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Parenthetical

I'm confused about the true positive rate. If 10% of the population has antibodies and the false negative rate is zero shouldn't we get 10 true positives for 100 tests?

Kaiser

(P): Be careful about the baseline number. Out of 100 people, 10 has antibodies; out of those 10, all 10 test positive so false negative rate is zero. And the true positive rate is 100%. But you can't say 10 true positives for 100 tests because the other 90 tests were done for those without antibodies - and there's where the false positives come in and make trouble!

Parenthetical

Maybe I am confused about the definition of prevalence. This is the phrase I'm stuck on: "while the other 10 percent truly positive begets 1 positive per 100". If ten out of every hundred people are truly positive, how come we only get one positive result from testing them?

TBW

"The 2 percent error rate when applied to 90 percent of the population who do not have the coronavirus generates 1.8 positive results per 100 while the other 10 percent truly positive begets 1 positive per 100, even assuming zero false negative. " - if the false negative rate is zero, then for those 10 people that actually have the virus they would all test positive. Compared to the 1.8 people out of 100 who would not have the virus but test positive anyway. It feels like the comparison is 1.8 false positive to 10 true positives, not 1 true positive.

Kaiser

(P), TBW: Yes, I see where I flipped the numbers. Fixed the text. Thanks!

Antonio Rinaldi

Or assume 2% prevalence, so with 2% false positive rate and 0% false negative rate you obtain 2 true positives among every nearly 4 positives (~50%).

Ben

"after they have recovered at which point they are not infectious."

This has yet to be proven. A fair assumption, but yet to be proven.

Kaiser

Ben: Yes that point can't be underlined enough although should we start with it, the entire enterprise of antibody testing is pointless! My understanding is that it is technically true that antibodies confer immunity but sometimes the duration of immunity is short especially if the virus may mutate.

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Kaiser Fung. Business analytics and data visualization expert. Author and Speaker.
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