title: Detecting hierarchical structure in molecular characteristics of disease using transitive approximations of directed graphs.
abstract: BACKGROUND
  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.
  
  
  BACKGROUND
  The software used in our analysis is freely available from http://compdiag.uni-regensburg.de/software/transApproxs.shtml.
authors.affiliation: Computational Diagnostics Group, Institute of Functional Genomics, University of Regensburg, 93053 Regensburg, Germany. Juby.Jacob@klinik.uni-regensburg.de
authors.forename: Juby
authors.initials: J
authors.lastname: Jacob
authors.forename: Marcel
authors.initials: M
authors.lastname: Jentsch
authors.forename: Dennis
authors.initials: D
authors.lastname: Kostka
authors.forename: Stefan
authors.initials: S
authors.lastname: Bentink
authors.forename: Rainer
authors.initials: R
authors.lastname: Spang
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D014408:Biomarkers, Tumor / Q000032:analysis*; D003936:Diagnosis, Computer-Assisted / Q000379:methods*; D006801:Humans; D008223:Lymphoma / Q000175:diagnosis* / Q000378:metabolism*; D015336:Molecular Probe Techniques; D009363:Neoplasm Proteins / Q000032:analysis*; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
chemical_list: D014408:Biomarkers, Tumor; D009363:Neoplasm Proteins