Adjusting for heritable covariates can bias effect estimates in genome-wide association studies

Abstract

In recent years, a number of large-scale genome-wide association studies have been published for human traits adjusted for other correlated traits with a genetic basis. In most studies, the motivation for such an adjustment is to discover genetic variants associated with the primary outcome independently of the correlated trait. In this report, we contend that this objective is fulfilled when the tested variants have no effect on the covariate or when the correlation between the covariate and the outcome is fully explained by a direct effect of the covariate on the outcome. For all other scenarios, an unintended bias is introduced with respect to the primary outcome as a result of the adjustment, and this bias might lead to false positives. Here, we illustrate this point by providing examples from published genome-wide association studies, including large meta-analysis of waist-to-hip ratio and waist circumference adjusted for body mass index (BMI), where genetic effects might be biased as a result of adjustment for body mass index. Using both theory and simulations, we explore this phenomenon in detail and discuss the ramifications for future genome-wide association studies of correlated traits and diseases.

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.

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 ρ_Y,C the correlation between the outcome and the covariate for different values of direct genetic effect on the covariate when simulating 2,000 individuals.

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.