However, there is as much controversy as enthusiasm about this new idea. In the minds of many people, the ethical implications come to the fore. People in difficult economic situations may, in a perverse way, be encouraged to contract the disease so that they can return to work. Others argue that privacy concerns about centralized storage of medical data are a stumbling block. The World Health Organization (WHO) has also questioned the extent to which people who have recovered from COVID-19 will be protected from future infections.
Test accuracy is perhaps the least understood of the concerns. The United States Food and Drug Administration (FDA) has granted emergency authorization to seven manufacturers to place antibody tests for COVID-19 on the market. One of the first tests to be authorized was developed by Cellex. If you have antibodies to COVID-19, their test will tell you correctly 93.8% of the time (this is the “sensitivity” of the test). If you don’t, it will get this correct 95.6% of the time (this is the “specificity” of the test). Getting the correct result more than 90% of the time seems quite encouraging.
But consider what would happen if the test were given to 10,000 people as in the diagram below. Although (estimates vary widely), WHO recently suggested that only 3% of the world’s population may have had COVID-19 and recovered. This means that 9,700 of the 10,000 tested will not have the disease and only 300 will have it. Of the 300 patients recovered, 93.8% – or 281 – will be correctly informed that they have antibodies to the disease. Of the vast majority (9,700) of people who have not had the disease, 4.4% – or 427 – will be mistakenly told that they have had the disease and have recovered.
In short, many more people will receive false positive results than truly positive results. Up to 60% of people returned to the workforce may themselves be at risk of infection and unknowingly spread the disease to others, triggering a second wave of epidemics. If the actual prevalence of the disease in the population is only 1%, this figure could reach 80%.
The problem of false positives outweighing true positives occurs in all situations where the prevalence of disease in the test population is low and the test yields a significant proportion of false positives. As I discovered in the mathematics of life and death, this is common in screening programs. In breast cancer screening, for example, false positives can outweigh true positives in a three-to-one ratio, leading to significant anxiety and the possibility of unnecessary procedures.
Repeating the same antibody test could, however, reduce the rate of false positives. Retesting those who tested positive on the first test and issuing immunity passports only to those who received two positive results could reduce the proportion of false positives to less than 7% (see diagram below) – one significant improvement.
But the double test only works if the results of the two tests are independent. If, however, the reason for false positives is systematic – detection of antibodies to other coronaviruses, for example, then there is no reason to believe that a second test will do better than the first.
While false positives are a problem in the wider community, hospitals can face an acute problem due to false negatives. For various reasons (including inaccurate swab and variable viral load), the RT-PCR test used to diagnose people who currently have COVID-19 gives a false negative rate of up to 30%. In the mirror image of the situation in the community at large, when the prevalence of a disease in a group is high (as in those admitted to hospitals suspected of COVID-19), false negatives flood the true negatives with potentially disastrous consequences.
It is natural to assume that hospitalized people with severe COVID-19 symptoms likely have the disease. These people must be properly diagnosed in order to be isolated from the general hospital population and treated.
Assuming that 90% of these cases will have the disease, it is natural to wonder what proportion of negative test results is correct. Using the same mathematical argument as before, considering a representative sample of 10,000 patients, the diagram below shows that, in this context, a negative result can be correct as rarely as one in four cases.
This is a huge problem for hospitals. Patients who should be isolated may be wrongly referred to COVID-negative departments and given inappropriate treatment, or even sent home with the belief that they are not contagious only for spreading the disease on a large scale.
Understanding the surprising rates of false positives and false negatives for tests that at first glance seem fairly accurate could have far-reaching consequences for health policy as we progress through this pandemic. Failure to do our mathematical due diligence has the potential to push us past the tipping point beyond which the epidemic begins to grow again, leading to even more preventable deaths.
This article is republished from The Conversation by Christian Yates, Lecturer in Mathematical Biology, University of Bath under a Creative Commons license. Read the original article.
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