title: Combining Shapley value and statistics to the analysis of gene expression data in children exposed to air pollution.
abstract: BACKGROUND
  In gene expression analysis, statistical tests for differential gene expression provide lists of candidate genes having, individually, a sufficiently low p-value. However, the interpretation of each single p-value within complex systems involving several interacting genes is problematic. In parallel, in the last sixty years, game theory has been applied to political and social problems to assess the power of interacting agents in forcing a decision and, more recently, to represent the relevance of genes in response to certain conditions.
  
  
  RESULTS
  In this paper we introduce a Bootstrap procedure to test the null hypothesis that each gene has the same relevance between two conditions, where the relevance is represented by the Shapley value of a particular coalitional game defined on a microarray data-set. This method, which is called Comparative Analysis of Shapley value (shortly, CASh), is applied to data concerning the gene expression in children differentially exposed to air pollution. The results provided by CASh are compared with the results from a parametric statistical test for testing differential gene expression. Both lists of genes provided by CASh and t-test are informative enough to discriminate exposed subjects on the basis of their gene expression profiles. While many genes are selected in common by CASh and the parametric test, it turns out that the biological interpretation of the differences between these two selections is more interesting, suggesting a different interpretation of the main biological pathways in gene expression regulation for exposed individuals. A simulation study suggests that CASh offers more power than t-test for the detection of differential gene expression variability.
  
  
  CONCLUSIONS
  CASh is successfully applied to gene expression analysis of a data-set where the joint expression behavior of genes may be critical to characterize the expression response to air pollution. We demonstrate a synergistic effect between coalitional games and statistics that resulted in a selection of genes with a potential impact in the regulation of complex pathways.
authors.affiliation: Epidemiology and Biostatistics, National Cancer Research Institute, Genova, Italy. stefano.moretti@istge.it
authors.forename: Stefano
authors.initials: S
authors.lastname: Moretti
authors.forename: Danitsja
authors.initials: D
authors.lastname: van Leeuwen
authors.forename: Hans
authors.initials: H
authors.lastname: Gmuender
authors.forename: Stefano
authors.initials: S
authors.lastname: Bonassi
authors.forename: Joost
authors.initials: J
authors.lastname: van Delft
authors.forename: Jos
authors.initials: J
authors.lastname: Kleinjans
authors.forename: Fioravante
authors.initials: F
authors.lastname: Patrone
authors.forename: Domenico Franco
authors.initials: DF
authors.lastname: Merlo