichments for HDL (data: Teslovich et al Nature)
Across 18 traits analyzed: % increase in # of
regions identified with
PPA > 0.9.
Pickrell 2014 AJHG

112. Improving association power using functional data: P-value weighting
P-value weighting approach:
• Assess enrichment of causal variants in a functional category
by maximizing likelihood under single causal variant model
(Maller et al Nat Genet).
• Set P-value weights equal to functional category enrichments
(Genovese et al Biometrika, Roeder et al Am H Hum Genet;
also see Eskin 2008 Genome Res, Darnell et al Bioinformatics)
• Evaluate number of independent association signals
(P < 3.5 x 10-9, based on 14.2 million SNPs in WGS data;
independent associations assessed via conditional analysis).
Sveinbjornsson et al Nat Genet

113. Improving association power using functional data: P-value weighting
Inferred enrichments using P < 1 x association signals:
• 181x enrichment for loss-of-function coding variants*.
• 37x enrichment for missense coding variants*.
• 1.3x enrichment for DHS non-coding variants.
*Note: coding variants account for >50% of significant associations
in this WGS data set (vs. 11% in GWAS; Hindorff et al PNAS).
Increase in power due to P-value weighting, across 219 traits:
• 14% increase in 1 x < P < 3.5 x 10-9 association signals;
3% increase in set of all P < 3.5 x 10-9 association signals.
Sveinbjornsson et al Nat Genet

114. Functional validation provides the best proof of biological causality
(from Week 6)
Price et al Proc Biol Sci (Table S1)

115. single causal variant approach
Fine-mapping using
single causal variant approach
Assumption: at most 1 biologically causal SNP.
(from Week 6)
Maller et al Nat Genet

116. single causal variant approach
Fine-mapping using
single causal variant approach
Let X denote genotypes, and Xi denote genotypes at SNP i.
Let Model M = union of models Mi over all SNPs i.
Bayes Factor BFi = =
Theorem 6: The posterior probability is
proportional to BFi , assuming equal priors
Proof: ,
which is equal to BFi up to a constant factor (indep. of i). Q.E.D.
(from Week 6)
Maller et al Nat Genet (see Section 6 of Supp Note)
also see Faye et al PLoS Genet, Farh et al Nature

117. Improving fine-mapping using functional priors:
single causal variant approach
Let X denote genotypes, and Xi denote genotypes at SNP i.
Let Model M = union of models Mi over all SNPs i.
Bayes Factor BFi = =
Use different priors based on category of SNP i.
Gusev et al Am J Hum Genet
also see Li & Kellis 2016 Nucleic Acids Res

118. Improving fine-mapping using functional priors:
single causal variant approach
Functional priors reduce 95% credible SNP sets at known loci
(under single causal variant assumption):
Gusev et al Am J Hum Genet
also see Li & Kellis 2016 Nucleic Acids Res

119. Increasing evidence in favor of multiple causal variants at a locus
• 8q24 locus in prostate cancer:
“We identified seven risk variants spanning 430kb
independently predicting risk for prostate cancer”
(Haiman et al 2007 Nat Genet; Table S1 of Price et al Proc Biol Sci)
• FGFR2 locus in breast cancer:
iCOGS chip genotyped in 89K Eur + 14K Asians + 2K AA
“rs , rs , rs are putative functional SNPs”
(Meyer et al Am J Hum Genet; Table S1 of Price et al Proc Biol Sci)
• Local heritability analyses of 9 WTCCC diseases:
“We find significant average increases in local heritability at
known associated loci [compared to heritability of lead SNPs],
consistent with multiple causal variants”
(Gusev et al PLoS Genet)
(from Week 6)

120. multiple causal variant approach
Fine-mapping using
multiple causal variant approach
Let X denote association z-scores for all m SNPs at the locus.
There are 2m different possibilities for the set S of causal variants.
Let MS denote the model in which S is the set of causal variants.
Then
, where γ = 0.01
(for computational efficiency: consider only causal sets S with |S| ≤ 6;
likewise, in denominator, consider only causal sets S’ with |S’| ≤ 6)
(from Week 6)
Hormozdiari et al Genetics

121. Improving fine-mapping using functional priors:
multiple causal variant approach
Let X denote association z-scores for all m SNPs at the locus.
There are 2m different possibilities for the set S of causal variants.
Let MS denote the model in which S is the set of causal variants.
Then
, where
Aik = 1 if SNP i is in functional annotation k, 0 otherwise
γk = effect size of functional annotation k on prob. of being causal
(fit using EM algorithm)
Kichaev et al PLoS Genet

122. Improving fine-mapping using functional priors:
multiple causal variants approach
Probabilistic model on z-scores (PAINTOR):
Inferred enrichments for HDL (data: Teslovich et al Nature)
Kichaev et al PLoS Genet; also see Kichaev & Pasaniuc
2015 Am J Hum Genet, Kichaev et al Bioinformatics, Chen et al Genetics

123. Improving fine-mapping using functional priors:
multiple causal variants approach
Probabilistic model on z-scores (PAINTOR):
90% credible SNP sets for 4 lipid traits (data: Teslovich et al Nature)
Note: simulations show that 90% credible SNP sets are well-calibrated for PAINTOR, but mis-calibrated for methods that assume a single causal variant.
Kichaev et al PLoS Genet; also see Kichaev & Pasaniuc
2015 Am J Hum Genet, Kichaev et al Bioinformatics, Chen et al Genetics

124. Conclusions
Valuable functional annotation data is being generated by ENCODE, Roadmap and other projects.
Stratified LD Score regression detects functional enrichment for coding regions, conserved regions, enhancer regions, etc. and also detects cell-type-specific functional enrichments.
Low-LD variants have larger causal effects (at a given MAF), consistent with the action of negative selection.
• Functional annotations can increase association power and improve fine-mapping.

125. EPI511, Advanced Population and Medical Genetics
Week 12:
• Functional interpretation of genetic associations
Final project: due date is officially May 17 at 5pm, but anytime before May 20 at 6am is ok.
Every registered student is encouraged to schedule a 15min meeting with Alkes May 1-10 to discuss the final project (
Apr 30 guest lecture: Alexander (Sasha) Gusev,
Assistant Professor, DFCI/Harvard Medical School
125

126. Acknowledgements • TA Margaux Hujoel. • Guest lecturer Sasha Gusev.
• Authors of the 29 papers listed on the course syllabus.
All of the other researchers whose work we have discussed.