Bioinformatics Advance Access originally published online on February 19, 2008
Bioinformatics 2008 24(7):995-1001; doi:10.1093/bioinformatics/btn056
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Detecting hierarchical structure in molecular characteristics of disease using transitive approximations of directed graphs
1Computational Diagnostics Group, Institute of Functional Genomics, University of Regensburg, 93053 Regensburg, Germany and 2Max Planck Institute for Molecular Genetics, Ihnestaße 63/73, 14195 Berlin, Germany
*To whom correspondence should be addressed.
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Abstract |
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Motivation: Molecular diagnostics aims at classifying diseases into clinically relevant sub-entities based on molecular characteristics. Typically, the entities are split into subgroups, which might contain several variants yielding a hierarchical model of the disease. Recent years have introduced a plethora of new molecular screening technologies to molecular diagnostics. As a result molecular profiles of patients became complex and the classification task more difficult.
Results: We present a novel tool for detecting hierarchical structure in binary datasets. We aim for identifying molecular characteristics, which are stochastically implying other characteristics. The final hierarchical structure is encoded in a directed transitive graph where nodes represent molecular characteristics and a directed edge from a node A to a node B denotes that almost all cases with characteristic B also display characteristic A. Naturally, these graphs need to be transitive. In the core of our modeling approach lies the problem of calculating good transitive approximations of given directed but not necessarily transitive graphs. By good transitive approximation we understand transitive graphs, which differ from the reference graph in only a small number of edges. It is known that the problem of finding optimal transitive approximation is NP-complete. Here we develop an efficient heuristic for generating good transitive approximations. We evaluate the computational efficiency of the algorithm in simulations, and demonstrate its use in the context of a large genome-wide study on mature aggressive lymphomas.
Availability: The software used in our analysis is freely available from http://compdiag.uni-regensburg.de/software/transApproxs.shtml
Contact: Juby.Jacob{at}klinik.uni-regensburg.de, Rainer.Spang{at}klinik.uni-regensburg.de
Supplementary information: Supplementary data are available at Bioinformatics online.
Associate Editor: Thomas Lengauer
Received on October 16, 2007; revised on November 16, 2007; accepted on February 7, 2008
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