Adjusting For Principal Components Of Molecular Phenotypes Induces Replicating False Positives

Abstract

High-throughput measurements of molecular phenotypes provide an unprecedented opportunity to model cellular processes and their impact on disease. Such highly-structured data is strongly confounded, and principal components and their variants reliably estimate latent confounders. Conditioning on PCs in downstream analyses is known to improve power and reduce multiple-testing miscalibration and is an indispensable element of thousands of published functional genomic analyses. Further clarifying this approach is of fundamental interest to the genomics and statistics communities. We uncover a novel bias induced by PC conditioning and provide an analytic, deterministic and intuitive approximation. The bias exists because PCs are, roughly, unshielded colliders on a causal path: because PCs partially incorporate a causal genotype effect on one phenotype, the genotype becomes correlated with every phenotype conditional on PCs. We empirically quantify this bias in realistic simulations. For small genetic effects, a nearly negligible bias is observed for all tested PC variants. For large genetic effects, or other differential covariates, dramatic false positives can arise. Though one PC variant (supervised SVA) largely avoids this bias, it is computationally prohibitive genome-wide; further, its immunity to this bias is novel. Our analysis informs best practices for confounder correction in genomic studies.