Screening test and interpretation for covid-19: sensitivity/specificity and positive/negative predictive values and the role of Bayes’ theorem (Part I)

“Math is the logic of certainty, and statistics is the logic of uncertainty.”

-Joseph Blitzstein, Harvard statistician

It is supremely frustrating for scientists who work with a few of the world leaders who have extreme form of confirmation bias and refuse to update their beliefs based on new observations in the COVID-19 reality. A screening test should be designed to reduce morbidity and mortality in the population by detecting the disease at an early phase to render a treatment effective and improve outcome. The scientists have incessantly discussed the critical issue of widespread screening as one of the essential strategies for containing this pandemic. It is therefore timely to discuss the screening tests for COVID-19 as well as its interpretation to having the disease. The two screening tests are: 1) the viral test (reverse transcriptase-polymerase chain reaction, or RT-PCR) is a swab from the respiratory system to check for nucleic acid sequences of SARS-CoV-2 virus and 2) the antibody test requires a blood sample to detect presence of antibodies that indicate a past infection; only the former is for detecting current infection.

It is essential that there is good understanding of the confusion matrix that numerically delineates the relationship between screening test and disease. The RT-PCR test has a sensitivity (the probability of a positive test result given that a person has COVID-19, or true positives/(true positives + false negatives); also called true positive rate or “recall”) of about 60-95% (depending on time of disease onset, swab technique and test execution). Assessment of the sensitivity of these screening tests remain elusive due to the proportion of infected people who remain asymptomatic and lack of scrutiny over checking against reference standards. The RT-PCR test has a specificity (also called true negative rate and is defined as the probability of a negative test result given that a person does not have COVID-19, or true negatives/(true negatives + false positives)) that is much higher (95+%). The RT-PCR test, therefore, is not an ideal screening test for this coronavirus since a false negative test has more dire consequences (leading to potentially a super spreader event or at least infectivity in the public) than a false positive test (leading to unnecessary quarantine and observation).

So a very low false negative rate is more important than a low false positive rate for COVID-19 surveillance as a false negative RT-PCR test is particularly dangerous given the high infectivity of this novel coronavirus. Even though some healthcare pundits have stated in the media that a high positive predictive value (true positives/(true positives + false positives), also called “precision”) is what a screening test is needed for COVID-19, perhaps they really mean a high negative predictive value (true negatives/(true negatives + false negatives)) is of more informative as it indicates a lower number of false negative tests. Overall, a high sensitivity as well as high negative predictive value are preferred given that a false negative test has deleterious consequences in this pandemic. In another clinical scenario, however, a false positive test may lead to similarly serious consequences (such as an invasive procedure for a falsely positive screening test).

The general observation is that we humans tend to over-rely on the screening test itself and concomitantly underestimate the importance of a pre-test assessment (patient symptoms, local prevalence, exposure risk, etc). Next time, we will discuss this essential pretest probability-screening test coupling in the context of Bayes’ theorem and prior probabilities.

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