Polygenic association analyses often use phenotypic covariates to test whether the PRS of interest is robust to potential confounders, but the effects of PRS may be biased by the inclusion of heritable covariates when the covariate is influenced by unmeasured confounding variables. In this work, we conducted a simulation to test PCA as a potential correction for this bias and subsequently applied the method in observed data. The results of the simulation suggest that using phenotypic PCs as covariates may correct or reduce collider bias under complementary assumptions about the proportion of confounding data that is measured and the correlation structure of the confounding data. When a larger proportion of confounding data is measured, the assumptions about the correlation structure of the confounding data are relaxed. When the correlations between confounding variables are higher, the assumptions about the proportion of confounding data that needs to be measured are relaxed.
