Hundreds of thousands of loci have been associated with complex traits via genome-wide association studies (GWAS), but an understanding of the mechanistic connection between GWAS loci and disease remains elusive. Genetic predictors of molecular traits are useful for identifying the mediating roles of molecular traits and prioritizing actionable targets for intervention, as demonstrated in transcriptome-wide association studies (TWAS) and related studies. Given the widespread polygenicity of complex traits, it is imperative to understand the effect of polygenicity on the validity of these mediator-trait association tests. We found that for highly polygenic target traits, the standard test based on linear regression is inflated (E χ^2_twas > 1). This inflation has implications for all TWAS and related methods where the complex trait can be highly polygenic---even if the mediating trait is sparse. We derive an asymptotic expression of the inflation, estimate the inflation for gene expression, metabolites, and brain image derived features, and propose a solution to correct the inflation.

On the problem of inflation in transcriptome-wide association studies