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CSE291: Personal genomics for bioinformaticians
Class meetings: TR 3:30-4:50 MCGIL 2315
Office hours: M 3:00-5:00, W 4:00-5:00 CSE 4216
Contact: [email protected]
Today’s schedule:
• 3:30-4:15 Scaling GWAS to millions of samples
• 4:15-4:20 Break
• 4:20-4:50 Journal discussion: PrediXan
Announcements:
• Evaluations
• Problem set 4 out on Tuesday
• Reminder about project proposals
Scaling GWAS to millions of
samples
CSE291: Personal Genomics for
Bioinformaticians
02/09/17
Outline
• Challenges in scaling GWAS
• Example: FastPCA
• Example: TeraStructure
• Example: Imputation with
Eagle
• Working with summary
statistics
Challenges in scaling GWAS
Pipeline overview
Reed et al. 2015
“Big data” comes with new challenges
• Logistical challenges
• Raw genotype datasets in the Gigabytes to
Terabytes range
• Often not all the data is stored in the same
place
• Often don’t have legal permission to share
raw data cross multiple analysis centers
• Computational bottlenecks
• Imputation
• Principal components analysis O(MN2+N3)
run time
• Linear mixed model analysis O(MN2+N3)
run time, O(N2) memory
Concepts for scaling GWAS
Randomization/Approximation
• Randomly sample data to get an approximate
answer
• e.g. use randomized algorithms to approximate top
PCs
Heuristics/Approximation
• Devise rules that are mostly right and speed up your
algorithm
• e.g. during imputation only consider most relevant
reference haplotypes
Using summary statistics
• Work with “summary” information, like p-values and
effect sizes, rather than raw genotype data
Example: fastPCA
Traditional PCA is slow
G = Cov(XT) = XTX/n
Eigendecomposition of GRM
Run time: O(MN2+N3)
fastPCA computational tricks
“Power iteration”
•
•
If you multiply a random vector by a square matrix, it
projects the vector on to the matrix’s eigenvectors, scales
by the eigenvalues
After repeated multiplications, the projection along the first
eigenvector grows fastest
“blanczos method”
•
•
•
Estimate (approximately) more PCs than desired using
power iteration method
Project genotypes on this set of eigenvectors to reduce
dimensionality while preserving the top PCs
Do traditional PCA on the reduced matrix
Galinksy et al. 2016
Performance comparison of PCA methods
Traditional PCA:
O(MN2+N3)
“flashPCA”
O(MN2)
FastPCA
O(MN)
Galinksy et al. 2016
Example: TeraStructure
TeraStructure
TeraStructure
Example: Imputation with
Eagle
Imputation bottlenecks
• Imputation run time grows with the number of
samples and number of markers
• More samples = more states in our HMM = run
time explosions. Number of possible haplotypes
can grow even superlinearly with number of
samples.
• Some solutions:
• Prephase individuals before imputation
• “Cluster” haplotypes into a reduced state
space
Galinksy et al. 2016
Long-range phasing using shared IBD tracts
Long-range phasing (LRP):
• Look for long IBD tracks shared among related individuals.
• Phase inference at these regions is obvious
Advantages:
• Highly accurate phasing and imputation, even for rare
variants
Disadvantages:
• Requires cohort consisting of a large fraction of the
population (e.g. Iceland pedigrees)
• Requires phasing first to find IBD (slow)
Eagle: LRP+conventional phasing
Eagle approach combines:
1. Long range phasing (LRP): make initial phase calls using
long (>4cM) tracks of IBD sharing in related individuals
(back to ~12 generations)
• Uses a new fast IBD scanning approach: first look for
long stretches with agreement at homozygous sites,
then score regions for consistency with expectation
under IBD
2. Hidden Markov Model: Use an approximate HMM to refine
phase calls
• Aggressively prune state space to use up to 80 local
reference haplotypes
Galinksy et al. 2016
Eagle algorithm
Loh et al. 2016
Eagle performance
Loh et al. 2016
Eagle summary
Advantages:
• Far faster than existing tools on large (e.g. >100,000)
cohorts
• More memory efficient than other methods
• Comparable switch error rates
Disadvantages:
• Requires cohorts consisting of a significant portion of the
entire population for accurate IBD mapping
• Pure HMM-based methods may be more accurate in local
regions
• Recommendation: prephase with Eagle, then switch to
SHAPEIT2 in regions of the genome lacking IBD chunks
Loh et al. 2016
Eagle 2
• For smaller cohorts (e.g. <100,000), statistical phasing
approach of Eagle limited by amount of data available
• Eagle 2 uses reference-based phasing, relying on an
external reference haplotype panel
• Key improvements:
• A new data structure based on the positional Burrows
Wheeler Transform to store reference haplotypes
• Rapid search algorithm exploring only the most relevant
paths through the HMM
Loh et al. 2016
Eagle 2
Loh et al. 2016
Eagle 2
Loh et al. 2016
Working with summary
statistics
What are summary statistics
Individual level data
0 1 0 0 1 0 0 0 1 0 0 0 1 0 2
1 0 0 0 1 0 0 0 1 0 0 0 1 0 2
2 2 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 1 0 0 0 1 0 0 0 1 0 1
Summary statistics
• Greatly reduce data size
• Alleviate privacy concerns
Effect size (β)
Std. error SE(β)
P-value (p)
Meta-analysis: combining GWAS studies
Diabetes GWAS #1
UCSD
Diabetes GWAS #2
Broad Institute
Diabetes GWAS #3
Sanger
5,000 cases
7,000 controls
20,000 cases
40,000 controls
2,000 cases
4,000 controls
Mega-analysis
Re-analyze individual level data
0 1 0 0 1 0 0 0 1 0 0 0 1 0 2
0 2 0 1 1 0 2 0 1 0 1 0 1 0 2
Meta-analysis
Jointly analyze summary statistics
β1,UCSD, SE(β1,UCSD), p1,UCSD
β1,Broad, SE(β1,Broad), p1,Broad
β1,Sanger, SE(β1,Sanger), p1,Sanger
β2,UCSD, SE(β2,UCSD), p2,UCSD
1 1 0 1 1 1 2 0 0 0 0 0 1 1 1
β2,Broad, SE(β2,Broad), p2,Broad
β2,Sanger, SE(β2,Sanger), p2,Sanger
27,000 cases
51,000 controls
27,000 cases
51,000 controls
Meta-analysis: combining GWAS studies
β1,UCSD, SE(β1,UCSD), p1,UCSD
β1,Broad, SE(β1,Broad), p1,Broad
β1,Sanger, SE(β1,Sanger), p1,Sanger
β2,UCSD, SE(β2,UCSD), p2,UCSD
β2,Broad, SE(β2,Broad), p2,Broad
β2,Sanger, SE(β2,Sanger), p2,Sanger
…
βn,UCSD, SE(βn,UCSD), pn,UCSD
βn,Broad, SE(βn,Broad), pn,Broad
βn,Sanger, SE(βn,Sanger), pn,Sanger
Fisher’s Method
•
•
•
•
Null hypothesis: all effects are 0
Alternative hypothesis: at least one effect !=
Based on average of –log(p) across studies
Doesn’t take into account direction of effect
Z-score based methods
•
•
•
Zi=βi/SE(βi)
Take (weighted) average of Z scores
Takes into account direction of effect
Fixed-effects meta-analysis
• Assume same effect size in each study
• Inverse-variance weighting: each study is
weighted by inverse of squared standard
error
Imputation from summary statistics
Traditional imputation requires individual-level data and is computationally
expensive:
AACACAAGCTAGCTACCTACGTAGCTACAT
AACACAAGCTAGCTACCTACGTAGGTACAT
Reference haplotype
panel (e.g. 1000
Genomes)
AACACTAGCTAGCTACCTATGTAGGTACAT
AACACTAGCAAGCTACCTACGTAGGTACAT
AACACTAGCAAGCTACCTACGTAGGTACGT
AACACTAGC?AGCTACCTA?GTAGGTAC?T
AACACAAGC?AGCTACCTA?GTAGGTAC?T
Your data genotyped on
SNP chip
AACACTAGC?AGCTACCTA?GTAGGTAC?T
AACACTAGC?AGCTACCTA?GTAGGTAC?T
AACACAAGC?AGCTACCTA?GTAGCTAC?T
Imputation from summary statistics
• Linkage disequilibrium
induces correlation in effect
sizes of nearby SNPs
• Model “zscores” as
multivariate normal, with
covariance defined by LD
(r2)
• Captures ~80% of
information compared to
using individual-level data
• Which reference panel to
use?
Rare variant association tests
• Association tests for individual rare variants likely to be
underpowered
• On the other hand, mutations under strong negative
selection are likely to be rare
• Burden test: aggregate rare variants by some
category, e.g. genes. Assume each SNP has same
direction of effect
• Tburden=wTZ, where w give weights of each SNP and
Z gives z-scores of each SNP. Meta-analysis of
burden tests using summary statistics via inversevariance weighting (i.e. upweight statistics with the
lowest variance)
• Over-dispersion test: assumes rare variants in the
same candidate gene can affect a complex trait in
either direction
Fine-mapping using summary statistics
Fine-mapping: aims to identify the causal variant(s)
driving a GWAS signal
Method 1: Prioritize variants based on p-value
Method 2: Compute posterior probability of causality
based on likelihood to observe given data conditioned
on a given SNP being causal.
Method 3: Use method 2, but weight SNPs based on
functional data (e.g. chromatin, expression, other
annotations)
PAINTOR: Fine-mapping using summary statistics
Kichaev et al. 2014
Partitioning heritability using LD-score regression
See Bulik-Sullivan et al. Nature
Genetics 2015 for more on LDscore regression
Much faster than LMMbased variance
partitioning, doesn’t
require individual-level
Finucane et al. 2015
Cross-trait analyses
See Bulik-Sullivan et al. Nature
Genetics 2015 for more on LD-score
regression
Bulik-Sullivan et al. 2015
PrediXan
Summary
• Using a reference transcriptome panel (e.g.
GTEx), build a model to predict genetically
regulated component of gene expression
(GReX)
• Using learned effect sizes, impute gene
expression values into GWAS cohort, for which
expression data isn’t usually available.
• Test for association between gene expression
and disease
Why this paper?
• Example of utility of summary statistic data
• Example of successfully integrating data from
multiple studies
• Example of a way to gain biological insight from
GWAS without necessarily having to collect a
lot more data
Figure 1
Figure 2
Advantages over vanilla GWAS
• Directly testing functional units (genes vs.
SNPs)
• Greatly reduces the multiple hypothesis testing
burden
• Tissue relevance: can impute expression for
different tissue types, measure which one most
correlated with the trait
• Direction of effect: not only which gene is
involved, but does under/over-expression lead
to disease?
• Doesn’t require transcriptome data from your
cohort
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7