ntr cis ntr trans · 0.0 0.2 0.4 0.6 0.8 1.0 0 5 1 0 1 5 2 0 metsim cis h2g d e n s i t y 12598 con...

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Supplementary Figure 1

Distribution of cis and trans SNP-heritability estimates cross three cohorts.

Cis (left) and trans (right) density plots shown for three cohorts investigated. Black line corresponds to all converged genes; red line corresponds to genes with cis-SNP-heritability >> 0 by LRT. Dotted lines show respective means.

Nature Genetics: doi:10.1038/ng.3506


Scaled Venn Diagram of overlap in genes with significant cis SNP-heritability across the METSIM, NTR and YFS data.


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Cross-validation prediction accuracy across three expression cohorts.

Using 10-fold cross-validation, prediction R^2 (divided by corresponding cis-h2g) was compuated in the METSIM, YFS and NTR (Wright et al.) cohorts by three methods: best eQTL in the gene, BLUP and BSLMM. Left panels show accuracy as a functino of cis h2g; right panels show accuracy as a function of LRT P-value for non-zero cis-h2g.


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Histogram of BSLMM prediction gains in three cohorts.

For each of the METSIM, YFS and NTR (Wright et al.), the difference between BSLMM R^2 and eQTL R^2 (computed by cross-validation) is plotted as histogram.


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Correlation of summary-based TWAS and individual-level association Z scores.

Genes with significant cis-h2g in YFS were directly tested for association with height (Z-score on y-axis) and plotted against corresponding Z-score from TWAS using only height summary association data (x-axis). Left panel shows test of height against total expression on the y-axis (\rho = 0.415); right panel shows test of height against BLUP genetic component of expression on the y-axis (\rho = 0.998). Right panel demonstrates that summary-based TWAS is essentially identical to individual-level TWAS when using in-sample LD.


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GWAS summary simulations over diverse disease architectures.

Power to detect a genome-wide significant association is shown for three methods (GWAS; eGWAS computed from best eQTL, and TWAS computed from summary statistics) over different disease architectures. Colors represent number of causal variants in each simulated gene. Left/right panels correspond to simulations with causal variants hidden/shown. Top/bottom panels correspond to simulations with each gene explaining 0.001/0.0005 of trait variance. x-axis shows simulations at increasing GWAS sample sizes (with expression panel fixed at 1,000 samples).


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TWAS power with expression and genetic component of expression.

Power to detect a genome-wide significant association is shown for summary-statistic TWAS using observed expression as well BLUP genetic value of expression. Left/right panels correspond to simulations with causal variants hidden/shown. Top/bottom panels correspond to simulations with each gene explaining 0.001/0.0005 of trait variance. x-axis shows simulations at increasing GWAS sample sizes (with expression panel fixed at 1,000 samples).


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GWAS summary simulations with heritable expression independent of phenotype.

Expression and trait were simulated as having the same causal variants but independent effect-sizes and power evaluated. For a single causal variant, this model is statistically identical to a true causal model. Colors indicate the method used (see Supplementary Fig. 4). Left/right panels correspond to simulations with causal variants hidden/shown. Top/bottom panels correspond to simulations with each gene explaining 0.001/0.0005 of trait variance. x-axis shows simulations at increasing GWAS sample sizes (with expression panel fixed at 1,000 samples).


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TWAS/eGWAS power with increased sample reference size.

: Results from simulations matching Supplementary Figure 4 (top left) model with variable reference panel size from 100-2,000 individuals. Phenotype generated under to the untyped, high effect variant model where expression explains 0.001 of trait variance. TWAS matches or outperforms eGWAS at 1,000 samples, with little additional power gained subsequently. GWAS power is unaffected by expression reference panel and not shown (identical to Supplementary Fig. 4).


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TWAS/COLOC power under causal model.

Single locus power comparison for causal variant hidden (left) and typed (right), high effect model where expression explains 0.001 of trait variance. Unlike other power simulations, results are not adjusted for genome/transcriptome-wide multiple testing. TWAS and COLOC significance thresholds set in a null expression simulation (with realistic heritable GWAS, see Methods) to achieve 5% FDR.


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Results from simulations matching Supplementary Figure 4 re-analyzed using HAPGEN2 to generate all GWAS sub-study individuals. After holding out 1,000 samples for the expression reference, SHAPEIT2 was used to phase 5,000 individuals in a cis-block for each of 100 random genes, yielding 100 random reference panels. For each reference panel we used HAPGEN to generate 60 sub-studies of 5,000 individuals using its haplotype-copying model (under neutrality). Phenotypes were generated with the same causal variants and effects for each sub-study, and the corresponding GWAS summary statistics were computed by meta-analyzing across these batches. Default parameters for SHAPEIT and HAPGEN were always used, and the appropriate genetic map was downloaded from the SHAPEIT2 website.


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TWAS/COLOC power under independent effects model.

Single locus power comparison for model where expression and trait have the same causal variants with independent effects. GWAS generated from high effect model where expression explains 0.001 of trait variance and causal variants are hidden (left) or typed (right). Unlike other power simulations, results are not adjusted for genome/transcriptome-wide multiple testing. TWAS and COLOC significance thresholds set in a null expression simulation (with realistic heritable GWAS, see Methods) to achieve 5% FDR. Single causal variant scenario is statistically identical to the causal expression model and has equivalent power.



LD Score regression (LDSC) provides a noisier local estimate than TWAS for quantifying correlation between complex trait and expression.

Left panel shows in-sample and summary-based estimate of association between height and cis genetic component of expression (correlation = 0.998). Right panel shows in-sample estimate of correlation between height and cis genetic component of expression (y-axis) and LDSC estimate of genetic correlation (x-axis); correlation between the two statistics was 0.7.


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Distribution of TWAS statistics for height as a function of expression panel size in the merged YFS + NTR (blood) cohorts.

To evaluate the effect of expression panel size on power in real data, we re-ran the TWAS for height using the merged YFS+NTR cohort with down-sampling. The histogram of TWAS Z^2 scores is shown for training from randomly sampled half of the cohort (1,200 samples, top) and the full cohort (2,400 samples, bottom). The mean TWAS Z^2 was 5.8 in the combined cohort and 5.6 in the down-sampled cohort, with the overall distribution of Z-scores largely consistent across the two studies. Importantly, there were four genes that were not previously significant in the YFS/NTR cohorts individually and were significant in the combined study, but all four had been detected by the omnibus test. This is consistent with our simulations showing that TWAS power is saturated beyond 1,000 expression samples. Only 652 genes that were significantly cis-heritable in both YFS and NTR were analyzed.


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Each line shows the histogram of number of GWAS risk loci overlapping a gene as a function of distance from the index SNP. Black line shows the closest gene. Red denotes genes with significant cis SNP heritability. Green shows the TWAS significant gene.


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Joint distribution of summary-level and individual-level TWAS Z-scores shown across all significant genes for four traits in the METSIM GWAS cohort.


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Evidence for allelic heterogeneity of expression

Novel TWAS genes were evaluated for allelic heterogeneity of expression using three different tests (left SKAT gene-based test; middle conditional analysis; right LASSO model selection). For each test, genes were categorized into those not reaching TWAS significance in a cohort, reaching TWAS significance but failing the permutation test, and reaching TWAS significance and passing the permutation test. The % of genes considered significant (SKAT/conditional) or the average number of associated variants selected (LASSO) are reported by each bar.For each of the 69 genes x 3 expression cohorts we ran the SKAT gene-based test with expression as outcome to look for evidence of allelic heterogeneity. As with TWAS, all SNPs in the 1-Mb locus around the gene were used, and SKAT was run in common+rare mode (Ionita-Laza et al. Am. J. Hum. Genet. 2013), which was most appropriate for array SNP data. Default parameters were used throughout. Genes were considered significant if they surpassed the multiple-testing burden of 69 genes. The conditional test was evaluated by including the top SNP as a covariate and testing for any secondary eQTLs at the locus that were significant after Bonferroni correction for the number of SNPs at the locus. The LASSO was run on all SNPs in the locus, penalized by the cis-h2g of expression.


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MuTHER expression data was used to train TWAS predictors using LD from 600 METSIM individuals (x-axis) or 6,000 METSIM individuals (y-axis). Joint distribution of TWAS Z-scores and trend are shown.


Supplementary Note

METSIM and YFS data. In this study, we included 11,484 participants from two Finnish population cohorts,

the METabolic Syndrome in Men (METSIM, n = 10,197)52,53 and the Young Finns Study (YFS, n = 1,414)22,23.

Both studies were approved by the local ethics committees, and all participants gave an informed consent. The

METSIM participants were all male with a median age of 57 years (range: 45-74 years) recruited at the

University of Eastern Finland and Kuopio University Hospital, Kuopio, Finland. Whole blood was collected

from all individuals for genotyping and biochemical measurements. Additionally, 1,400 randomly selected

individuals from the 10,197 METSIM participants underwent a subcutaneous abdominal adipose biopsy of

which 600 RNA samples were analyzed using RNA-seq. Traits BMI, TG, WHR, and INS were inverse rank

transformed and adjusted for age and age-square. INS was additionally adjusted for T1D and T2D. There was

little correlation between genome-wide SNP principal components and phenotype. A strictly unrelated subset of

5,501 individuals was computed by removing one of any individual with off-diagonal GRM entries >0.05 (with

priority given to individuals that had expression measured). This procedure guaranteed no relatedness between

the training set and the samples without expression. YFS participants were originally recruited from five regions

in Finland: Helsinki, Kuopio, Oulu, Tampere, and Turku. We collected whole blood into PAXgene tubes from

all individuals for genotyping, RNA microarray assay, and biochemical measurements. Samples from 1,414

individuals (638 men with a median age of 43 years and 776 women with a median age of 43) with gene

expression, phenotype, and genotype data available were included in the blood expression analysis. Traits

height, BMI, TG, TC, HDL and LDL were inverse rank transformed and adjusted for age, age-square and sex.

TC was also adjusted for Statin intake. The biochemical lipid, glucose, and other clinical and metabolic

measurements of METSIM and YFS were performed as described previously22,52,54.

METSIM RNA-Seq data. We prepared and sequenced mRNA samples isolated from subcutaneous adipose

tissue using Illumina TrueSeq RNA Prep Kit and the Illumina Hiseq 2000 platform to generate 50-bp long

paired-end reads. Reads were aligned to the Human reference genome, HG19, using the aligner STAR55,

allowing up to 4 mismatches for each read-pair. Transcript quantification was calculated as reads per kilobase

per million (RPKM) using Flux Capacitor48 based on transcript and gene definitions from the Gencode ver.18

annotation. The gene quantification is the sum of all transcripts of a gene. We applied Anscombe

transformation to the RPKM values for variance stabilization followed by PEER56 correction to remove

technical biases. The PEER-corrected gene quantification was then inverse rank transformed to a normal

distribution to eliminate effect from outliers.

Nature Genetics doi:10.1038/ng.3506

YFS and NTR microarray data. We measured mRNA expression in whole blood of the YFS cohort using the

Illumina HumanHT-12 version 4 Expression BeadChip. Probe density data were exported from GenomeStudio

and analyzed in R using Bioconductor packages. We normalized probe density data using control probes with

the neqc function from the limma package implemented in R57. To account for technical artifacts, we first log2

transformed the normalized density and adjusted for 20 potential confounding factors using PEER56. The final

adjusted probe density was inverse rank transformed to approximate normality in order to minimize the effect of

outliers. Probes which contained a SNP in the 1000 Genomes were removed. Data from the NTR was processed

as described in the original paper24, followed by removal of any individuals with GRM values > 0.05. For genes

with multiple probes, total gene expression was measured as the sum across all probes (including all transcripts)

followed by standardization to unit variance (rank normalization had no substantial effect). Probes which

contained a SNP in the 1000 Genomes were removed. Principal components and batch were included as

covariates in all analyses. We unified the YFS and NTR blood expression cohorts to perform cross-cohort

analyses. Because the cohorts were genotyped on different arrays, we imputed the YFS to the 1000 Genomes

and then retained only those markers that were genotyped in NTR and genotyped or imputed with high quality

in YFS. The following exclusion criteria were used for imputed SNPs: HWE P <1e-5; MAF <1%; INFO < 0.9.

Additionally, SNPs that were strand inconsistent across cohorts or had A-T/C-G alleles where strand could not

be determined were also excluded. After all exclusions, the final combined cohort contained 492,420 SNPs. We

made no adjustment to the expression after merging.

Prediction accuracy using cross-validations. On average, the cis-eQTL yielded prediction R2 = 0.08,

corresponding to half of the accuracy of the best possible linear prediction (as inferred from average ℎ!,!"#! =

0.16 for these genes). Using all SNPs in the locus, the BLUP attained an R2 = 0.09; and the BSLMM attained an

R2 = 0.10 (Fig. 2 and Supplementary Fig. 1). The pattern was roughly the same for randomly selected genes

(Supplementary Fig. 18). This empirical measure of accuracy deviates from theory in two ways: assuming a

small number of independent SNPs at each locus, we would expect normalized BLUP accuracy (R2/ℎ!,!"#! ) to be

near 1.0 (see Equation 1 of ref. 21) but it is only 0.55 on average; and for a given ℎ!,!"#! accuracy is not directly

proportional to training sample size (e.g. the highest accuracy is observed in the smallest METSIM cohort,

Supplementary Fig. 1). This suggests that data quality and population homogeneity (which differ between

these cohorts) play an important role in empirical prediction accuracy.

We also evaluated cross-cohort prediction in the combined YFS and NTR cohort (see above). We analyzed the

same set of significantly heritable genes that were used for cross-validation, retaining only those that passed QC

and converged in both cohorts. As observed previously, the same genes yielded different ℎ!,!"#! in the two


cohorts, with genes in YFS significantly more heritable on average than the same genes in NTR

(Supplementary Table 3). Surprisingly, we observed increased prediction accuracy across- relative to within-

cohort when predicting from NTR to YFS; and decreased prediction accuracy from YFS into NTR. This would

be consistent with YFS having higher heritability, but NTR having better predictive accuracy due to larger

sample size. The increased accuracy is in contrast to the findings of Gamazon et al.16, where a substantial drop

in prediction r2 was observed when performing cross-cohort prediction with blood expression (using different

data and prediction models). However, after accounting for cis-heritability in the test cohort, our cross-cohort

standardized accuracy (i.e. r2/ ℎ!,!"#! ) was broadly consistent with in-cohort cross-validation accuracy

(Supplementary Table 3). The BSLMM was again the most accurate predictor, with an average cross-cohort

r2/ℎ!,!"#! of 72%, outperforming the best eQTL by an average 1.17x. The differences in heritability and

prediction accuracy across cohorts further underscore the heterogeneity in expression across studies.

Individual-level analysis of METSIM GWAS. We imputed the significantly heritable genes into the METSIM

GWAS cohort of 5,500 unrelated individuals with individual-level genotypes (and unmeasured expression). We

then tested the imputed expression for obesity-related traits: body mass index (BMI); triglycerides (TG); waist-

hip-ratio (WHR); and fasting insulin levels (INS). Overall, the evaluated traits exhibited high phenotypic and

genetic correlation as well as highly significant genome-wide ℎ!! ranging from 23-36% (Supplementary Table

15) consistent with common variants having a major contribution to disease risk7. Association was assessed

using standard regression as well as a mixed-model that accounted for relatedness and phenotypic correlation31

with similar results. The effective number of tests for each trait was estimated by permuting the phenotypes

10,000 times and, for each permutation, re-running the association analysis on all predicted genes. For each trait

Pperm, the P-value in the lowest 0.05 of the distribution, was computed and the effective number of tests was

0.05/Pperm, reported in Supplementary Table 16. All phenotypes were shuffled together, so any phenotypic

correlation was preserved. The effective number of tests corresponded to 88-95% of the total number of genes,

indicating a small amount of statistical redundancy.

After accounting for multiple testing in each trait, six loci were significant (Supplementary Table 17), five of

which were confirmed by genome-wide significant SNP associations in this cohort or in larger studies. The best

cis-eQTL in each locus was less significantly associated than the imputed expression in 5/6 loci, further

underscoring the increased power of the TWAS approach. The TWAS identified one novel gene that had not

been previously observed in this or published GWAS: ENO3 associated with TG and fasting insulin (INS). We

investigated this gene further in the METSIM samples with both phenotypes and expression, and found a

nominal association between the genetic value of expression and INS at P = 0.02, explaining 1.8% of trait

variance (with phenotypes which had not been used to identify the initial association). This association was


primarily driven by the top eQTL (rs9914087, P = 8 × 10-09 for eQTL, P = 0.03 for association to INS). Though

validation in a larger cohort is needed, this initial result supports a link between ENO3 expression and fasting

insulin in this population.

Gene permutation test. The standard TWAS Z-score is a test against the null of no SNP-trait association; that

is ZTWAS = !"

!!!,!!! is well calibrated (i.e. has a 0 mean and unit variance) only under the null model of

𝑍~ 𝑁(0,𝛴!,!). In the alternate model where Z is drawn from a non-zero mean distribution64,65, ZTWAS has a

distribution that depends both on Z as well as the weights W. To quantify the impact of the weights on ZTWAS

regardless of whether Z is null or non-null we conduct permutations conditional on the observed Z vector. For

each gene, the expression labels were randomly shuffled and the summary-based TWAS analysis trained on the

resulting expression to compute a permuted new null for ZTWAS. Testing against this permuted null distribution

is equivalent to testing for an expression-trait association (or genetic correlation between expression and trait,

see below) conditional on the observed GWAS statistics at the locus (which may not be drawn from the null of

no association). We validated this test empirically by focusing on known loci in the height GWAS and the YFS

cohort with height measured independently (see main text). Using YFS expression as training, we used the

TWAS approach in the independent height GWAS data to identify 181 significant genes that overlapped

previously known height loci, of which 33 passed the permutation test. These 33 genes had evidence of a

significant contribution to trait beyond the SNP-trait effects at the locus, indicative of allelic heterogeneity at

these loci. As before, we constructed a risk score using the genetic value of these 33 genes weighted by their Z-

score in the TWAS; and a standard genetic risk score66 using the best GWAS SNP in each locus. The two scores

were evaluated for association to the true height phenotype in the YFS, yielding an R2 of 0.008 (best SNP) and

0.016 (TWAS gene), respectively (Supplementary Table 3). In a joint regression with both scores, only the

TWAS score was significant (P = 2 x 10-3). This confirms that TWAS predictions that remain significant after

permutation are more strongly associated with phenotype than the single best SNP at the locus.

Relationship to genetic covariance/correlation. To evaluate the relationship between TWAS and genetic

correlation empirically, we compared to the recently proposed method of cross-trait LD-score regression

(LDSC) that estimates genome-wide genetic correlation between traits37. Unfortunately, LDSC is not intended

for local analyses due to model assumptions on polygenicity and use of block-jackknife across loci for

estimating standard errors. We evaluated LDSC and TWAS using expression and phenotype (height) from the

YFS cohort, which offers the opportunity to compare performance from individual and summary data. We used

the results from individual data as the “gold standard” and measured how accurate the two methods are in

recovering signal when only given summary association data. Summary statistics for association to height were

computed genome-wide in the YFS using standard linear regression with 10 principal components as covariates.


Likewise, for each gene, summary eQTL data in the YFS was computed from all cis SNPs by standard linear

regression. The effect-sizes (signed betas) from height/eQTL were then analyzed one gene at a time by LDSC

using default parameters (with convergence achieved for 1,517 out of 3,836 genes). We compared the LDSC

estimate of genetic correlation to the actual correlation between height and the cis genetic value of expression

(estimated by BLUP). These values are expected to be equivalent up to scaling by the local height heritability

(we attempted to estimate the true genetic correlation using bivariate REML but could not achieve convergence

for 90% of genes at this low sample size). We find that the LDSC estimate of genetic correlation from summary

data is highly correlated with the in-sample correlation (correlation = 0.7, Supplementary Fig. 16), but the

correlation is much noisier than that of the TWAS estimates of significance (correlation > 0.99, Supplementary

Fig. 16). This suggests that TWAS will attain more power in locally relating expression to complex traits.

Power analysis of summary-based method. Our main simulation procedure is equivalent to assuming that LD

and MAF do not change across sub-studies, and we believe these assumptions are reasonable for large studies of

a homogenous population where individual-level data is not used. To verify this assumption, we re-ran the main

set of simulations using the HAPGEN2 algorithm60 to simulate new genotypes for each sub-study from a phased

reference panel of the 5,000 held-out samples. This method models population demography and uses a

haplotype-copying model to generate new individuals based on a phased reference panel. Under this complex

model, none of the results were substantially different from the previous simulations (Supplementary Fig. 12),

and so we used the phenotype regeneration procedure due to its computational efficiency.

Simulations of same SNP impacting independently trait and expression. Lastly, we evaluated the

confounded model where expression and trait had the same causal variants but independent effect-sizes (Fig.

2g). The case of a single causal variant with independent effects is statistically indistinguishable from a true

causal model. Consider the following generative model for expression (E) where x is the causal variant, β is the

effect, and ε is the scaled environmental effect:

𝐸 = 𝑥𝛽 + 𝜀

for two possible models for phenotype (Y):

Independent: 𝑌 = 𝑥𝛼 + 𝜀

Causal: 𝑌 = 𝐸𝛼! + 𝜀 = 𝑥𝛽𝛼! + 𝜀

the models will be identical if 𝛼 = 𝛽𝛼!and therefore cannot be distinguished by a statistical test of 𝛼! being

non-zero without direct mediation analysis. Similar intuition applies when multiple causal variants or tags are

present, where power is expected to decrease with the r2 between the true and observed effect61. Consistent with

theory, our simulations show that the two models are equally likely to be detected by all methods

(Supplementary Fig. 9). In the case of multiple causal variants, the detection rate of the independent scenario

is much lower and roughly equal for TWAS or eGWAS (Supplementary Fig. 9).


Prediction using summary eQTL data as reference. For imputation using an external cis-eQTL study,

𝛴!,!estimated from the available cis-eQTL association statistics instead of directly in the training data. For the

MuTHER SNPs, this was estimated by computing the corresponding cis-eQTL T-statistic; solving for

R2=T2/(T2+N-2) where N was the study size; and converting back to signed r using the effect-size direction.

The LD matrix was estimated from the METSIM as before. In the case where the LD matrix matches that of the

eQTL study, this approach is mathematically identical to training on individual-level data. Otherwise,

differences in LD will introduce noise which is expected to be unbiased assuming no relationship between these

differences and eQTL effect-size. These out-of-sample expression effect-sizes from the MuTHER study

allowed us to evaluate the impact of the LD-reference panel size on accuracy. We compared predictors trained

using an LD-reference panel from the ~600 METSIM expression samples to those trained on the 6,000

unrelated METSIM GWAS individuals and found highly significant consistency (ρ = 0.97; Supplementary

Fig. 19) with slight Z-score inflation in the smaller panel.


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