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153 – Recent Developments in Functional Data Analysis and Empirical Likelihood Methods in Biostatistics

Influence of Biological Conditions to Temporal Gene Expressions Based on Variance Analysis

at Anhui Normal University

Temporal gene expression data are of particular interest to researchers as they contain rich information in characterization of gene functions and have been widely used in biomedical studies and cancer early detection. In contrast to the rich literature on how to estimate the gene expressions over the time under a given condition, few researchers consider identifying the different effects of multiple conditions on the gene expression profiles. Besides its intrinsic effect, a gene has various expression patterns under different biological conditions and these conditions result in the variation of gene expression variance. In this paper, we will investigate the effects of conditions to the gene expressions and then classify the conditions according to the variational variance functions of gene expressions. We propose a non-linear regression model with log-normal distribution to characterize the variance functions of genes under the given conditions. Then, based on the parameter estimates, a chi-square test is proposed to test the equality of variance functions for different conditions. Furthermore, the Mahalanobis distance is used for the classification of conditions. The proposed methods are applied to the dataset of 18 genes in \emph{P. aeruginosa} expressed in 24 biological conditions. The simulation studies show that our methods are well performed for the classification of conditions for the temporal gene expressions.