A Polygenic Quincunx

Abstract

Sequential addition of SNPs (single nucleotide polymorphism) to a risk model repeatedly splits risk groups in two, generating a branching tree. As SNPs are independent, the path of an individual through the tree is a form of random walk. This resembles the path of a ball through a Galton quincunx, but the rules for a polygenic quincunx are more complex. The result is that individuals zigzag to higher and lower risks with each additional SNP. Patient flows through a polygenic quincunx for a few SNPs that aggregate these individual random walks is presented. Longer random walks calculated from Monte-Carlo simulations illustrate how different the individual random walks can be. As random walks do not have unique termini, polygenic risk values dont converge on unique individual risk estimates. However, the more steps in a random walk, the greater the dispersion of the termini around the starting point. So more SNPs can result in more disperse population polygenic risk distributions, and potentially greater clinical benefit when allocating preventive measures based on risk level.