tagged by an individual SNP (Figure 5, Supplementary Figures 6–11). The greatest power gains were observed in the case of multiple causal variants: 92% power for TWAS compared to 18% and 25% for GWAS and eGWAS. This scenario would correspond to expression caused by allelic heterogeneity9,34,35, or “apparent” heterogeneity at common variants (due to tagging of unobserved causal variant)36. TWAS was comparable to other approaches when a single causal variant was directly typed, in which case combining the effects of neighboring SNPs does not add signal. Under the null where expression was completely independent of phenotype (with either being heritable, Figure 2A–D), the TWAS false positive rate was well controlled (Supplementary Table 4). As expected, all methods were confounded in the case where the same causal variants had independent effects on trait and expression (Figure 2F–G; Supplementary Figures S8, 12).
