Table 1.

Assumptions in 2SMR adapted from ref. (56) and expressions based on variable definitions in Appendix 1

Assumption	Description
General IV assumptions
IV1	${\gamma }_j>0$, the SNP predicts the exposure
IV2	$k_x{\psi }_j=0, k_y{\psi }_j=0$, there is no SNP-confounder association
IV3	${\alpha }_j=0$, the SNP does not exhibit horizontal pleiotropy
2SMR assumptions
2SMR1	The causal relationship is identical in the two samples
2SMR2	$cov\left({\epsilon }_{x_j},{\epsilon }_{y_j}\right)=0$
2SMR3	The error variances are known
No measurement error in the exposure (NOME)
	$var\left({\epsilon }_{x_j}\right)\approx 0$, the SNP-exposure effect is estimated with negligible error
Instrument Strength Independent of Direct Effect (InSIDE)
	$cov\left({\gamma }_j, {\alpha }_j\right)=0$