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. 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. Adjustment for covariates or correlated secondary traits in genome-wide association studies (GWASs) can have two purposes: first, to account for potential confounding factors that can bias SNP effect estimates, and second, to improve statistical power by reducing residual variance. For example, researchers routinely adjust for principal components of individual genotypes to account for population structure,1Price A.L. Patterson N.J. Plenge R.M. Weinblatt M.E. Shadick N.A. Reich D. Principal components analysis corrects for stratification in genome-wide association studies.Nat. Genet. 2006; 38: 904-909Crossref PubMed Scopus (6867) Google Scholar or principal components of gene expression to capture batch effects in gene-expression analysis.2Pickrell J.K. Marioni J.C. Pai A.A. Degner J.F. Engelhardt B.E. Nkadori E. Veyrieras J.B. Stephens M. Gilad Y. Pritchard J.K. Understanding mechanisms underlying human gene expression variation with RNA sequencing.Nature. 2010; 464: 768-772Crossref PubMed Scopus (942) Google Scholar Besides confounding factors, human traits can also be adjusted for correlated environmental or demographic factors such as gender and age to increase statistical power.3Mefford J. Witte J.S. The Covariate’s Dilemma.PLoS Genet. 2012; 8: e1003096Crossref PubMed Scopus (38) Google Scholar, 4Pirinen M. Donnelly P. Spencer C. Efficient computation with a linear mixed model on large-scale data sets with applications to genetic studies.Ann. Appl. Stat. 2013; 7: 369-390Crossref Scopus (69) Google Scholar The intuition here is that accounting for a true risk factor decreases the residual variance of the outcome and therefore increases the ratio of the true effect size of a predictor of interest over the total phenotypic variance, which leads to increased statistical power. Recently, researchers have conducted GWAS of human traits and diseases while adjusting for other heritable covariates with the motivation of identifying genetic variants associated only with the primary outcome.5Kaplan R.C. Petersen A.K. Chen M.H. Teumer A. Glazer N.L. Döring A. Lam C.S. Friedrich N. Newman A. Müller M. et al.A genome-wide association study identifies novel loci associated with circulating IGF-I and IGFBP-3.Hum. Mol. Genet. 2011; 20: 1241-1251Crossref PubMed Scopus (58) Google Scholar, 6Heid I.M. Jackson A.U. Randall J.C. Winkler T.W. Qi L. Steinthorsdottir V. Thorleifsson G. Zillikens M.C. Speliotes E.K. Mägi R. et al.MAGICMeta-analysis identifies 13 new loci associated with waist-hip ratio and reveals sexual dimorphism in the genetic basis of fat distribution.Nat. Genet. 2010; 42: 949-960Crossref PubMed Scopus (722) Google Scholar, 7Manning A.K. Hivert M.F. Scott R.A. Grimsby J.L. Bouatia-Naji N. Chen H. Rybin D. Liu C.T. Bielak L.F. Prokopenko I. et al.DIAbetes Genetics Replication And Meta-analysis (DIAGRAM) ConsortiumMultiple Tissue Human Expression Resource (MUTHER) ConsortiumA genome-wide approach accounting for body mass index identifies genetic variants influencing fasting glycemic traits and insulin resistance.Nat. Genet. 2012; 44: 659-669Crossref PubMed Scopus (566) Google Scholar, 8Randall J.C. Winkler T.W. Kutalik Z. Berndt S.I. Jackson A.U. Monda K.L. Kilpeläinen T.O. Esko T. Mägi R. Li S. et al.DIAGRAM ConsortiumMAGIC InvestigatorsSex-stratified genome-wide association studies including 270,000 individuals show sexual dimorphism in genetic loci for anthropometric traits.PLoS Genet. 2013; 9: e1003500Crossref PubMed Scopus (273) Google Scholar, 9Scott R.A. Lagou V. Welch R.P. Wheeler E. Montasser M.E. Luan J. Mägi R. Strawbridge R.J. Rehnberg E. Gustafsson S. et al.DIAbetes Genetics Replication and Meta-analysis (DIAGRAM) ConsortiumLarge-scale association analyses identify new loci influencing glycemic traits and provide insight into the underlying biological pathways.Nat. Genet. 2012; 44: 991-1005Crossref PubMed Scopus (613) Google Scholar An important difference between environmental/demographic factors and heritable human traits is that the latter have genetic associations. Therefore, a genetic variant can in theory be associated with both the primary outcome and the covariate used for adjustment. When that happens, the adjusted and unadjusted estimated effects of the genetic variant on the outcome will differ. If the correlation between the covariate and the outcome results from a direct effect of the covariate on the outcome (Figure 1A), the adjusted and unadjusted estimates correspond to the direct (i.e., not mediated through the covariate) and total (i.e., direct + indirect) genetic effect of the variant on the outcome, respectively. In all other situations where the observed correlation is due to shared genetic and/or environmental risk factors, the adjusted estimate can be biased relative to the true direct effect. To understand when a bias is introduced, consider the causal diagrams for a single genetic variant g, an outcome of interest Y, and a covariate C (Figures 1B–1D). Besides the genetic variant in question, the two variables, Y and C, are influenced by either other genetic loci, which we denote by G-g, or other environment factors and noise, denoted by E. For simplicity, assume that the genetic variant g and other causal factors, G-g and E, are uncorrelated. Furthermore, assume that the covariate C and the outcome of interest, Y are correlated through (G-g,E). If we are interested in estimating the direct effect of g on Y (the black arrow in Figure 1), then in scenario from Figure 1B adjusting for the covariate C does not bias the effect estimate and increases the power as we implicitly adjust for some environmental and other (uncorrelated) shared genetic effects. However, in scenario from Figure 1C where g only influences the covariate and not the outcome, adjusting for the covariate induces an association between the genetic variant and Y. The strength of this association depends on ρCY, the correlation between the covariate and the outcome due to shared risk factors, and the strength of βC, the effect of the genetic variant on the covariate. For normalized g, C, and Y with mean 0 and variance 1, the bias of the genetic effect estimate, βˆY, on the covariate adjusted trait is approximately equal to −βCρCY when βC is small and sample size is sufficiently large (see Appendix A). Finally, consider scenario from Figure 1D, where both the covariate and the outcome are influenced by the genetic variant. Here, the association between the genetic variant and the covariate will bias the estimated genetic effect on the outcome by the same amount as before, i.e., −βCρCY. This bias observed is illustrated in Figure 2A, and as expected, it is well approximated by the product between the direct genetic effect estimate on the covariate and the correlation between the outcome and the covariate. As shown in Figure 2B, this bias leads to increased false discovery rates under the null (no direct effect of the genetic variant on the outcome). This phenomenon also implies that when there truly is a direct genetic effect on the outcome, the adjusted statistical test can have increased power to detect the genetic variant, as compared to the unadjusted test, if the genetic effect and the phenotypic correlation are in opposite directions (Figure S2, left panel). Conversely, if the genetic effect and the correlation are in the same direction, the adjusted statistical test has, in many cases, a decreased power to detect the genetic variant (Figure S2, right panel). The difficulty of estimating direct effects of genetic variants on a covariate-adjusted outcome is well appreciated in causal inference literature10Pearl J. Causal inference from indirect experiments.Artif. Intell. Med. 1995; 7: 561-582Abstract Full Text PDF PubMed Scopus (46) Google Scholar and by many epidemiologists,11Greenland S. Pearl J. Robins J.M. Causal diagrams for epidemiologic research.Epidemiology. 1999; 10: 37-48Crossref PubMed Scopus (2503) Google Scholar, 12Schisterman E.F. Cole S.R. Platt R.W. Overadjustment bias and unnecessary adjustment in epidemiologic studies.Epidemiology. 2009; 20: 488-495Crossref PubMed Scopus (1208) Google Scholar, 13Hernán M.A. Hernández-Díaz S. Werler M.M. Mitchell A.A. Causal knowledge as a prerequisite for confounding evaluation: an application to birth defects epidemiology.Am. J. Epidemiol. 2002; 155: 176-184Crossref PubMed Scopus (979) Google Scholar but has received little attention in the context of GWASs.14Vansteelandt S. Goetgeluk S. Lutz S. Waldman I. Lyon H. Schadt E.E. Weiss S.T. Lange C. On the adjustment for covariates in genetic association analysis: a novel, simple principle to infer direct causal effects.Genet. Epidemiol. 2009; 33: 394-405Crossref PubMed Scopus (39) Google Scholar In Appendix B, we review 15 scenarios depicted as direct acyclic graphs in Figure S1 where adjusting for a covariate is either recommended or not and validated the interpretation of each case through simulation (see Table S3). In the absence of a clear underlying causal model or diagram, one cannot guarantee that effect estimates for covariate adjusted outcomes correspond to the desired estimates (e.g., direct versus total genetic effect). In GWASs, the potential presence of bias due to adjustment is proportional to the product of βC and ρCY. Hence, adjusting for a covariate that does not have a genetic component, such as an environmental exposure, will not bias the estimate for the genotype effect on the outcome of interest as βC = 0. On the other hand, when adjusting for a covariate that has a genetic component (potentially βC ≠ 0), then the adjusted association signals can be difficult to interpret, because it does not necessarily imply an association with the outcome of interest only but can correspond also to a bivariate signal on Y and C, or in some extreme case to an association with the covariate only. Therefore, unless we can unequivocally determine which model in Figure 1 is the right one or rule out an effect from the genetic variant on the covariate, the reported adjusted associations should be considered with caution. For illustrative purpose, we considered the SNPs reported to be associated at genome-wide significance levels with waist hip ratio (WHR) or waist circumference (WC), after adjustment on BMI.6Heid I.M. Jackson A.U. Randall J.C. Winkler T.W. Qi L. Steinthorsdottir V. Thorleifsson G. Zillikens M.C. Speliotes E.K. Mägi R. et al.MAGICMeta-analysis identifies 13 new loci associated with waist-hip ratio and reveals sexual dimorphism in the genetic basis of fat distribution.Nat. Genet. 2010; 42: 949-960Crossref PubMed Scopus (722) Google Scholar, 8Randall J.C. Winkler T.W. Kutalik Z. Berndt S.I. Jackson A.U. Monda K.L. Kilpeläinen T.O. Esko T. Mägi R. Li S. et al.DIAGRAM ConsortiumMAGIC InvestigatorsSex-stratified genome-wide association studies including 270,000 individuals show sexual dimorphism in genetic loci for anthropometric traits.PLoS Genet. 2013; 9: e1003500Crossref PubMed Scopus (273) Google Scholar The observed correlations between BMI and WHR and between BMI and WC in the GIANT data are 0.49 and 0.85, respectively (see Appendix C). Table 1 displays the gender-specific significant SNPs from these studies and the summary statistics that we extracted from the GIANT consortium website. It shows that SNPs harboring opposite marginal effects on the two traits are significantly enriched (p = 0.005). This agrees well with theory and our simulations showing increased power when the SNP has effect in opposite directions on the outcome and the covariate (Figure S2A). In the absence of a genetic effect on BMI, we expect the number of SNPs with opposite directions of effect estimates to follow a binomial distribution with probability of 0.5 (see Appendix C and Figure S3). The observed enrichment of SNPs with opposite directions indicates that a substantial fraction of those SNPs are associated with BMI in the opposite direction. Indeed, when removing the SNPs with the most significant marginal associations with BMI, the fraction of variants displaying an opposite effect becomes non-significant (Figure S4). None of the SNPs with opposite effects on BMI and either WHR or WC show significant marginal association with BMI after correction for multiple testing (although 5 out of 23 are nominally significant). However, as shown in Figure S2B, even non-significant genetic effects on the covariate can influence power when correlation between the outcome and the covariate is large (e.g., ≥ 0.5). To assess whether the p values from the adjusted analysis reflect direct genetic effects on the outcome or a mixture of effects on the outcome and the covariate, we derived a statistical test of whether the BMI-adjusted effect of a SNP, βˆYadj, was equal to its expectation when βC = 0, which is βˆY. This test only uses GWAS summary information and the correlation between the covariate and the phenotype (see Appendix A). It is approximately equivalent to testing for the marginal effect of the SNP on the covariate in the exact same set of subjects used in the adjusted analysis. To verify this, we conducted a GWAS of WHR, BMI, and WHR adjusted for BMI for 15,949 individuals on more than 6 million SNPs and found the correlation between the two test statistics, the direct marginal and the proposed one based on GWAS summary level information, to be 0.98 (see Appendix A). We then applied our test to the WHR and WC GWAS summary statistics to test for a direct genetic effect on BMI among the reported SNP associations from the GIANT study (see Table 1) as we did not have access to the marginal associations for BMI in the same samples. We observed that half of the reported associations with WHR adjusted for BMI are likely influenced by a (direct) genetic association with BMI. This does not mean that those SNPs have no effect on WHR; in fact, their marginal (unadjusted) associations with WHR and BMI suggest that most of these loci are truly associated with WHR. Instead, this means that the reported effect estimates and the p values in the covariate adjusted analysis should be interpreted with caution, because they are not necessarily representative of the direct genetic effect on WHR and WC.Table 1Estimates and p Values of Genetic Effects from the GIANT Study for Genetic Variants Found Associated with Waist to Hip Ratio and Waist Circumference after Adjusting for Body Mass IndexMarkerNameA1A2FrequencyEstimated EffectsOpposite EffectReferencePβ.deviationap value from the test of βˆYadj = βˆY.WHR adjusted for BMI in womenBMI (pval)WHR (pval)WHRadjBMI (pval)rs9491696cg0.4800−0.0068(2.7E-01)−0.0479(1.0E-11)−0.0472(1.6E-12)Heid et al.0.81rs6905288ag0.5620−0.0083(2.4E-01)0.0484(4.7E-10)0.0523(7.7E-13)XHeid et al.0.22rs984222cg0.63500.0108(8.5E-02)-0.0284(9.0E-05)-0.0359(1.2E-07)XHeid et al.0.012rs1055144tc0.2100-0.0126(1.1E-01)0.0314(4.2E-04)0.0398(2.3E-06)XHeid et al.0.021rs10195252tc0.5990-0.0184(3.3E-03)0.0447(7.0E-10)0.0529(6.3E-15)XHeid et al.0.0061rs4846567tg0.71700.0098(1.4E-01)-0.0543(5.3E-12)-0.0641(4.7E-18)XHeid et al.0.0025rs1011731ag0.4280−0.0058(3.5E-01)−0.0280(7.0E-05)−0.0284(2.1E-05)Heid et al.0.89rs718314ag0.25900.0077(2.7E-01)−0.0444(3.9E-08)−0.0467(8.3E-10)XHeid et al.0.49rs1294421tg0.6130−0.0007(9.1E-01)−0.0357(1.2E-06)−0.0380(3.4E-08)Heid et al.0.45rs1443512ac0.2390−0.0014(8.5E-01)0.0415(7.6E-07)0.0479(1.4E-09)XHeid et al.0.063rs6795735tc0.59400.0114(6.4E-02)-0.0264(2.2E-04)-0.0330(7.9E-07)XHeid et al.0.023rs4823006ag0.56900.0046(4.6E-01)0.0337(3.4E-06)0.0366(6.9E-08)Heid et al.0.33rs6717858tc0.5417-0.0185(3.1E-03)0.0439(8.1E-10)0.0536(2.8E-15)XRandall et al.0.00072rs2820443tc.-0.0099(1.4E-01)0.0544(4.8E-12)0.0643(3.7E-18)XRandall et al.0.0025rs1358980tc0.4500-0.0148(3.8E-02)0.0498(7.1E-10)0.0565(1.1E-13)XRandall et al.0.041rs2371767cg0.20830.0199(4.1E-03)-0.0302(1.2E-04)-0.0418(1.6E-08)XRandall et al.0.00040rs10478424at0.7833−0.0052(5.1E-01)0.0320(3.3E-04)0.0372(1.0E-05)XRandall et al.0.16rs4684854cg0.43330.0025(7.0E-01)0.0401(7.6E-08)0.0396(2.4E-08)Randall et al.0.88WC adjusted for BMI in womenBMI (pval)WC (pval)WCadjBMI (pval)rs11743303ag0.80.0078(3.2E-01)−0.0186(3.7E-02)−0.0276(2.3E-06)XRandall et al.0.12WHR adjusted for BMI in menBMI (pval)WHR (pval)WHRadjBMI (pval)rs9491696cg0.48000.0004(9.5E-01)−0.0295(1.1E-04)−0.0255(1.7E-04)XRandall et al.0.26rs984222cg0.63500.0146(2.4E-02)-0.0299(1.3E-04)-0.0407(3.3E-09)XRandall et al.0.0030rs1055144tc0.2100−0.0007(9.3E-01)0.0273(4.3E-03)0.0289(6.0E-04)XRandall et al.0.72rs1011731ag0.42800.0082(2.0E-01)−0.0307(5.4E-05)−0.0341(4.9E-07)XRandall et al.0.34SNPs nominally significant for the test of bias (Pβ.deviation < 0.05) are indicated in bold.a p value from the test of βˆYadj = βˆY. Open table in a new tab SNPs nominally significant for the test of bias (Pβ.deviation < 0.05) are indicated in bold. We extended our analysis to other GWAS of covariate adjusted outcomes and found evidence that reported genetic associations with the primary outcome were in part explained by the effect of the SNP on the covariate. For example, the SNP rs11977526 has been reported to be associated with insulin-like growth factor-binding protein-3 (IGFBP3 [MIM 146732]) at very high significance level 3.3 × 10−101 while no association was observed for Insulin-like growth factor-I (IGF1 [MIM 147440]) before any adjustment.5Kaplan R.C. Petersen A.K. Chen M.H. Teumer A. Glazer N.L. Döring A. Lam C.S. Friedrich N. Newman A. Müller M. et al.A genome-wide association study identifies novel loci associated with circulating IGF-I and IGFBP-3.Hum. Mol. 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