Gene set analysis using biological pathways has become a widely used statistical approach for gene expression analysis. A biological pathway can be represented through a graph where genes and their interactions are, respectively, nodes and edges of the graph. From a biological point of view only some portions of a pathway are expected to be altered; however, few methods using pathway topology have been proposed and none of them tries to identify the signal paths, within a pathway, mostly involved in the biological problem. Here, we present a novel algorithm for pathway analysis , that tries to fill in this gap. implements a two-step empirical approach based on the exploitation of graph decomposition into a junction tree to reconstruct the most relevant signal path. In the first step selects significant pathways according to statistical tests on the means and the concentration matrices of the graphs derived from pathway topologies. Then, it identifies within these pathways the signal paths having the greatest association with a specific phenotype. We test our approach on simulated and two real expression datasets. Our results demonstrate the efficacy of in the identification of signal transduction paths totally coherent with the biological problem.
Background Recently, a great effort in microarray data analysis is directed towards the study of the so-called gene sets. A gene set is defined by genes that are, somehow, functionally related. For example, genes appearing in a known biological pathway naturally define a gene set. The gene sets are usually identified from a priori biological knowledge. Nowadays, many bioinformatics resources store such kind of knowledge (see, for example, the Kyoto Encyclopedia of Genes and Genomes, among others). Although pathways maps carry important information about the structure of correlation among genes that should not be neglected, the currently available multivariate methods for gene set analysis do not fully exploit it. Results We propose a novel gene set analysis specifically designed for gene sets defined by pathways. Such analysis, based on graphical models, explicitly incorporates the dependence structure among genes highlighted by the topology of pathways. The analysis is designed to be used for overall surveillance of changes in a pathway in different experimental conditions. In fact, under different circumstances, not only the expression of the genes in a pathway, but also the strength of their relations may change. The methods resulting from the proposal allow both to test for variations in the strength of the links, and to properly account for heteroschedasticity in the usual tests for differential expression. Conclusions The use of graphical models allows a deeper look at the components of the pathway that can be tested separately and compared marginally. In this way it is possible to test single components of the pathway and highlight only those involved in its deregulation.
LoessM R function is freely available at http://gefu.cribi.unipd.it/papers/miRNA-simulation/
We consider likelihood based inference for the parameter of a skewnormal distribution. One of the problems shown by this model is the singularity of the Fisher information matrix when skewness is absent. We derive the rate of convergence to the asymptotic distribution of the maximum likelihood estimator and study an alternative parameterization which overcomes problems related to the singularity of the information matrix.
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