In order to formally test for potential violations of Mendelian randomization assumptions, a number of sensitivity analyses were undertaken. I2 statistics were calculated to estimate heterogeneity. We also ran a random-effects model to account for heterogeneity, and performed MR Egger regression34. This latter method relaxes the assumption made in MR that the effects of genetic variants on the outcome are entirely mediated via the exposure. This is achieved by allowing an intercept term in the weighted regression of the SNP-outcome coefficients on the SNP-exposure coefficients. The intercept parameter represents the average pleiotropic effect of a SNP on the outcome (the direct effect on the outcome not via the exposure of interest). This intercept value can therefore provide a test of directional pleiotropy; if the intercept term is close to the null, then bias in the causal estimate due to pleiotropy is less likely. The beta coefficient from this regression provides a consistent estimate of the causal effect under the assumption that the pleiotropic effects on SNPs on the outcome are uncorrelated with the associations of the SNPs with the exposure.
