correlation structure of the confounding data are complementary. If a larger proportion of the confounders is measured, the required assumptions about the correlation structure of the confounders are relaxed. If the confounders are highly correlated, the assumptions about the proportion of confounders that are measured is relaxed. This pattern aligns with derivations in Akimova et al. (2021) which indicate that confounders are less influential in the collider bias expression when rGE is smaller. In this simulation, the PCA corrected model outperforms an uncorrected model, even with as few as 10% of the confounders measured, if the confounders are highly correlated.
