# Warped linear mixed models for the genetic analysis of transformed phenotypes

Nicoló Fusi, Microsoft Research, New England
Christoph Lippert, Human Longevity, Inc
Neil D. Lawrence, University of Sheffield
Oliver Stegle, European Bioinformatics Institute

Nature Communications 5

#### Abstract

Linear mixed models (LMMs) are a powerful and established tool for studying genotype–phenotype relationships. A limitation of the LMM is that the model assumes Gaussian distributed residuals, a requirement that rarely holds in practice. Violations of this assumption can lead to false conclusions and loss in power. To mitigate this problem, it is common practice to pre-process the phenotypic values to make them as Gaussian as possible, for instance by applying logarithmic or other nonlinear transformations. Unfortunately, different phenotypes require different transformations, and choosing an appropriate transformation is challenging and subjective. Here we present an extension of the LMM that estimates an optimal transformation from the observed data. In simulations and applications to real data from human, mouse and yeast, we show that using transformations inferred by our model increases power in genome-wide association studies and increases the accuracy of heritability estimation and phenotype prediction.

  @Article{fusi-warped14, title = {Warped linear mixed models for the genetic analysis of transformed phenotypes}, journal = {Nature Communications}, author = {Nicoló Fusi and Christoph Lippert and Neil D. Lawrence and Oliver Stegle}, year = {2014}, volume = {5}, number = {4890}, month = {00}, edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2014-01-01-fusi-warped14.md}, url = {http://inverseprobability.com/publications/fusi-warped14.html}, abstract = {Linear mixed models (LMMs) are a powerful and established tool for studying genotype–phenotype relationships. A limitation of the LMM is that the model assumes Gaussian distributed residuals, a requirement that rarely holds in practice. Violations of this assumption can lead to false conclusions and loss in power. To mitigate this problem, it is common practice to pre-process the phenotypic values to make them as Gaussian as possible, for instance by applying logarithmic or other nonlinear transformations. Unfortunately, different phenotypes require different transformations, and choosing an appropriate transformation is challenging and subjective. Here we present an extension of the LMM that estimates an optimal transformation from the observed data. In simulations and applications to real data from human, mouse and yeast, we show that using transformations inferred by our model increases power in genome-wide association studies and increases the accuracy of heritability estimation and phenotype prediction.}, key = {Fusi-warped14}, doi = {10.1038/ncomms5890}, linksoftware = {http://github.com/pmbio/warpedLMM}, OPTgroup = {} }
 %T Warped linear mixed models for the genetic analysis of transformed phenotypes %A Nicoló Fusi and Christoph Lippert and Neil D. Lawrence and Oliver Stegle %B %C Nature Communications %D %F fusi-warped14 %J Nature Communications %P -- %R 10.1038/ncomms5890 %U http://inverseprobability.com/publications/fusi-warped14.html %V 5 %N 4890 %X Linear mixed models (LMMs) are a powerful and established tool for studying genotype–phenotype relationships. A limitation of the LMM is that the model assumes Gaussian distributed residuals, a requirement that rarely holds in practice. Violations of this assumption can lead to false conclusions and loss in power. To mitigate this problem, it is common practice to pre-process the phenotypic values to make them as Gaussian as possible, for instance by applying logarithmic or other nonlinear transformations. Unfortunately, different phenotypes require different transformations, and choosing an appropriate transformation is challenging and subjective. Here we present an extension of the LMM that estimates an optimal transformation from the observed data. In simulations and applications to real data from human, mouse and yeast, we show that using transformations inferred by our model increases power in genome-wide association studies and increases the accuracy of heritability estimation and phenotype prediction. 
 TY - CPAPER TI - Warped linear mixed models for the genetic analysis of transformed phenotypes AU - Nicoló Fusi AU - Christoph Lippert AU - Neil D. Lawrence AU - Oliver Stegle PY - 2014/01/01 DA - 2014/01/01 ID - fusi-warped14 SP - EP - DO - 10.1038/ncomms5890 UR - http://inverseprobability.com/publications/fusi-warped14.html AB - Linear mixed models (LMMs) are a powerful and established tool for studying genotype–phenotype relationships. A limitation of the LMM is that the model assumes Gaussian distributed residuals, a requirement that rarely holds in practice. Violations of this assumption can lead to false conclusions and loss in power. To mitigate this problem, it is common practice to pre-process the phenotypic values to make them as Gaussian as possible, for instance by applying logarithmic or other nonlinear transformations. Unfortunately, different phenotypes require different transformations, and choosing an appropriate transformation is challenging and subjective. Here we present an extension of the LMM that estimates an optimal transformation from the observed data. In simulations and applications to real data from human, mouse and yeast, we show that using transformations inferred by our model increases power in genome-wide association studies and increases the accuracy of heritability estimation and phenotype prediction. ER - 
 Fusi, N., Lippert, C., Lawrence, N.D. & Stegle, O.. (2014). Warped linear mixed models for the genetic analysis of transformed phenotypes. Nature Communications 5(4890):-