  Genome-wide association studies (GWAS) have emerged as a rich source of
genetic clues into disease biology, and they have revealed strong genetic
correlations among many diseases and traits. Some of these genetic correlations
may reflect causal relationships. We developed a method to quantify causal
relationships between genetically correlated traits using GWAS summary
association statistics. In particular, our method quantifies what part of the
genetic component of trait 1 is also causal for trait 2 using mixed fourth
moments $E(\alpha_1^2\alpha_1\alpha_2)$ and $E(\alpha_2^2\alpha_1\alpha_2)$ of
the bivariate effect size distribution. If trait 1 is causal for trait 2, then
SNPs affecting trait 1 (large $\alpha_1^2$) will have correlated effects on
trait 2 (large $\alpha_1\alpha_2$), but not vice versa. We validated this
approach in extensive simulations. Across 52 traits (average $N=331$k), we
identified 30 putative genetically causal relationships, many novel, including
an effect of LDL cholesterol on decreased bone mineral density. More broadly,
we demonstrate that it is possible to distinguish between genetic correlation
and causation using genetic association data.
