Fig. 3.

Directed acyclic graph of association of SNPs G_i with prognosis Y conditional on incidence X. U is as in Fig. 1. Conditioning on X induces the moralised associations shown by dotted lines. These create association of each G_i with Y via the path $G_i-U\to Y$ and all paths $G_i-G_j\to Y$ where $i\ne j$. Under a polygenic model in which individual SNPs explain little covariation between X and Y, the combined effect of U and all $G_{j\ne i}$ is approximately constant across SNPs G_i. If a SNP G_k has a major effect on X and/or Y, the associations of $G_{j\ne k}$ can be conditioned on G_k to prevent the major gene contributing to index event bias