Operating characteristics of the rank-based inverse normal transformation for quantitative trait analysis in genome-wide association studies

Abstract

Quantitative traits analyzed in Genome-Wide Association Studies (GWAS) are often nonnormally distributed. For such traits, association tests based on standard linear regression are subject to reduced power and inflated type I error in finite samples. Applying the rank-based inverse normal transformation (INT) to nonnormally distributed traits has become common practice in GWAS. However, the different variations on INT-based association testing have not been formally defined, and guidance is lacking on when to use which approach. In this paper, we formally define and systematically compare the direct (D-INT) and indirect (I-INT) INT-based association tests. We discuss their assumptions, underlying generative models, and connections. We demonstrate that the relative powers of D-INT and I-INT depend on the underlying data generating process. Since neither approach is uniformly most powerful, we combine them into an adaptive omnibus test (O-INT). O-INT is robust to model misspecification, protects the type I error, and is well powered against a wide range of nonnormally distributed traits. Extensive simulations were conducted to examine the finite sample operating characteristics of these tests. Our results demonstrate that, for nonnormally distributed traits, INT-based tests outperform the standard untransformed association test, both in terms of power and type I error rate control. We apply the proposed methods to GWAS of spirometry traits in the UK Biobank. O-INT has been implemented in the R package RNOmni, which is available on CRAN.

Keywords: direct and indirect rank-based inverse normal transformation; nonnormality; omnibus test; quantitative traits; transformation; type I error rate.

FIGURE 1

Distribution of association p-values under the null at sample size n =10³ across R =10⁸ simulation replicates. Rows correspond to different phenotype distributions. The first phenotype has normal residuals; the second has ${\chi }_1^2$ residuals; the third phenotype has t₃ residuals; and the log of the fourth phenotype has normal residuals. Columns correspond to different association tests. The first is the untransformed association test (UAT), the second is the direct INT (D-INT), the third is indirect INT (I-INT), and the fourth column is omnibus INT (O-INT). Note that this figure appears in color in the electronic version of this article, and any mention of color refers to that version

FIGURE 2

Power curves at α =10⁻⁶ and sample size n =10³ across R =10⁶ simulation replicates. Simulations were conducted at heritabilities ranging from 0.1% and 1.0%. Gray is the UAT, blue is D-INT, I-INT, and red is O-INT. Each panel corresponds to a different phenotype. The first phenotype has normal residuals; the second has ${\chi }_1^2$ residuals; the third phenotype has t₃ residuals; and the log of the fourth phenotype has normal residuals. Note that this figure appears in color in the electronic version of this article, and any mention of color refers to that version