In a one‐sample setting, the exposure and outcome data are collected on the same individuals, in which case εXj and εYj are correlated. If exposure and outcome data are collected on different sets of individuals (known as two‐sample Mendelian randomization (Pierce and Burgess, 2013)), then these error terms are independent. We assume throughout this manuscript that all genetic variants are uncorrelated (i.e., not in linkage disequilibrium), so that the information provided by each genetic variant is independent. Extensions to allow for correlated variants in a straightforward application of Mendelian randomization have been developed (Burgess et al., 2013), but the situation of uncorrelated variants is usual in applied practice.
