Designing and interpreting coronavirus disease 2019 (COVID-19) diagnostics mathematics, visual logistics, and low prevalence

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1 Scopus citations


Context.—Coronavirus infectious disease-19 (COVID-19) diagnostics require understanding of how predictive values depend on sensitivity, specificity, and especially, low prevalence. Clear expectations, high sensitivity and specificity, and manufacturer disclosure will facilitate excellence of tests. Objectives.—To derive mathematical equations for designing and interpreting COVID-19 tests, assess US Food and Drug Administration (FDA) Emergency Use Authorization and Health Canada minimum requirements, establish sensitivity and specificity tiers, and enhance clinical performance in low prevalence settings. Design.—PubMed and other sources generated articles on COVID-19 testing and prevalence. EndNote X9.1 consolidated references. Mathematica and open access software helped prove equations, perform recursive calculations, graph multivariate relationships, and visualize patterns, including a new relationship, predictive value geometric mean-squared. Results.—Derived equations were used to illustrate shortcomings of COVID-19 diagnostics in low prevalence. Visual logistics helped establish sensitivity/specificity tiers. FDA/Canada’s 90% sensitivity, 95% specificity minimum requirements generate excessive false positives at low prevalence. False positives exceed true positives at prevalence lower than 5.3%, or if sensitivity is improved to 100% and specificity to 98%, at prevalence lower than 2%. Recursive testing improves predictive value. Three tiers emerged from these results. With 100% sensitivity, physicians can select desired predictive values, then input local prevalence, to determine suitable specificity. Conclusions.—Understanding low prevalence impact will help health care providers meet COVID-19 needs for effective testing. Laypersons should receive clinical performance disclosure when submitting specimens. Home testing needs to meet the same high standards as other tests. In the long run, it will be more cost-effective to improve COVID-19 point-of-care tests rather than repeat testing multiple times.

Original languageEnglish (US)
Pages (from-to)291-307
Number of pages17
JournalArchives of Pathology and Laboratory Medicine
Issue number3
StatePublished - Mar 2021

ASJC Scopus subject areas

  • Pathology and Forensic Medicine
  • Medical Laboratory Technology


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