International Journal of Analytical, Pharmaceutical and Biomedical Sciences Page 65 Available online at www.ijapbs.com Research Article Volume: 4: Issue-1: January-2015 Copyrights@2014 ISSN:2278-0246 Coden : IJAPBS www.ijapbs.com NONPARAMETRIC CORRELATION COEFFICIENT METHODS TO CONSTRUCTING THREE-WAY GENE INTERACTIONS IN MICROARRAY DATA Hamid Alavi Majd 1 , Atefeh Talebi 2 , Kambiz Gilany 3 , Seyyed-Mohammad Tabatabaei 4 1 Professor at Shahid Beheshti University of Medical Sciences, Department of Biostatistics, School of Paramedical Sciences. E-mail: alavimajd@gmail.com 2 PhD Student of Biostatistics, School of Paramedial Sciences, Students’ research committee, Shahid Beheshti University of Medical Sciences. Email: a_talebi5855@yahoo.com. Corresponding author. Phone number: 021-22707347, Fax number: 021-22721150 3 PhD in Science Biomedicine. Avicenna Research Institute (ARI), Academic Center for Education, Culture and Research (ACECR), Reproductive Biotechnology Research Center (RBRC), Department of Embryology and Andrology. E-mail: k.gilany@avicenna.ac.ir. 4 Seyyed-Mohammad Tabatabaei, Department of Medical Informatics, Department of Medical Informatics, Students’ research committee, Shahid Beheshti University of Medical Sciences. Email: sm.tabatabaei@sbmu.ac.ir. ABSTRACT: In the study we extract the venous thromboembolism (VTE) data set from KEGG database including 70 adults with one or more prior VTE on warfarin and 63 healthy controls. Then we construct three- way gene networks by using arithmetic mean nonparametric methods such as Gini index, Kendall correlation coefficient, Spearman rank correlation coefficient. The R software version R-3.1.2 was used for statistical analysis. Ranks have a number of desirable properties: they are invariant under monotonic transformations of the individual variables, robust in outliers and unexpected observations. They are able to detect not only the linear relationships, but also any kind of monotone relation without making any assumptions about the distributions of the variables. The results of nonparametric correlation coefficients are not the same. The result in based on Spearman rank and Gini index are the same and both are different from Kenall’s tau. The relationships were based on the arithmetic mean and the threshold of P-value greater than 0.95. Abreviations: GSE, Gene Set Enrichment, VTE, Venous thrombosis, RNA, Ribonucleic acid, KEGG, Kyoto Encyclopedia of Genes and Genomes. Keywords: Gene Network, Gene Interaction, Gene Expression Data, Correlation Indices. INTRODUCTION High-throughput genomic data is a full resource for explaining how genes are jointed [1-4]. A usual method is to cluster genes and gene set analysis by using pair-wise correlation as a distance metric [5, 6]. Although, pair-wise correlation is too simple to explain the complicated connections among genes since it is rare to search pair of genes that are fundamentally co-expressed. There are a lot of gene network constructions such as Boolean network [7, 8] , mutual information and Bayesian network [9] to discover more complex interactions and to detect interaction networks from gene expression data. One of disadvantage of these methods is the need for large samples of expression data. Networks offer a natural way to model interactions between genes, with nodes representing genes and edges representing various interaction types inferred from different data sources [10]. Each node represents a gene and each edge between two genes represents significant relationship in the network that is evaluated from expression profiles of a subset of the microarray data set. In several studies were assumed that certain biological conditions/modules may affect the co-expression relationship between a gene pair, they assumed that there is a third gene, the controller gene, associated with the