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

Nicoló Fusi, Christoph Lippert, Neil D. Lawrence, Oliver Stegle, 5(4890), 2014.

#### 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.

#### Cite this Paper

BibTeX

```
@InProceedings{pmlr-v-fusi-warped14,
title = {Warped linear mixed models for the genetic analysis of transformed phenotypes},
author = {Nicoló Fusi and Christoph Lippert and Neil D. Lawrence and Oliver Stegle},
year = {},
editor = {},
volume = {5},
number = {4890},
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.}
}
```

Endnote

```
%0 Conference Paper
%T Warped linear mixed models for the genetic analysis of transformed phenotypes
%A Nicoló Fusi
%A Christoph Lippert
%A Neil D. Lawrence
%A Oliver Stegle
%B
%C Proceedings of Machine Learning Research
%D
%E
%F pmlr-v-fusi-warped14
%I PMLR
%J Proceedings of Machine Learning Research
%P --
%R 10.1038/ncomms5890
%U http://inverseprobability.com
%V
%N 4890
%W PMLR
%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.
```

RIS

```
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
BT -
PY -
DA -
ED -
ID - pmlr-v-fusi-warped14
PB - PMLR
SP -
DP - PMLR
EP -
DO - 10.1038/ncomms5890
L1 -
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 -
```

APA

`Fusi, N., Lippert, C., Lawrence, N.D. & Stegle, O.. (). Warped linear mixed models for the genetic analysis of transformed phenotypes. `*, in PMLR* (4890):-

#### Related Material

BibTeX

```
@InProceedings{/fusi-warped14,
title = {Warped linear mixed models for the genetic analysis of transformed phenotypes},
author = {Nicoló Fusi and Christoph Lippert and Neil D. Lawrence and Oliver Stegle},
year = {},
editor = {},
volume = {5},
number = {4890},
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.}
}
```

Endnote

```
%0 Conference Paper
%T Warped linear mixed models for the genetic analysis of transformed phenotypes
%A Nicoló Fusi
%A Christoph Lippert
%A Neil D. Lawrence
%A Oliver Stegle
%B
%C Proceedings of Machine Learning Research
%D
%E
%F /fusi-warped14
%I PMLR
%J Proceedings of Machine Learning Research
%P --
%R 10.1038/ncomms5890
%U http://inverseprobability.com
%V
%N 4890
%W PMLR
%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.
```

RIS

```
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
BT -
PY -
DA -
ED -
ID - /fusi-warped14
PB - PMLR
SP -
DP - PMLR
EP -
DO - 10.1038/ncomms5890
L1 -
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 -
```

APA

`Fusi, N., Lippert, C., Lawrence, N.D. & Stegle, O.. (). Warped linear mixed models for the genetic analysis of transformed phenotypes. `*, in PMLR* (4890):-