3 ms·

There's an amazing mathematical paradox, maybe even better than the birthday paradox, related to screening for rare diseases, that dramatically changes the form

There's an amazing mathematical paradox, maybe even better than the birthday paradox, related to screening for rare diseases, that dramatically changes the formula. Imagine there's some terrible disease affects 1 in 1 million people. And there's a test that's 99% accurate. You go get screened for the disease, and it comes up positive. Oh no! What are the chances that it was a false positive? Intuition would tell you 1%. In reality? It's 99.99% likely to be a false positive. Why? Imagine 1 million people get tested. Well we know exactly 1 person (on average) in that group is going to have the disease. But our 99% accurate test will ring a positive 1%, or 10,000 times. So the odds that you really have the disease are the odds that you're that 1 in 10,000 which is 99.99% against! Well just run the test again. Oh no! It turns up positive again! What are the odds it's two false positives? 99%! Same math. Now we know that 1 person has the disease, but our test will show 1%, 100 people, in the 10,000 as being positive. So your odds of having it are 1 in 100, or 99% against. I'm not especially interested in being tested for rare conditions.

dullcrisp 3y ago
Oh no! But what if we run the test a third time?
- ethanbond 3y ago
  You have exhausted your region's capacity for testing. Game over womp womp
  - dullcrisp 3y ago
    Well if I only have to re-test 1% of cases maybe I can even use a more accurate test the second go-round.
jahnu 3y ago
Aye that’s a great one. Even testing and treating not so rare conditions can lead to statements that seem different when you know the details. Imagine you test early and often for a condition in country A much more often than country B which waits until some more late stage easier to detect symptoms occur. Now compare survivor rates. Much higher in country A! We should clearly also be testing in country B, right? Depends. If the condition is something that doesn’t often actually kill and typically remains at a non lethal but detectable state then all you might have done is treat a lot of extra non fatal conditions that usually only is detected in country B once it evolves to a more advanced and dangerous state. You may have put many people in country A through an unnecessary, expensive, and frightening treatment regime. The point is that these things are complex and need thorough analysis.

dullcrisp 3y ago

Oh no! But what if we run the test a third time?

ethanbond 3y ago
You have exhausted your region's capacity for testing. Game over womp womp
- dullcrisp 3y ago
  Well if I only have to re-test 1% of cases maybe I can even use a more accurate test the second go-round.

jahnu 3y ago

Aye that’s a great one. Even testing and treating not so rare conditions can lead to statements that seem different when you know the details. Imagine you test early and often for a condition in country A much more often than country B which waits until some more late stage easier to detect symptoms occur. Now compare survivor rates. Much higher in country A! We should clearly also be testing in country B, right? Depends. If the condition is something that doesn’t often actually kill and typically remains at a non lethal but detectable state then all you might have done is treat a lot of extra non fatal conditions that usually only is detected in country B once it evolves to a more advanced and dangerous state. You may have put many people in country A through an unnecessary, expensive, and frightening treatment regime. The point is that these things are complex and need thorough analysis.