A Fully-Adjusted Two-Stage Procedure for Rank Normalization in Genetic Association Studies

Abstract

When testing genotype-phenotype associations using linear regression, departure of the trait distribution from normality can impact both Type I error rate control and statistical power, with worse consequences for rarer variants. While it has been shown that applying a rank-normalization transformation to trait values before testing may improve these statistical properties, the factor driving them is not the trait distribution itself, but its residual distribution after regression on both covariates and genotype. Because genotype is expected to have a small effect (if any) investigators now routinely use a two-stage method, in which they first regress the trait on covariates, obtain residuals, rank-normalize them, and then secondly use the rank-normalized residuals in association analysis with the genotypes. Potential confounding signals are assumed to be removed at the first stage, so in practice no further adjustment is done in the second stage. Here, we show that this widely-used approach can lead to tests with undesirable statistical properties, due to both a combination of a mis-specified mean-variance relationship, and remaining covariate associations between the rank-normalized residuals and genotypes. We demonstrate these properties theoretically, and also in applications to genome-wide and whole-genome sequencing association studies. We further propose and evaluate an alternative fully-adjusted two-stage approach that adjusts for covariates both when residuals are obtained, and in the subsequent association test. This method can reduce excess Type I errors and improve statistical power.