New Conversion Factor Corrects Inflated Genetic Effects in Covariate-Adjusted GWAS

Genome-wide association studies of disease routinely adjust for heritable risk factors such as body mass index, hoping to isolate genetic effects that operate through pathways other than the adjusted trait. A new theoretical study shows that this common practice creates two intertwined problems for interpreting effect sizes: adjustment can induce spurious associations through collider bias, and the standard method for converting the resulting log-odds estimates onto the liability scale—the continuous measure of disease susceptibility that researchers use to compare effect magnitudes across studies—relies on information that adjusted analyses do not contain. The work, published in PLOS Genetics by Siyi Chen of the School of Public Health at LSU Health Sciences Center in New Orleans, derives a corrected conversion that accounts for how disease risk varies across the values of the adjusted covariates, and demonstrates in simulations that it substantially reduces the inflation of estimated genetic effects.

The liability-threshold model, a long-standing framework in quantitative genetics, represents disease susceptibility as a continuous, normally distributed variable, with disease occurring above a threshold. An effect expressed on standardized liability is a change in susceptibility measured in population standard deviations, which makes it comparable across studies and traits in a way that log-odds ratios from logistic regressions are not. Transformations from the observed binary outcome to this underlying scale are well established for disease heritability, and the usual conversion for individual genetic associations depends on the population prevalence—the overall frequency of the disease in the population.

Chen’s key insight is that an adjusted analysis compares individuals who share the same covariate values, not individuals drawn from the population at large. In a study of type 2 diabetes adjusted for body mass index, the relevant comparisons occur within BMI groups, and those groups can carry different disease risks. Two populations with exactly the same overall prevalence can differ in how much risk varies across BMI levels, and therefore require different conversions from log odds to liability. Removing collider bias from the association, the study shows, does not by itself determine this change of scale. The conversion factor depends on the conditional distribution of disease risk given the covariates, a quantity that prevalence alone cannot supply.

The derivation proceeds under a Gaussian liability model with small genetic effects, the standard regime in which first-order approximations are accurate. The causal model distinguishes the direct genetic effect on disease liability—excluding any pathway that runs through the adjusted covariates—from the total effect, which includes mediation through those traits. When a single nucleotide polymorphism and an unmeasured cause of disease both influence the adjusted covariate, conditioning on that covariate opens a collider path: people with the same BMI can differ in the unmeasured cause according to their genotype, and this association distorts the estimated genetic effect on disease. Crucially, the analysis shows that the direct effect and this signed collider contribution shift conditional disease risk through the same derivative, and therefore share a single common conversion factor.

That shared factor is characterized as a conditional-prevalence approximation built from the population prevalence and the covariate-explained liability variance—the fraction of liability variation accounted for by the adjusted covariates. The numerator of the factor reflects the average sensitivity of disease risk to a unit shift in liability across covariate values, while the denominator is the average conditional Bernoulli variance of the disease outcome within covariate groups. By the law of total variance, greater variation in conditional risk reduces the average Bernoulli variance and increases the conversion factor. The paper also establishes a lower bound: under the Gaussian model, the conditional factor is at least as large as the marginal factor based on prevalence alone, with equality only when the covariates explain no liability variance at all. The bound is evaluated numerically by Gauss-Hermite quadrature.

The practical payoff appears in individual-level simulations. In designs without collider bias, where the subtraction term is zero in expectation and rescaling can be isolated, marginal scaling based solely on prevalence increasingly overstated the direct effect as the explained liability variance rose. Conditional scaling kept the absolute relative bias below 2 percent in every setting examined, with 20,000 individuals and 500 replicates per configuration. Coverage of 95 percent confidence intervals stayed close to the nominal level under conditional scaling, while marginal-scaled coverage deteriorated as explained variance increased. In designs with an explicit collider contribution, where the known first-order log-odds bias was subtracted before conversion, marginal scaling still left substantial bias, whereas conditional scaling and the fitted working-logistic factor both gave small residual bias and near-nominal coverage.

The study extends the derivation to case-control sampling, the design used by most large genetic consortia, in which cases and controls are recruited in fixed proportions that do not reflect population prevalence. Under this ascertainment, the conversion factor averages over the sampled covariate distribution and its fitted null logistic risk, and requires the population risk model in addition to the sample design. A correctly specified logistic model has a sampling-invariant slope, but the working logistic projection of probit risk can vary with ascertainment, so the factor appropriate for a case-control GWAS differs from the population factor. Simulations combining bias-slope estimation with liability conversion in both population and case-control GWAS showed that design-specific factors recovered the true scale of direct effects, while applying the population factor to case-control data retained appreciable bias.

Calibration emerges as the dominant practical concern. When the assumed covariate-explained liability variance was deliberately misspecified in sensitivity analyses, the resulting scale errors exceeded the small approximation error of the conditional-prevalence formula itself. Underestimating the explained variance yields a factor that is too small and overstates the direct effect; overestimating it reverses the sign of the error. In a population sample, the fitted GWAS logistic model supplies the required factor directly, without a separate estimate of explained liability variance, since the numerator comes from the Gaussian risk model and the denominator from the average fitted Bernoulli variance of the null logistic fit. For ascertained calibration cohorts, sampling weights or a retrospective likelihood are needed to recover the population fit, and applicability to a target study depends on prevalence, covariate measurement, ancestry, age distribution, and the covariate-risk relationship.

The framework also reaches downstream analyses that consume GWAS summary statistics. For Mendelian randomization, which uses genetic associations to estimate exposure-outcome effects, rescaling the outcome associations by the appropriate factor changes inverse-variance weighted estimates by the exposure- and outcome-specific factor ratios while preserving the fit’s structure. In simulated type 2 diabetes-to-coronary artery disease experiments with the bias slope fitted by regression, conditional scaling substantially reduced the absolute bias of inverse-variance weighted estimates, with the remaining attenuation explained by the regression dilution that first-order weighting does not model. Multivariable Mendelian randomization showed the same pattern, with each coefficient changing by its exposure-specific factor. Rescaling likewise changes the genetic-component variance of direct effects, alters polygenic score scale while preserving ranking and predictive R-squared, and leaves genetic correlations unchanged.

The author emphasizes the limits of the framework. The causal model is hypothetical, and its application to real data draws on biological knowledge and study design, because genetic summary associations alone cannot establish the pathways involving unmeasured confounders. The derivation assumes the focal instrument is independent of the hidden confounder, Gaussian covariates, and small effects, with discrete or strongly skewed covariates requiring separate risk modeling and prevalence calibration. Bias-slope estimation remains tied to the identifying assumptions of each method: in the full simulation, the corrected weighted least squares estimator recovered the log-odds bias slope closely, while Slope-Hunter overestimated its magnitude, though both recovered the aggregate scale of direct effects when direct effects and covariate associations were independently generated. Sensitivity calculations using public GWAS data showed that conditional-prevalence conversion reduced a marginal-scaled body mass index-to-type 2 diabetes estimate by 13 percent, illustrating the magnitude of scale change an adjusted outcome can undergo. The R package implementing the method is publicly available, and the study recommends that reports of adjusted genetic associations state the adjusted covariates, population prevalence, sampling design, bias estimator, and conversion factor with its calibration source and uncertainty.

Subject of Research: Liability-scale conversion methods for covariate-adjusted binary genome-wide association studies

Article Title: Conditional-prevalence correction for liability-scale analyses of covariate-adjusted binary GWAS

Article References: Chen, S. (2026). Conditional-prevalence correction for liability-scale analyses of covariate-adjusted binary GWAS. PLOS Genetics, 22(10), e1012348. https://doi.org/10.1371/journal.pgen.1012348

Image Credits: AI Generated

DOI: 10.1371/journal.pgen.1012348

Keywords: GWAS, liability scale, collider bias, covariate adjustment, case-control sampling, Mendelian randomization, polygenic scores, population prevalence, effect-size conversion, genetic association studies, Conditional-prevalence, correction