Unaware of Bayes’s insight, consumers will interpret positive test result as a near-certain indication that they are immune.

抗体検査であっても偽陽性の問題があり信用出来るデータにならないので、免疫パスポートなんて無理、という議論。アメリカの「検査が全て」病はどうもこの辺の議論に踏みこまないので、ようやく検査の精度の問題が出てきたという印象。 https://t.co/PIx4iT0xRc

— Kazuto Suzuki (@KS_1013) May 1, 2020

Immunity passports are controversial for many reasons: We don’t know the extent to which exposure to the novel coronavirus protects against future infection, for example, and a passport system raises important issues involving medical privacy. (To prevent potential cheating, testing would have to be officially verified and, most likely, stored in a centralized database.) Passports could create perverse incentives for people in precarious economic circumstances to deliberately catch the disease so that — if they recover — they can return to normal life. They could rend social cohesion by splitting the population into groups with greater and fewer rights.

But there’s an even more basic problem with immunity passports: They might fail entirely because of false positive test results. When it comes to PCR testing for the active virus, false negatives get most of the attention, because they open the door to the disease being spread by people who wrongly think they don’t have it. But in the context of immunity passports, false positives are especially pernicious: People would stop social distancing yet would continue to be at risk of infection.


Bayes’ Theorem reveals that, when you are testing for a condition that is rare, the actual false positive rate can be much greater than it first appears.

To grasp why, imagine testing members of a secluded tribe that had not come in contact with outsiders — and so could not possibly have been infected by the coronavirus. If we gave antibody tests that were “96 percent accurate” to all members of the tribe, a small number would receive a positive test result. Whenever this happened, we could be 100 percent sure it was a false positive.


Is there any way out of the false-positive cul-de-sac? The lesson of Bayes is not to discard test results, but to make use of all available information. A positive test result for a member of a secluded tribe, or from a population with rates known to be very low, can be assumed to be a false positive. Conversely, when we test people who we know had exposure to an infected person, or who showed active symptoms, the true prevalence of the virus among those being tested is higher; the rate of false positives will be lower. By focusing on specific populations in the United States, we can make best use of antibody tests.

　検査、検査って、感染率が低い段階や他に証拠のない場合にやっても偽陽性、偽陰性が多く出るからあまり意味ないんですね。これは事前確率、事後確率云々で随分前に日本では話題になっていたねーー検査狂はいまでも日本にいるけど。