title: Beyond the 2×2 -contingency table: a primer on entropies and mutual information in various scenarios involving m diagnostic categories and n categories of diagnostic tests.
abstract: BACKGROUND
  Usual evaluation tools for diagnostic tests such as, sensitivity/specificity and ROC analyses, are designed for the discrimination between two diagnostic categories, using dichotomous test results. Information theoretical quantities such as mutual information allow in depth-analysis of more complex discrimination problems, including continuous test results, but are rarely used in clinical chemistry. This paper provides a primer on useful information theoretical concepts with a strong focus on typical diagnostic scenarios.
  
  
  RESULTS
  Information theoretical concepts are shortly explained. Mathematica CDF documents are provided which compute entropies and mutual information as function of pretest probabilities and the distribution of test results among the categories, and allow interactive exploration of the behavior of these quantities in comparison with more conventional diagnostic measures. Using data from a previously published study, the application of information theory to practical diagnostic problems involving up to 4×4 -contingency tables is demonstrated.
  
  
  CONCLUSIONS
  Information theoretical concepts are particularly useful for diagnostic problems requiring more than the usual binary classification. Quantitative test results can be properly analyzed, and in contrast to popular concepts such as ROC analysis, the effects of variations of pre-test probabilities of the diagnostic categories can be explicitly taken into account.
authors.affiliation: Institute of Physiological Chemistry, Center of Physiological Medicine, Medical University of Graz, A-8010 Graz, Austria. Electronic address: gilbert.reibnegger@medunigraz.at.
authors.forename: Gilbert
authors.initials: G
authors.lastname: Reibnegger
mesh_terms: D000293:Adolescent; D015415:Biomarkers / Q000097:blood / Q000134:cerebrospinal fluid; D002648:Child; D002675:Child, Preschool; D003955:Diagnostic Tests, Routine / Q000706:statistics & numerical data*; D019277:Entropy; D005260:Female; D006801:Humans; D007257:Information Theory; D007963:Leukocytes, Mononuclear / Q000378:metabolism / Q000473:pathology; D020852:Lyme Neuroborreliosis / Q000097:blood / Q000134:cerebrospinal fluid / Q000175:diagnosis* / Q000473:pathology; D008297:Male; D019798:Neopterin / Q000097:blood / Q000134:cerebrospinal fluid; D011336:Probability; D012680:Sensitivity and Specificity; D012984:Software
chemical_list: D015415:Biomarkers; D019798:Neopterin
keywords: Diagnostic test evaluation; Entropy; Information theory; Mutual information