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

Nicolo Fusi,Neil D Lawrence,Christoph Lippert,Oliver Stegle

doi:10.1038/ncomms5890

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.

Highlights

In an effort to keep our simulations as realistic as possible, we considered a set of transformations that have previously been identified in the genetic analysis of a diverse set of global quantitative traits in mouse[15]
We found that applying WarpedLMM to fit a separate warping functions for each of the four phenotypes, led to an increase of pairwise (Pearson) correlations between these phenotypes, which can be important for multivariate genetic analyses with linear Gaussian models[28,29] (Supplementary Fig. 7)
Discussion preprocessing methods are widely used in practice to approximately identify and invert an unknown phenotype transformation[11,12,13,14,17,20,22,23,24,30,31], so far there has been no principled approach to assess and fit these transformations while accounting for genetic information and covariates

Summary

Introduction

We first simulated phenotype values from a linear additive genetic model (see Methods), and applied a nonlinear function g (see Supplementary Fig. 1), yielding the final observed phenotype. We compared the ability of the WarpedLMM and the LMM to estimate the true simulated heritability from the transformed phenotypes.

Results

Conclusion