Fig. 1.

Directed acyclic graphs illustrating scenarios when an unexpected genetic instrumental variable-non-exposure trait association could be observed. Z: genetic instrumental variable; X: exposure of interest; Y: outcome of interest; U: unmeasured confounders; W: non-exposure traits; C: confounding factors, e.g. population stratification, cryptic relatedness and assortative mating; S, selection. For simplicity, we use single nodes even when there may be multiple variables, and these scenarios do not consider time-varying exposures and critical/sensitive-period exposure effects [2, 17]. Scenarios illustrated by 1.1, 1.2, 3.1–3.3, 5.1–5.4 would be expected to bias the MR estimate of X–Y effect; 1.3, 1.4, 2.1, 2.2 and 3.4 would not; 5.2 and 5.4 would be unbiased under the null