Power and instrument strength requirements for Mendelian randomization studies using multiple genetic variants

Mendelian Randomization (MR) studies assess the causality of an exposure-disease association using genetic determinants [i.e. instrumental variables (IVs)] of the exposure. Power and IV strength requirements for MR studies using multiple genetic variants have not been explored.

We simulated cohort data sets consisting of a normally distributed disease trait, a normally distributed exposure, which affects this trait and a biallelic genetic variant that affects the exposure. We estimated power to detect an effect of exposure on disease for varying allele frequencies, effect sizes and samples sizes (using two-stage least squares regression on 10,000 data sets-Stage 1 is a regression of exposure on the variant. Stage 2 is a regression of disease on the fitted exposure). Similar analyses were conducted using multiple genetic variants (5, 10, 20) as independent or combined IVs. We assessed IV strength using the first-stage F statistic.