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Nonparametric analysis of replicated microarray experiments

UMR CNRS 5149, Université Montpellier II, France, Department of Microbiology, Howard University, Washington, DC, USA, Statistical Genetics and Bioinformatics Unit, Howard University, National Human Genome Center, Washington, DC, USA, gannoun{at}math.univ

Jérôme Saracco

UMR CNRS 5149, Université Montpellier II, France

Wolfgang Urfer

Department of Statistics, University of Dortmund, Germany

George E. Bonney

Department of Microbiology, Howard University, Washington, DC, USA, Statistical Genetics and Bioinformatics Unit, Howard University, National Human Genome Center, Washington, DC, USA

Microarrays are part of a new class of biotechnologies, which allow the monitoring of expression levels of thousands of genes simultaneously. In microarray data analysis, the comparison of gene expression profiles with respect to different conditions and the selection of biologically interesting genes are crucial tasks. Multivariate statistical methods have been applied to analyze these large data sets. To identify genes with altered expression under two experimental conditions, we propose a nonparametric statistical approach. Specifically, we propose estimating the distributions of a t-type statistic and its null statistic, using kernel methods. A comparison of these two distributions by means of a likelihood ratio test can identify genes with significantly changed expressions. A new method to provide more stable estimates of tail probabilities is proposed, as well as a method for the calculation of the cut-off point and the acceptance region. The methodology is applied to a leukaemia data set containing expression levels of 7129 genes, and is compared with normal mixture model and the traditional t-test.

Key Words: Kernel estimator • microarray • mixture modelling • regression modelling • t-test

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