By third assumption, you mean SNP marginally not associated with outcome?
Replying to “By third assumption, you mean SNP marginally not …”:
Marginally, it is expected to be associated (via the exposure variable). But the SNP is not associated with the outcome conditional on the exposure (i.e., over and above the SNP-outcome association mediated through the exposure)
Replying to “By third assumption, you mean SNP marginally not …”:
That’s correct- one subtlety is that the SNP must not be associated with the outcome conditional on BOTH the exposure AND confounders. Conditioning just on the exposure will actually open a path from SNP to confounders to outcome since exposure is a collider (i.e. caused by the SNP and confounders)- therefore important to condition on both exposure and confounders. See here for more info: Collider scope: when selection bias can substantially influence observed associations - PubMed