Abstract
Many methods, including parametric, nonparametric, and Bayesian methods, have been used for detecting differentially expressed genes based on the assumption that biological systems are linear, which ignores the nonlinear characteristics of most biological systems. More importantly, those methods do not simultaneously consider means, variances, and high moments, resulting in relatively high false positive rate. To overcome the limitations, the SWang test is proposed to determine differentially expressed genes according to the equality of distributions between case and control. Our method not only latently incorporates functional relationships among genes to consider nonlinear biological system but also considers the mean, variance, skewness, and kurtosis of expression profiles simultaneously. To illustrate biological significance of high moments, we construct a nonlinear gene interaction model, demonstrating that skewness and kurtosis could contain useful information of function association among genes in microarrays. Simulations and real microarray results show that false positive rate of SWang is lower than currently popular methods (T-test, F-test, SAM, and Fold-change) with much higher statistical power. Additionally, SWang can uniquely detect significant genes in real microarray data with imperceptible differential expression but higher variety in kurtosis and skewness. Those identified genes were confirmed with previous published literature or RT-PCR experiments performed in our lab.
Highlights
DNA microarray technologies have been widely used in biological studies, and simultaneously measure expression levels of thousands of genes across cells or tissues under different conditions [1]
To evaluate the performance of SWang, we carried out two statistical simulations to measure and compare the false positive rate (FPR) and statistical power (SP)
Our proposed SWang test has the lowest false positive rate in simulations and the best performance using real microarray data to detect differentially expressed genes (DEGs) compared with those popular tested methods, because SWang latently considers the complicated gene interaction relationships acting on gene expression in biological systems and incorporates more concealed information of the microarray data, like kurtosis, skewness, and high moments which are ignored by other methods [20,27]
Summary
DNA microarray technologies have been widely used in biological studies, and simultaneously measure expression levels of thousands of genes across cells or tissues under different conditions [1]. The selection of the DEGs is associated with both statistical and biological problems [2]. Gene interactions are nonlinear [3,4,5]. In nonlinear systems such parameters (mean, variance, skewness, kurtosis) can be interdependence [6], where skewness and kurtosis are defined as nonlinear index [7] and can be preserved even in a weakly nonlinear network or system [8,9]. The limitation of resources and high cost of the microarray experiments make the sample sizes usually much smaller relative to the number of considered genes, which results in the decrease of the statistical power (SP), high false positive rate (FPR), and the enlargement of sample’s error [10]
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