Measures, Metrics, and Indicators Derived from the Ubiquitous Two-by-Two Contingency Table, Part B: Examples
Asian Journal of Medical Principles and Clinical Practice,
Page 26-50
Abstract
This paper (the second of two sibling papers) continues the tutorial exposition presented in the first part of indicators derived from the ubiquitous two-by-two contingency table (confusion matrix). The indicators considered herein are those given in the context of clinical testing or binary classification. We present a pedagogical program that computes all important indicators based on knowledge of either (a) the set of four entries of the contingency table , , , , or (b) the set of true (pre-test) prevalence, sensitivity, and specificity , . The paper presents a potpourri of test cases to reveal and unravel many of the properties and inter-relationships among the indicators studied. All our test cases confirm the theoretical results and arguments in the sister paper. In particular, these test cases collectively assert that the Matthews correlation coefficient (MCC) is the most reliable single metric derivable from the contingency matrix. A concise classification of types of prediction is given in terms of the set of four basic indicators , , or in terms of MCC alone.
Keywords:
- Diagnostic testing
- binary classification
- sensitivity
- specificity
- positive predictive value
- negative predictive value
- Matthews correlation coefficient
How to Cite
Rushdi, A. M. A., & Alghamdi, S. M. (2021). Measures, Metrics, and Indicators Derived from the Ubiquitous Two-by-Two Contingency Table, Part B: Examples. Asian Journal of Medical Principles and Clinical Practice, 4(3), 26-50. Retrieved from https://journalajmpcp.com/index.php/AJMPCP/article/view/30147
References
Rushdi RA, Rushdi AM, Talmees FA. Novel pedagogical methods for conditional-probability computations in medical disciplines. Journal of Advances in Medicine and Medical Research. 2018;25(10):1-15.
Rushdi AMA, Talmees FA. An exposition of the eight basic measures in diagnostic testing using several pedagogical tools. Journal of Advances in Mathematics and Computer Science. 2018;26(3):1-17.
Rushdi RA, Rushdi AM. Common fallacies of probability in medical context: A simple mathematical exposition. Journal of Advances in Medicine and Medical Research. 2018;26(1):1-21.
Rushdi RA, Rushdi AM. Karnaugh-map utility in medical studies: The case of Fetal Malnutrition. International Journal of Mathematical, Engineering and Management Sciences. 2018;3(3):220-244.
Rushdi AMA, Talmees FA. Computations of the eight basic measures in diagnostic testing. Chapter 6 in Advances in Mathematics and Computer Science. Book Publishers International, Hooghly, West Bengal, India: 2019;2:66-87.
Rushdi RAM, Rushdi AMA. Mathematics and examples for avoiding common probability fallacies in medical disciplines. Chapter 11 in Current Trends in Medicine and Medical Research, Vol. 1, Book Publishers International, Hooghly, West Bengal, India. 2019;1:106-132.
Rushdi AMA, Serag HA. Solutions of ternary problems of conditional probability with applications to mathematical epidemiology and the COVID-19 pandemic. International Journal of Mathematical, Engineering and Management Sciences. 2020;5(5):787-811.
Serag HA, Rushdi AMA. Checking consistency among the four basic indicators of diagnostic testing in Saudi medical Journals. Asian Journal of Medical Principles and Clinical Practice. 2021; 4(1):14-27.
Rushdi AMA, Serag HA. Inter-relationships among the four basic measures of diagnostic testing: A signal-flow-graph approach, Journal of King Abdulaziz University: Computing and Information Technology Sciences. 2021;10(1):49-72.
Rushdi AM, Serag HA. Has the pandemic triggered a ‘paperdemic’? Towards an assessment of diagnostic indicators for COVID-19. International Journal of Pathogen Research. 2021;6(2):28-49.
Rushdi, RA, Rushdi, AM, Talmees, FA. Review of Methods for Conditional-Probability Computations in Medical Disciplines, a Chapter in Highlights on Medicine and Medical Research, Book Publishers International, Hooghly, West Bengal, India, 2021.
Rushdi MA, Rushdi AM. Measures, metrics and indicators derived from the ubiquitous two-by-two contingency table, Part A: Background. Asian Journal of Medical Principles and Clinical Practice; 2021.
Chicco D. Ten quick tips for machine learning in computational biology. BioData Mining. 2017;10(1):1-7.
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(1):1-3.
Yao J, Shepperd M. Assessing software defection prediction performance: Why using the Matthews correlation coefficient matters. In Proceedings of the Evaluation and Assessment in Software Engineering. 2020;120-129.
Chicco D, Tötsch N, Jurman G. The Matthews correlation coefficient (MCC) is more reliable than balanced accuracy, bookmaker informedness, and markedness in two-class confusion matrix evaluation. BioData Mining. 2021;14(1):1-22.
Gigerenzer G, Gaissmaier W, Kurz-Milcke E, Schwartz LM, Woloshin S. Helping doctors and patients make sense of health statistics. Psychological Science in the Public Interest. 2007;8(2):53-96.
Glaros AG, Kline RB. Understanding the accuracy of tests with cutting scores: The sensitivity, specificity, and predictive value model. Journal of Clinical Psychology. 1988;44(6):1013-1023.
Gaddis GM, Gaddis ML. Introduction to biostatistics: part 3, sensitivity, specificity, predictive value, and hypothesis testing. Annals of Emergency Medicine. 1990; 19(5):591-597.
Buckland M, Gey F. The relationship between recall and precision. Journal of the American Society for Information Science. 1994;45(1):12-19.
Brenner H, Gefeller OL. Variation of sensitivity, specificity, likelihood ratios and predictive values with disease prevalence. Statistics in Medicine. 1997;16(9):981-891.
Moons KG, van Es GA, Deckers JW, Habbema JD, Grobbee DE. Limitations of sensitivity, specificity, likelihood ratio, and Bayes' theorem in assessing diagnostic probabilities: a clinical example. Epidemiology. 1997;8(1):12-17.
Chu K. An introduction to sensitivity, specificity, predictive values and likelihood ratios. Emergency Medicine. 1999; 11(3):175-181.
Grimes DA, Schulz KF. Uses and abuses of screening tests. The Lancet. 2002; 359(9309):881-884.
Goutte C, Gaussier E. A probabilistic interpretation of precision, recall and F-score, with implication for evaluation. In European Conference on Information Retrieval 2005 Mar 21 (pp. 345-359). Springer, Berlin, Heidelberg.
Akobeng AK. Understanding diagnostic tests 1: sensitivity, specificity and predictive values. Acta Paediatrica. 2007; 96(3):338-341.
Parikh R, Mathai A, Parikh S, Sekhar GC, Thomas R. Understanding and using sensitivity, specificity and predictive values. Indian Journal of Ophthalmology. 2008; 56(1):45-50.
Rushdi AMA, Talmees FA. An exposition of the eight basic measures in diagnostic testing using several pedagogical tools. Journal of Advances in Mathematics and Computer Science. 2018;26(3):1-17.
Rushdi RA, Rushdi AM. Common fallacies of probability in medical context: A simple mathematical exposition. Journal of Advances in Medicine and Medical Research. 2018;26(1):1-21.
Rushdi RA, Rushdi AM. Karnaugh-map utility in medical studies: The case of Fetal Malnutrition. International Journal of Mathematical, Engineering and Management Sciences. 2018;3(3):220-244.
Rushdi AMA, Talmees FA. Computations of the eight basic measures in diagnostic testing. Chapter 6 in Advances in Mathematics and Computer Science. Book Publishers International, Hooghly, West Bengal, India: 2019;2:66-87.
Rushdi RAM, Rushdi AMA. Mathematics and examples for avoiding common probability fallacies in medical disciplines. Chapter 11 in Current Trends in Medicine and Medical Research, Vol. 1, Book Publishers International, Hooghly, West Bengal, India. 2019;1:106-132.
Rushdi AMA, Serag HA. Solutions of ternary problems of conditional probability with applications to mathematical epidemiology and the COVID-19 pandemic. International Journal of Mathematical, Engineering and Management Sciences. 2020;5(5):787-811.
Serag HA, Rushdi AMA. Checking consistency among the four basic indicators of diagnostic testing in Saudi medical Journals. Asian Journal of Medical Principles and Clinical Practice. 2021; 4(1):14-27.
Rushdi AMA, Serag HA. Inter-relationships among the four basic measures of diagnostic testing: A signal-flow-graph approach, Journal of King Abdulaziz University: Computing and Information Technology Sciences. 2021;10(1):49-72.
Rushdi AM, Serag HA. Has the pandemic triggered a ‘paperdemic’? Towards an assessment of diagnostic indicators for COVID-19. International Journal of Pathogen Research. 2021;6(2):28-49.
Rushdi, RA, Rushdi, AM, Talmees, FA. Review of Methods for Conditional-Probability Computations in Medical Disciplines, a Chapter in Highlights on Medicine and Medical Research, Book Publishers International, Hooghly, West Bengal, India, 2021.
Rushdi MA, Rushdi AM. Measures, metrics and indicators derived from the ubiquitous two-by-two contingency table, Part A: Background. Asian Journal of Medical Principles and Clinical Practice; 2021.
Chicco D. Ten quick tips for machine learning in computational biology. BioData Mining. 2017;10(1):1-7.
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(1):1-3.
Yao J, Shepperd M. Assessing software defection prediction performance: Why using the Matthews correlation coefficient matters. In Proceedings of the Evaluation and Assessment in Software Engineering. 2020;120-129.
Chicco D, Tötsch N, Jurman G. The Matthews correlation coefficient (MCC) is more reliable than balanced accuracy, bookmaker informedness, and markedness in two-class confusion matrix evaluation. BioData Mining. 2021;14(1):1-22.
Gigerenzer G, Gaissmaier W, Kurz-Milcke E, Schwartz LM, Woloshin S. Helping doctors and patients make sense of health statistics. Psychological Science in the Public Interest. 2007;8(2):53-96.
Glaros AG, Kline RB. Understanding the accuracy of tests with cutting scores: The sensitivity, specificity, and predictive value model. Journal of Clinical Psychology. 1988;44(6):1013-1023.
Gaddis GM, Gaddis ML. Introduction to biostatistics: part 3, sensitivity, specificity, predictive value, and hypothesis testing. Annals of Emergency Medicine. 1990; 19(5):591-597.
Buckland M, Gey F. The relationship between recall and precision. Journal of the American Society for Information Science. 1994;45(1):12-19.
Brenner H, Gefeller OL. Variation of sensitivity, specificity, likelihood ratios and predictive values with disease prevalence. Statistics in Medicine. 1997;16(9):981-891.
Moons KG, van Es GA, Deckers JW, Habbema JD, Grobbee DE. Limitations of sensitivity, specificity, likelihood ratio, and Bayes' theorem in assessing diagnostic probabilities: a clinical example. Epidemiology. 1997;8(1):12-17.
Chu K. An introduction to sensitivity, specificity, predictive values and likelihood ratios. Emergency Medicine. 1999; 11(3):175-181.
Grimes DA, Schulz KF. Uses and abuses of screening tests. The Lancet. 2002; 359(9309):881-884.
Goutte C, Gaussier E. A probabilistic interpretation of precision, recall and F-score, with implication for evaluation. In European Conference on Information Retrieval 2005 Mar 21 (pp. 345-359). Springer, Berlin, Heidelberg.
Akobeng AK. Understanding diagnostic tests 1: sensitivity, specificity and predictive values. Acta Paediatrica. 2007; 96(3):338-341.
Parikh R, Mathai A, Parikh S, Sekhar GC, Thomas R. Understanding and using sensitivity, specificity and predictive values. Indian Journal of Ophthalmology. 2008; 56(1):45-50.
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