Not everybody undergoes four Covid rapid antigen tests on the same day. Elon Musk does. “Two tests came back negative, two came back positive. Same machine, same test, same nurse,” Musk tweeted. He expressed disgust at the fiasco: “Something extremely bogus is going on,” and rushed to get PCR tests done from different labs. Earlier, Musk downplayed the pandemic and criticised coronavirus-related restrictions and lockdowns, referring to those as “fascist” and an infringement on individual liberty. The Tesla CEO then questioned the veracity of Covid testing. Afterwards, he said that he “most likely” had a moderate case of Covid-19. The SpaceX boss was forced to miss his firm’s historic rocket launch on November 15.
In response to Musk’s tweet, Emma Bell, a postdoctoral researcher specialising in bioinformatics, wrote: “Rapid antigen tests trade sensitivity for speed. They return a result in <30 minutes, but can only detect Covid-19 when you’re absolutely riddled with it. What’s bogus is that ... (he) didn’t read up on the test before complaining to his millions of followers.” This response to Musk’s tweet got tremendous attention in the media. However, while it was meant to confront Musk, hasn’t this strengthened his newest point that Covid-testing errors need serious introspection, at least?
Testing errors are inevitable in clinical diagnoses. In a New England Journal of Medicine article in 1989, American nephrologist Jerome P Kassirer wrote: “Absolute certainty in diagnosis is unattainable, no matter how much information we gather, how many observations we make or how many tests we perform.” No denying. While a 2009 British National Health System survey reported 15% misdiagnosis in the UK and a 2014 BMJ Quality & Safety article reported a 5% figure in the US, what’s the quantum of error of Covid-19 tests? We know that each of RT-PCR, rapid antigen and antibody-based tests are subject to possible errors.
An individual undergoing a test might be infected or not and the outcome may also be positive or negative. The likelihood of a positive finding when a disease is present is known as ‘sensitivity’ and the likelihood of a negative finding when the disease is absent is called ‘specificity’. Higher likelihoods of these events are desirable. In contrast, a person without the disease being diagnosed positive is called a ‘false positive’, while someone having the disease being diagnosed negative is a ‘false negative’. While both are errors, a false negative is more serious for a pandemic-causing disease as it leaves many infected people, who might be instrumental in spreading the pandemic, undetected. However, widely different estimates of these probabilities are obtained in different studies.
What’s the exact effect of such wrong diagnoses? For 90% sensitivity of a test, for example, about 10,000 false negative cases come up if one lakh infected people are tested. If two negative reports in two tests are used to declare someone Covid-free, about 1,000 false negatives would arise. And if all negative results in four tests are used to decide someone is Covid-free, there will still be 10 false negatives, on an average.
Even if sensitivity and specificity are too high (say, both are 99%), for one-time tests, there will be 950 false positive and 50 false negative cases on an average in a populace of 1,00,000, having the population prevalence rate of 5%. The number of false negative cases would increase if sensitivity is less or the population prevalence rate is higher. For example, if sensitivity and specificity are 95% each, and the population prevalence rate is 10%, there will be 500 false negative cases. In reality, a significant number of false negatives occur due to inefficient testing.
What would be the probability that a person actually has the disease provided two positive and two negative reports are obtained in four tests, as in the case of Elon Musk? Well, half the tests being positive doesn’t imply that the chance of disease is 50%—it depends on the prior condition of the individual. With 95% sensitivity and 90% specificity of a test, if someone is randomly picked from a community having 10% prevalence rate, a simple application of Bayes’ theorem for probability calculation yields this conditional probability to be 3%. On the other hand, the conditional probability of the person being Covid-affected is 21.8% for an individual having mild symptoms (say, 50% chance of disease). If the symptom is strong (i.e. 90% chance of Covid), the conditional likelihood of the person being Covid-affected will become 27%. Thus, the test results are utterly inconclusive in such a situation. It would take us nowhere except downplaying the chance of disease.
In response to Musk, Emma Bell, the academic who confronted him, also went into detail on Medium, sharing a graph exhibiting the probabilities of Covid detection for the available tests along different time points of the progression of the disease. It was explained why “two false negatives are in line with the known limitations of rapid antigen testing”. All these are indicative of limitations of the available test procedures in identifying the disease. In his 2015 book The Laws of Medicine, Pulitzer Prize-winning author Dr Siddhartha Mukherjee emphasised on “a strong intuition” and imagined medicine as a “machine that modifies probabilities”. Are strong medical intuitions still missing in the available Covid-19 testing mechanisms? Who knows, in retrospective studies in future, unavailability of efficient test procedures might be cited as a prime reason for the spread of this world-ravaging pandemic.
Atanu Biswas
Professor of Statistics, Indian Statistical Institute, Kolkata
(appubabale@gmail.com)