Fig. 1: Directed acyclic graph for associations of different SNPs with an outcome P conditional on a trait I.
From: A robust method for collider bias correction in conditional genome-wide association studies
(a) association of a SNP (GI.) with an outcome P conditional on a trait I such that the SNP GI. affects I with no direct effect on P; (b) association of a SNP (GIP) with P conditional on I such that the SNP GIP has direct effects on both I and P; (c) as in (b) but the SNP GIP affects both I and P through a single exposure E; (d) association of a SNP (G.P) with P conditional on I such that the SNP G.P affects P with no effect on I; (e) a SNP (G..) with neither effects on I nor P. In all graphs, U is a composite variable including all common causes of I and P, involving common polygenic effect on I and P as well as non-genetic factors. Conditioning on I induces the association between GI. and U in (a), as well as GIP and U in (b) and (c), shown by the dashed lines. This leads to biased association for each of GI. and GIP with P via the path GI. − U → P in (a) and the path GIP − U → P in (b) and (c). Since the SNPs G.P and G.. do not affect I, conditioning on I does not induce biased association between either SNP and P as no associations between G.P or G.. and U are produced.
