Adjusting for Heritable Covariates Can Bias Effect Estimates in Genome-Wide Association Studies  Hugues Aschard, Bjarni J. Vilhjálmsson, Amit D. Joshi, Alkes L. Price, Peter Kraft  The American Journal of Human Genetics  Volume 96, Issue 2, Pages 329-339 (February 2015) DOI: 10.1016/j.ajhg.2014.12.021 Copyright © 2015 The American Society of Human Genetics Terms and Conditions

Figure 1 Underlying Causal Diagrams Four causal diagrams describing the causal relationship between the genotypes G, environment E, a covariate C, and the outcome of interest Y are shown. In (A), the correlation between Y and C is due to a direct effect of C on Y, whereas in (B)–(D,) the correlation between Y and C is explained by shared risk factors. The American Journal of Human Genetics 2015 96, 329-339DOI: (10.1016/j.ajhg.2014.12.021) Copyright © 2015 The American Society of Human Genetics Terms and Conditions

Figure 2 Effect Estimates and False Discovery Rate Results for simulations of correlated outcomes and covariates and a genetic variant that influences the covariate only are shown. In (A), the average observed bias of the genetic effect estimate in the covariate adjusted analysis is plotted as a function of the correlation between the outcome and the covariate for different values of direct genetic effect on the covariate. The dashed lines correspond to the theoretical bias as derived in the method section. In (B), the average false discovery rate (α = 0.05) of over 5,000 replicates is plotted as a function of ρY,C the correlation between the outcome and the covariate for different values of direct genetic effect on the covariate when simulating 2,000 individuals. The American Journal of Human Genetics 2015 96, 329-339DOI: (10.1016/j.ajhg.2014.12.021) Copyright © 2015 The American Society of Human Genetics Terms and Conditions

Figure 3 Heritability of Adjusted Phenotypes We compared the heritability of a given phenotype against the heritability estimated after adjustment for a correlated variable. We simulated a trait Y adjusted for a correlated trait C. The genetic variance of each trait (upper panel) splits into trait-specific effects, shared effects, and shared loci with opposite effects. We vary heritability of Y and C from 0.8 (A), 0.5 (B), and 0.2 (C) and the proportion of shared environmental variance (bottom panel) from 0 to 1. The American Journal of Human Genetics 2015 96, 329-339DOI: (10.1016/j.ajhg.2014.12.021) Copyright © 2015 The American Society of Human Genetics Terms and Conditions