Our results should be considered in the context of the limitations of the study. Foremost, this method assumes that the observed confounders included in the PCA adequately capture the underlying mechanism of collider bias. If observed confounders do not account for this, either directly or as proxies of unmeasured confounders, bias due to these factors may remain. The observed changes in PRS beta and R-squared in the applied analysis in COGA were modest, and in all examples, the 95% confidence intervals for PRS beta estimates overlapped. This may be attributable to COGA being a high-risk sample with participants from extended families enriched for AUD. Accordingly, thresholding in phenotype and genotype may have reduced observed associations. Additionally, we generated a normally distributed outcome variable in our simulation and modeled AUD-Sx as a continuous variable with ordinary least squares regression in the applied examples presented here. Thus, this approach to addressing collider bias may not extend to outcome variables with other distributions. An extension of our simulation pipeline to accommodate logistic regression for binary outcomes performed poorly. The addition of PCs increased
