We provide an index that quantifies the extent to which an observed vector of univariate regression effects of a given SNP on each of the phenotypes can be explained by a common pathway model that assumes that the effects are entirely mediated by the common genetic factor(s). In other words, the index enables the identification of loci that do and do not plausibly operate on the individual phenotypes exclusively by way of their associations with the common factor(s). Because of its intuitive and mathematical similarity to the meta-analytic Q-statistic used in standard meta-analyses to index heterogeneity of effect sizes16 we label this heterogeneity statistic, QSNP. QSNP is a χ2-distributed test statistic with larger values indexing a violation of the null hypothesis that the SNP acts entirely through the common factor(s).
