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Rank-Based Inverse Normal Transformations are Increasingly Used, But are They Merited?

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Abstract

Many complex traits studied in genetics have markedly non-normal distributions. This often implies that the assumption of normally distributed residuals has been violated. Recently, inverse normal transformations (INTs) have gained popularity among genetics researchers and are implemented as an option in several software packages. Despite this increasing use, we are unaware of extensive simulations or mathematical proofs showing that INTs have desirable statistical properties in the context of genetic studies. We show that INTs do not necessarily maintain proper Type 1 error control and can also reduce statistical power in some circumstances. Many alternatives to INTs exist. Therefore, we contend that there is a lack of justification for performing parametric statistical procedures on INTs with the exceptions of simple designs with moderate to large sample sizes, which makes permutation testing computationally infeasible and where maximum likelihood testing is used. Rigorous research evaluating the utility of INTs seems warranted.

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Acknowledgments

We thank Christian Dina for asking cogent questions that inspired this commentary and for making useful comments on an earlier draft and also thank Jay Conover, Roger Berger, Brian Hicks, Rui Feng, Michael C. Neale, Goncalo Abecasis, Bernard S. Gorman and Alfred A. Bartolucci for their helpful advice or comments on earlier drafts. This article is supported in part by NIH grants P30DK056336, U54CA100949, R01ES09912, and T32HL072757.

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  1. Department of Biostatistics, Section on Statistical Genetics, University of Alabama at Birmingham, Ryals Public Health Building, Suite 327, Birmingham, AL, 35294, USA

    T. Mark Beasley, Stephen Erickson & David B. Allison

  2. Department of Nutrition Sciences, University of Alabama at Birmingham, Birmingham, AL, USA

    David B. Allison

  3. Clinical Nutrition Research Center, University of Alabama at Birmingham, Birmingham, AL, USA

    David B. Allison

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  1. T. Mark Beasley
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Beasley, T.M., Erickson, S. & Allison, D.B. Rank-Based Inverse Normal Transformations are Increasingly Used, But are They Merited?. Behav Genet 39, 580–595 (2009). https://doi.org/10.1007/s10519-009-9281-0

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