M-quantile regression analysis of temporal gene expression data.

In this paper, we explore the use of M-quantile regression and M-quantile coefficients to detect statistical differences between temporal curves that belong to different experimental conditions. In particular, we consider the application of temporal gene expression data. Here, the aim is to detect genes whose temporal expression is significantly different across a number of biological conditions. We present a new method to approach this problem. Firstly, the temporal profiles of the genes are modelled by a parametric M-quantile regression model. This model is particularly appealing to small-sample gene expression data, as it is very robust against outliers and it does not make any assumption on the error distribution. Secondly, we further increase the robustness of the method by summarising the M-quantile regression models for a large range of quantile values into an M-quantile coefficient. Finally, we fit a polynomial M-quantile regression model to the M-quantile coefficients over time and employ a Hotelling T(2)-test to detect significant differences of the temporal M-quantile coefficients profiles across conditions. Extensive simulations show the increased power and robustness of M-quantile regression methods over standard regression methods and over some of the previously published methods. We conclude by applying the method to detect differentially expressed genes from time-course microarray data on muscular dystrophy.