A Nonparametric Approach to Detect Nonlinear Correlation in Gene Expression

We propose a distribution-free approach to detect nonlinear relationships by reporting local correlation. The effect of our proposed method is analogous to piecewise linear approximation although the method does not utilize any linear dependency. The proposed metric, maximum local correlation, was applied to both simulated cases and expression microarray data comparing the rd mouse with age-matched control animals. The rd mouse is an animal model (with a mutation for the gene Pde6b) for photoreceptor degeneration. Using simulated data, we show that maximum local correlation detects nonlinear association, which could not be detected using other correlation measures. In the microarray study, our proposed method detects nonlinear association between the expression levels of different genes, which could not be detected using the conventional linear methods. The simulation dataset, microarray expression data, and the Nonparametric Nonlinear Correlation (NNC) software library, implemented in Mat lab, are included as part of the online supplemental materials.