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Biometrics. 2019 Dec 28. doi: 10.1111/biom.13214. [Epub ahead of print]

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

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Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts.
Center for Human Genetic Research, Massachusetts General Hospital, Boston, Massachusetts.
Division of Sleep and Circadian Disorders, Brigham and Women's Hospital, Boston, Massachusetts.
Department of Statistics, Harvard University, Cambridge, Massachusetts.


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.


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


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