You can follow this conversation by subscribing to the comment feed for this post.

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?

(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!

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?

"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.

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

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%).

"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.

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.

The comments to this entry are closed.

##### Get new posts by email:
Kaiser Fung. Business analytics and data visualization expert. Author and Speaker.
Visit my website. Follow my Twitter. See my articles at Daily Beast, 538, HBR, Wired.

## Search3

•  only in Big Data
Amazon - Barnes&Noble

Numbersense:
Amazon - Barnes&Noble

## Junk Charts Blog

Graphics design by Amanda Lee

## Next Events

Jan: 10 NYPL Data Science Careers Talk, New York, NY

## Past Events

Aug: 15 NYPL Analytics Resume Review Workshop, New York, NY

Apr: 2 Data Visualization Seminar, Pasadena, CA

Mar: 30 ASA DataFest, New York, NY

See more here