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

Adjustment for heritable covariates in genome-wide association studies of disease can induce collider bias, creating spurious genetic associations. Following bias correction, interpretation on the liability scale, which represents continuous disease susceptibility, requires an appropriate conversion from log odds. We derive this conversion under a Gaussian liability model for small genetic effects. The direct effect, excluding pathways through the adjusted covariates, and the collider-bias component share a common conversion factor. We characterize how this factor depends on variation in disease risk across covariate values and extend the derivation to case-control sampling. In simulations, the proposed conversion reduced the effect-size inflation associated with scaling based solely on disease prevalence. These results link existing collider-bias corrections to estimation of direct liability effects and clarify the interpretation of covariate-adjusted associations in population and case-control studies.Author summary: Genetic studies of disease often account for risk factors such as body mass index. This adjustment can create a spurious association, called collider bias, which several methods aim to remove. Researchers also convert genetic associations to a scale of underlying disease susceptibility, or liability, so that their magnitudes can be compared across studies. The usual conversion uses the overall frequency of disease. We show why adjusted studies need more information: people with different values of the adjusted risk factors can have different disease risks, even within the same population. We derive a conversion that accounts for this variation and show how it combines with collider-bias correction. In population studies, the fitted association model provides the required factor directly. Studies that recruit cases and controls in fixed proportions require a conversion that also accounts for that sampling design. Our results provide a basis for interpreting adjusted genetic associations in units of disease liability.