Small errors in coronavirus testing can lead to surprisingly large problems

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New antibody tests could turn the tide by protecting the public from infection while restarting the economy. Giving “immunity passports” to those who tested positive for the disease would allow thousands of people to return to work.

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.