expression measurements. For the associated genes, it remains possible that the effect is actually mediated by phenotype (i.e. SNP → phenotype → cis-expression, Figure 2F). We attempted to quantify this in the YFS data by conditioning the heritability analyses on all the evaluated phenotypes (height, BMI, and lipids) but observed no significant change at individual genes or in the mean cis-hg2. These results suggest that confounding from phenotype does not substantially affect the tested cis expression, though at the current sample size we cannot completely rule out such confounders for individual genes. An alternative confounder arises from independent effects on phenotype and expression at the same SNP/tag (Figure 2G, Methods). Such instances could be indistinguishable from the desired causal model (Methods) without analyzing individual-level data, though we believe they are still biologically interesting cases of co-localization. Both types of confounding could potentially be quantified by training the SNP-expression relationships in control individuals where phenotype is fixed, or by interrogating the gene experimentally. Lastly, the summary-based TWAS cannot account for rare variants that are poorly captured by the LD reference panel, or optimally capture non-linear relationships between SNPs and expression. Additional sources of information could potentially be incorporated to improve the
