title: Algebraic stability indicators for ranked lists in molecular profiling.
abstract: BACKGROUND
  We propose a method for studying the stability of biomarker lists obtained from functional genomics studies. It is common to adopt resampling methods to tune and evaluate marker-based diagnostic and prognostic systems in order to prevent selection bias. Such caution promotes honest estimation of class prediction, but leads to alternative sets of solutions. In microarray studies, the difference in lists may be bewildering, also due to the presence of modules of functionally related genes. Methods for assessing stability understand the dependency of the markers on the data or on the predictor's type and help selecting solutions.
  
  
  RESULTS
  A computational framework for comparing sets of ranked biomarker lists is presented. Notions and algorithms are based on concepts from permutation group theory. We introduce several algebraic indicators and metric methods for symmetric groups, including the Canberra distance, a weighted version of Spearman's footrule. We also consider distances between partial lists and an aggregation of sets of lists into an optimal list based on voting theory (Borda count). The stability indicators are applied in practical situations to several synthetic, cancer microarray and proteomics datasets. The addressed issues are predictive classification, presence of modules, comparison of alternative biomarker lists, outlier removal, control of selection bias by randomization techniques and enrichment analysis.
  
  
  BACKGROUND
  Supplementary Material and software are available at the address http://biodcv.fbk.eu/listspy.html
authors.affiliation: FBK, via Sommarive 18, I-38100 Povo (Trento), Italy.
authors.forename: Giuseppe
authors.initials: G
authors.lastname: Jurman
authors.forename: Stefano
authors.initials: S
authors.lastname: Merler
authors.forename: Annalisa
authors.initials: A
authors.lastname: Barla
authors.forename: Silvano
authors.initials: S
authors.lastname: Paoli
authors.forename: Antonio
authors.initials: A
authors.lastname: Galea
authors.forename: Cesare
authors.initials: C
authors.lastname: Furlanello
mesh_terms: D000465:Algorithms; D014408:Biomarkers, Tumor / Q000032:analysis*; D003627:Data Interpretation, Statistical; D020869:Gene Expression Profiling / Q000379:methods*; D006801:Humans; D009363:Neoplasm Proteins / Q000032:analysis*; D009369:Neoplasms / Q000378:metabolism*; D020411:Oligonucleotide Array Sequence Analysis / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
chemical_list: D014408:Biomarkers, Tumor; D009363:Neoplasm Proteins