Skip to main content
SpringerLink
Log in

Unitary Measures

  • Chapter
  • First Online:
The 2x2 Matrix

  • 435 Accesses

Abstract

This chapter considers unitary measures of test outcome which can be derived from the 2 × 2 contingency table. In different disciplines, different measures are typically used, for example Youden index in medical decision making and F measure in information retrieval and machine learning. Of these various measures, Matthews’ correlation coefficient may be the optimal choice.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Boughorbel S, Jarray F, El-Anbari M. Optimal classifier for imbalanced data using Matthews Correlation Coefficient metric. PLoS One. 2017;12(6):e0177678.

    Article  Google Scholar 

  2. Brenner H, Gefeller O. Variation of sensitivity, specificity, likelihood ratios and predictive values with disease prevalence. Stat Med. 1997;16:981–91.

    Article  Google Scholar 

  3. Chicco D. Ten quick tips for machine learning in computational biology. BioData Min. 2017;10:35.

    Article  Google Scholar 

  4. Chicco D, Jurman G. The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation. BMC Genomics. 2020;21:6.

    Article  Google Scholar 

  5. Connell FA, Koepsell TD. Measures of gain in certainty from a diagnostic test. Am J Epidemiol. 1985;121:744–53.

    Article  Google Scholar 

  6. De Vet HCW, Mokkink LB, Terwee CB, Hoekstra OS, Knol DL. Clinicians are right not to like Cohen’s κ. BMJ. 2013;346:f2515.

    Google Scholar 

  7. Dice LR. Measures of the amount of ecological association between species. Ecology. 1945;26:297–302.

    Article  Google Scholar 

  8. Doswell CA III, Davies-Jones R, Keller DL. On summary measures of skill in rare event forecasting based on contingency tables. Weather Forecast. 1990;5:576–85.

    Article  Google Scholar 

  9. Gilbert GK. Finley’s tornado predictions. Am Meteorol J. 1884;1:166–72.

    Google Scholar 

  10. Heston TF. Standardized predictive values. J Magn Reson Imaging. 2014;39:1338.

    Article  Google Scholar 

  11. Hilden J, Glasziou P. Regret graphs, diagnostic uncertainty and Youden’s index. Stat Med. 1996;15:969–86.

    Article  Google Scholar 

  12. Hsieh S, McGrory S, Leslie F, Dawson K, Ahmed S, Butler CR, et al. The Mini-Addenbrooke’s Cognitive Examination: a new assessment tool for dementia. Dement Geriatr Cogn Disord. 2015;39:1–11.

    Article  Google Scholar 

  13. Hunink MGM, Weinstein MC, Wittenberg E, Drummond MF, Pliskin JS, Wong JB, et al. Decision making in health and medicine. Integrating evidence and values. 2nd ed. Cambridge: Cambridge University Press; 2014.

    Book  Google Scholar 

  14. Jaccard P. The distribution of the flora in the alpine zone. New Phytologist. 1912;11:37–50.

    Article  Google Scholar 

  15. Jolliffe IT. The Dice co-efficient: a neglected verification performance measure for deterministic forecasts of binary events. Meteorol Appl. 2016;23:89–90.

    Article  Google Scholar 

  16. Larner AJ. MACE for diagnosis of dementia and MCI: examining cut-offs and predictive values. Diagnostics (Basel). 2019;9:E51.

    Article  Google Scholar 

  17. Larner AJ. New unitary metrics for dementia test accuracy studies. Prog Neurol Psychiatry. 2019;23(3):21–5.

    Article  Google Scholar 

  18. Larner AJ. Applying Kraemer’s Q (positive sign rate): some implications for diagnostic test accuracy study results. Dement Geriatr Cogn Dis Extra. 2019;9:389–96.

    Article  Google Scholar 

  19. Larner AJ. What is test accuracy? Comparing unitary accuracy metrics for cognitive screening instruments. Neurodegener Dis Manag. 2019;9:277–81.

    Article  Google Scholar 

  20. Larner AJ. Defining “optimal” test cut-off using global test metrics: evidence from a cognitive screening instrument. Neurodegener Dis Manag. 2020;10:223–30.

    Article  Google Scholar 

  21. Larner AJ. Manual of screeners for dementia: pragmatic test accuracy studies. London: Springer; 2020.

    Book  Google Scholar 

  22. Larner AJ. Mini-Addenbrooke’s Cognitive Examination (MACE): a useful cognitive screening instrument in older people? Can Geriatr J. 2020;23:199–204.

    Article  Google Scholar 

  23. Larner AJ. Mini-Cog versus Codex (cognitive disorders examination): is there a difference? Dement Neuropsychol. 2020;14:128–33.

    Article  Google Scholar 

  24. Larner AJ. Screening for dementia: Q* index as a global measure of test accuracy revisited. medRxiv. 2020; https://doi.org/10.1101/2020.04.01.20050567.

  25. Larner AJ. The “attended alone” and “attended with” signs in the assessment of cognitive impairment: a revalidation. Postgrad Med. 2020;132:595–600.

    Article  Google Scholar 

  26. Larner AJ. Assessing cognitive screening instruments with the critical success index. Prog Neurol Psychiatry. 2021;25(3):33–7.

    Google Scholar 

  27. Linn S, Grunau PD. New patient-oriented summary measure of net total gain in certainty for dichotomous diagnostic tests. Epidemiol Perspect Innov. 2006;3:11.

    Article  Google Scholar 

  28. Matthews BW. Comparison of the predicted and observed secondary structure of T4 phage lysozyme. Biochem Biophys Acta. 1975;405:442–51.

    Google Scholar 

  29. Mitchell AJ. Index test. In: Kattan MW, editor. Encyclopedia of medical decision making. Los Angeles: Sage; 2009. p. 613–7.

    Google Scholar 

  30. Mitchell AJ. Sensitivity x PPV is a recognized test called the clinical utility index (CUI+). Eur J Epidemiol. 2011;26:251–2.

    Article  Google Scholar 

  31. Palmer WC, Allen RA. Note on the accuracy of forecasts concerning the rain problem. U.S. Weather Bureau manuscript: Washington, DC; 1949.

    Google Scholar 

  32. Pencina MJ, D’Agostino RB Sr, D’Agostino RB Jr, Vasan RS. Evaluating the added predictive ability of a new marker: from area under the ROC curve to reclassification and beyond. Stat Med. 2008;27:157–72.

    Article  MathSciNet  Google Scholar 

  33. Perkins NJ, Schisterman EF. The inconsistency of “optimal” cutpoints obtained using two criteria based on the receiver operating characteristic curve. Am J Epidemiol. 2006;163:670–5.

    Article  Google Scholar 

  34. Powers DMW. Evaluation: from precision, recall and F-measure to ROC, informedness, markedness and correlation. J Mach Learn Technol. 2011;2:37–63.

    Google Scholar 

  35. Powers DMW. What the F measure doesn’t measure … Features, flaws, fallacies and fixes. arXiv. 2015; 1503.06410.2015.

    Google Scholar 

  36. Richard E, Schmand BA, Eikelenboom P, Van Gool WA. The Alzheimer’s Disease Neuroimaging Initiative. MRI and cerebrospinal fluid biomarkers for predicting progression to Alzheimer’s disease in patients with mild cognitive impairment: a diagnostic accuracy study. BMJ Open. 2013;3:e002541.

    Article  Google Scholar 

  37. Schaefer JT. The critical success index as an indicator of warning skill. Weather Forecast. 1990;5:570–5.

    Article  Google Scholar 

  38. Schisterman EF, Perkins NJ, Liu A, Bondell H. Optimal cut-point and its corresponding Youden Index to discriminate individuals using pooled blood samples. Epidemiology. 2005;16:73–81.

    Article  Google Scholar 

  39. Smits N. A note on Youden’s J and its cost ratio. BMC Med Res Methodol. 2010;10:89.

    Article  Google Scholar 

  40. Sørensen T. A method of establishing groups of equal amplitude in plant sociology based on similarity of species and its application to analyses of the vegetation on Danish commons. K Dan Vidensk Sels. 1948;5:1–34.

    Google Scholar 

  41. Youden WJ. Index for rating diagnostic tests. Cancer. 1950;3:32–5.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Cognitive Function Clinic, Walton Centre for Neurology and Neurosurgery, Liverpool, UK

    A. J. Larner

Authors
  1. A. J. Larner
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Larner, A.J. (2021). Unitary Measures. In: The 2x2 Matrix. Springer, Cham. https://doi.org/10.1007/978-3-030-74920-0_4

Download citation

Publish with us

Policies and ethics

Search

Navigation