Distance-based differential analysis of gene curves

Time course gene expression experiments are performed to study time-varying changes in mRNA levels of thousands of genes. Statistical methods from functional data analysis (FDA) have recently gained popularity for modelling and exploring such time courses. Each temporal profile is treated as the realization of a smooth function of time, or curve, and the inferred curve becomes the basic unit of statistical analysis. The task of identifying genes with differential temporal profiles then consists of detecting statistically significant differences between curves, where such differences are commonly quantified by computing the area between the curves or the l₂ distance.

We propose a general test statistic for detecting differences between gene curves, which only depends on a suitably chosen distance measure between them. The test makes use of a distance-based variance decomposition and generalizes traditional MANOVA tests commonly used for vectorial observations. We also introduce the visual l₂ distance, which is shown to capture shape-related differences in gene curves and is robust against time shifts, which would otherwise inflate the traditional l₂ distance. Other shape-related distances, such as the curvature, may carry biological significance. We have assessed the comparative performance of the test on realistically simulated datasets and applied it to human immune cell responses to bacterial infection over time.