New antibody tests might be game-changers in keeping the public safe from infection while restarting the economy. Giving “immunity passports” to those who have tested positive for having had the disease would allow thousands of people to return to work.

However, there is as much controversy as there is excitement about this new idea. Foremost in many people’s minds are the ethical implications. People in difficult economic circumstances may, perversely, be incentivized to contract the disease so they can return to work. For others, privacy issues related to centralized storage of medical data is a stumbling block. The World Health Organization (WHO) has also cast doubt on the extent to which people who have recovered from COVID-19 will be protected from future infection.

Perhaps the least well understood of the concerns is the accuracy of the tests. The US Food and Drug Administration (FDA) has granted an emergency use authorization to seven manufacturers to bring antibody tests for COVID-19 to market. One of the first tests to gain authorization was developed by Cellex. If you have antibodies against COVID-19 their test will tell you this correctly 93.8% of the time (this is the test’s “sensitivity”). If you don’t, it will get this correct 95.6% of the time (this is the test’s “specificity”). Getting the correct result more than 90% of the time sounds pretty encouraging.

But let’s consider what would happen if the test were given to 10,000 people as in the diagram below. Although (estimates vary significantly), the WHO suggested recently that as few as 3% of the global population may have had COVID-19 and recovered. This means that 9,700 of the 10,000 tested will not have had the disease and only 300 will have. Of the 300 recovered patients, 93.8% – or 281 – will be correctly told they have antibodies against the disease. Of the vast majority (9,700) of people who haven’t had the disease, 4.4% – or 427 – will be incorrectly told that they have had the disease and recovered.