Fig. 1From: A data-adaptive method for investigating effect heterogeneity with high-dimensional covariates in Mendelian randomizationDiagram illustrating the rank preserving assumption for a dichotomous instrumental variable Z with counterfactual covariate distributions \(\varvec{M}(0)\) (the black group) and \(\varvec{M}(1)\) (the blue group). The dashed arrow represents the one-to-one mapping from the counterfactual covariate value with \(Z=0\) to the counterfactual covariate value with \(Z=1\)Back to article page