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 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 <5.3% prevalence, or if sensitivity is improved to 100% and specificity to 98%, at <2% prevalence. 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 healthcare 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 POC tests rather than repeat testing multiple times.

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Author notes

The author has no relevant financial interest in the products or companies referenced in this article.