Detecting Non-linear Dependence through Genome Wide Analysis

Abstract

In the current study we introduce statistical methods based on trigonometry, to infer the shape of a (non)-linear bivariate genetic relationship. We do this based on a series of piecemeal GWASs of segments of a target (continuous) trait distribution, and the genetic correlations between those GWASs and a second trait. Simulations confirm that we are able to retrieve the shape of the relationship given certain assumptions about the nature of the relationship between the traits. We applied the method to the genetic relationship between BMI, sleep duration, and height, and psychiatric disorders (ADHD, anorexia nervosa, and depression) using data from approximately 450K individuals from UK Biobank. In the relationship between BMI and psychiatric traits, we found that the expected value of depression is a nonlinear function of BMI i.e. there is a nonlinear genetic relationship between both traits. We observed similar findings for the genetic relationship between BMI and anorexia, sleep duration and depression, and sleep duration and ADHD. We observed no underlying nonlinearity in the genetic relationship between height and psychiatric traits. Using a novel statistical approach, we show that nonlinear genetic relationships between traits are detectable and genetic associations as quantified using global estimators like genetic correlations are not informative about underlying complexities in these relationships. Our findings challenge assumptions of linearity in genetic epidemiology and suggest that bivariate genetic associations are not uniform across the phenotypic spectrum, which may have implications for the development of targeted interventions.