One limitation is that the significance of the SMR statistic is the lower of the top eQTL association (genotype to expression) or the GWAS association (genotype to phenotype) as shown in Fig. 5e, f. Given the much larger sample sizes of GWAS studies, for most genes, the combined significance will be determined by the eQTL association. The combined statistic forces us to apply multiple testing correction for all genes, even those that are distant to GWAS associated loci, which is unnecessarily conservative. Keep in mind that currently both SMR and PrediXcan only use cis associations. An example may clarify this further. Let us suppose that for a given phenotype there is only one causal SNP and that the GWAS yielded a highly significant p-value, say 10−50. Let us also suppose that there is only one gene (gene A) in the vicinity (we are only using cis predictors) associated with the causal SNP with p = 10−5. SMR would compute the p-values of all genes and yield a p-value ≈ 10−5 for gene A (the less significant p-value). However, after multiple
