In summary, principal component analysis reduces collider bias in polygenic risk score effect size estimation under particular statistical assumptions about missingness and correlations in the confounding data. Although the changes in beta and R2 we observed here were modest, PRS effect sizes for complex phenotypes in general are usually small. Correlations between PRS and heritable environments are likely to increase as discovery GWAS become larger and PRS become more powerful. The magnitude of collider bias and the importance of adequately accounting for this bias will increase in turn. Efficient use of existing data resources should be treated as a high priority in complex trait genetics, where data collection is costly and polygenic effect sizes are often small. Application of this method may improve PRS effect size estimation in some cases by reducing the effect of collider bias, making efficient use of data resources that are immediately available in many studies.
