Operating Characteristics of the Rank-Based Inverse Normal Transformation for Quantitative Trait Analysis in Genome-Wide Association Studies

SummaryQuantitative traits analyzed in Genome-Wide Association Studies (GWAS) are often non-normally 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 non-normally 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 non-normally distributed traits. Extensive simulations were conducted to examine the finite sample operating characteristics of these tests. Our results demonstrate that, for non-normally distributed traits, INT-based tests outperform the standard untransformed association test (UAT), 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.