Table 1. Summary of polygenic methods used to test contribution of eQTLs to trait variation.

Method*	Goal	Description and assumptions	Limitations	eQTL set used	GWAS data types
eQTLEnrich, Rank and permutation-based GWAS-eQTL enrichment method	Tests whether eQTLs from a given tissue are significantly enriched for trait associations more than would be expected by chance and estimates adjusted fold-enrichment.	Estimates the probability of observing a given fold-enrichment of top ranked trait associations (e.g. GWAS p<0.05) amongst eQTLs in a given tissue, relative to the fold-enrichment of nonsignificant eVariants (adjusted fold-enrichment), using a null distribution derived from multiple randomly sampled variants matched on MAF, distance to TSS, and local LD. Per GWAS tested, tissues are ranked based on their adjusted fold-enrichment.	Adjusted fold-enrichment is correlated with GWAS sample size.	Best eQTL per eGene	Variant association p-values
TORUS, Bayesian and MLE approach for quantifying GWAS-eQTL enrichment	Estimates an enrichment parameter that represents the relationship between the log-odds ratio of the trait associations being causal and their eQTL effect size.	Estimates the relationship between the (absolute value of) single variant eQTL z-scores and the corresponding log odds of a variant being causally associated with the complex trait of interest. A confident positive estimate of the log odds ratio indicates the increased odds of a variant being causally associated with the trait with stronger effect of eQTL association. Uses z-scores from all gene-variant pairs for a given tissue, and assumes a single causal trait association per LD block (following the assumption of fgwas).	Enrichment parameter estimation (esp. standard error) is correlated with tissue sample size of eQTLs	All variant-gene pairs tested	Variant association test statistics
π1 method	Estimates the fraction of eQTLs in a given tissue that are likely to be associated with a given complex trait.	Estimates the fraction of true trait associations amongst eQTLs in a given tissue, using the π1 statistic, which assumes a standard uniform distribution for the null distribution and independence between variants.	Results not robust to small variant sets.	Best eQTL per eGene	Variant association p-values
Summary statistics-based heritability estimation	Estimates the relative contribution of eQTLs in aggregate to the heritability of complex traits, using LD Score regression applied to publicly available GWAS summary statistics.	Estimates the per-variant effect of the trait association by an annotated eQTL vs. an unannotated variant. A larger difference indicates a higher degree of enrichment of contribution of eQTLs to trait associations.	Works optimally when the per-variant variance is not correlated with the LD score.	All significant variant-gene pairs	Variant association test statistics
Mixed-effects-model heritability estimation	Estimates proportion of complex trait variance explained by eQTL variants in aggregate using GWAS genotype data.	Estimates the heritability attributable to eQTL variants using the Restricted Maximum Likelihood approach. The approach assumes a normal distribution of trait effect sizes for the eQTL variants and uses a genetic similarity matrix generated from the eQTL variants.	Requires genotype data.	All significant variant-gene pairs	Individual genotype data

^*See URLs for links to methods’ software.