Normalizing a large number of quantitative traits using empirical normal quantile transformation

Variance-components and regression-based methods are frequently used to map quantitative trait loci. The normality of the trait values is usually assumed and violation of this assumption can have a detrimental effect on the power and type I error of such analyses. Various transformations can be used, but appropriate transformations usually require careful analysis of individual traits, which is not feasible for data sets with a large number of traits like those in Problem 1 of Genetic Analysis Workshop 15 (GAW15). A semiparametric variance-components method can estimate the transformation along with the model parameters, but existing methods are computationally intensive. In this paper, we propose the use of empirical normal quantile transformation to normalize the scaled rank of trait values using an inverse normal transformation. Despite its simplicity and potential loss of information, this transformation is shown, by extensive simulations, to have good control of power and type I error, even when compared with the semiparametric method. To investigate the impact of such a transformation on real data sets, we apply variance-components and variance-regression methods to the expression data of GAW15 and compare the results before and after transformation.