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485
[–] • 9 pts

The value that the doctors SHOULD have been calculating is the PPV (Positive Predictive Value) (See: https://en.wikipedia.org/wiki/Positive_and_negative_predictive_values)

This is a probability that given a positive test result that the test is a True Positive.

This is calculated as:

PPV = sensitivity x prevalence / (sensitivity x prevalence + (1-specificity) x(1-prevalence))

In the sample question, you don't really have enough information to calculate this exactly, as they only give the "False Positive Rate", this allows the calculation of specificity (1 - FPR) as 0.95. The sensitivity is not defined, lets just assume for the sake of the example that the sensitivity (1 - FNR) is also 0.95.

So....

PPV = (0.95 x 0.001) / (0.95 x 0.001 + (1 - 0.95) x (1 - 0.0001))

PPV = 0.018664

i.e. Given the prevalence of the disease, the likelihood that a positive test result represents a TRUE positive is: 1.8% Even if you assume that the sensitivity of the test is 99.5%, the PPV still comes out around 16%. It's a bit of a silly question, as the data required to actually calculate the answer isn't supplied (you need the False Negative Rate as well as False Positive Rate to do the calculations properly. Tests rarely include this required information though).

A test with a sensitivity as low as 95% should only ever be used as a screening test, never as a diagnostic test. Basically, you want something that is very sensitive, but with the possibility of a high False Positive Rate which is used as a screening test, combined with a follow up test that has a much higher specificity (very low False Positive Rate). Only when the confirmatory test comes back positive can you make any conclusions about the diagnosis (even then, you should be doing the PPV calculation to determine the likelihood that the positive result is a True positive.

I was running a rough calculation of PPV during the main panic stages of COVID, when they were doing mass testing and reporting the results daily. During most of it, the PPV, as per my calculations (which did have some assumptions, as the specific accuracy details of the tests were not disclosed and the prevalence had to be somewhat inferred by the number of positive test results), was running around 10%. So, when they were saying that they tested 50k people, and found 75 "cases", probably 90% of those "cases" were false positives.

I'm not a doctor, not even very good at math.

[–] • 3 pts (edited )

The question is concerning a person who "has a positive result", so it seems like the 1/1000 is irrelevant information.

Based on your answer, my initial thinking must not be correct.

If 100 out of 1000 cavemen have an apple, but 5% of the apples are actually a plastic replica of an actual apple.. then only 95 cavemen have apples grown from a tree.

Using your formula, for the above statment to determine how many cavemen have actual apples, I get a value of .65519?

[–] • 2 pts

In that example, you're not calculating how many cavemen have apples. Rather you are calculating the probability, given that you are that a caveman has an apple, that is a real apple rather than a fake one.

So given a prevalence of 0.1 specificity of the test of 0.95 then a PPV around 0.65 seems about right. If your "test" detected an apple, there's about a 65% chance that it's really an apple.

[–] • 3 pts

I guess I'm too retarded to wrap my head around 5/100 equating a 65% chance. I knew there was a reason I chose to stay out of professions that puts the lives of others in my hands. :D

[–] [deleted] • 2 pts

Thank you. The question throws out "prevalence of 1/1000" but then asks about only people with a positive result... a result that is wrong 5% of the time. It doesn't ask about the odds of some random dude having the disease, which is what people are trying to answer. It only asks about people who already have tested positive. And if the test gives a false positive 5% of the time, then 5% of the people who tested positive got the wrong result. People who tested negative aren't part of the actual question. It's more about reading comprehension than maths skills.

[–] • 0 pt

If thats an accurate take, then there is a subset of people who are lacking in one life skill, who believe they are more intelligent than the majority because they don't get the same answer..

Now I think I've got to re-examine/reaffirm my beliefs on covid, the 6 million, and lord knows what else..

[–] • 6 pts

They are trained monkeys who dare not bite the hand that feeds them.

[–] • 3 pts

the rubbing hands that feed them.

[–] • 5 pts

A positive test has about a 2% chance of also having disease by my reckoning. Am I right? Can't see the answer for lack of twitter account. 1/51 to be exact.

[–] • 1 pt

https://pic8.co/sh/2gHKje.png

1/1000 chance of true positive (0.001%) minus 5% false positives.

0.00095%

I think, i'm not a doctor or mathemagician

[–] • 0 pt

The patient in front of you had a positive test. 1/1000 it is true positive 50/1000 false positive. 949/1000 are now excluded for negative test.

I estimate the odds now as 1 true positive per 51 true+false positive.

1/51 or about 2%.

[–] • 4 pts

All doctors know is what the drug company reps tell them, and that if they prescribe so much of certain drugs, they get bonuses. They won't tell you to stop eating sugar and carbs, they'll just prescribe insulin and statins to treat diabetes and high blood pressure.

[–] • 5 pts

I work in medical IT. The crap we do to cover for these morons is insane. We spend millions a year crunching numbers to give them bonuses on them just doing their damned jobs. If they document a certain amount of things, bonus, if they document on time, bonus, if they collect stats that we send to the gov, bonus. It's disgusting. We track how much opiates they prescribe because they can be sued and so the company I work for can be sued if they over prescribe. We track everything they do and they still demand 'AI' write their damned notes for them. 99% are greedy, lazy, despicable people and most are now Indians which makes the Idiocracy and greed even worse.

[–] • 2 pts

A 'Doctor' has always been about Money and Pharma Bought the AMA and forced/PAID it to force/pay all Drs. to push the shots and MORE importantly NOT allow any Real Cures. I KNOW this, because i requested Ivermectin in 2020 and my Dr. said i was 'crazy' and THEN retired very quickly.

[–] • 1 pt

Doctors are technicians, not mechanics.

All they do, all their job is, "You have X problem, try X meds. That didn't work? Try Xa meds." That's all their job is (yes I said it twice). Doctors being "smart" is that they've memorized all of the meds they are supposed to prescribe.

[–] • 1 pt

They are jewish poison dealers.

[–] • 0 pt (edited )

According to the laws of Aryan math the answer is (((Kauffman))).

I probably confuse "False positive rate" with something else.

I was thinking the prevalence is irrelevant to the question and the question could be rewritten as:

If a test to detect a disease whose prevalence is 1 out of 1,000 has a false positive rate of 5 percent, what is the chance that a person found to have a positive result actually has the disease?

cut

If a test to detect a disease has a false positive rate of 5 percent, what is the chance that a person found to have a positive result actually has the disease?

Question makes complete sense (no?) and 95% is the obvious answer.

Update:

I misunderstood false positive rate. A rate is per something, I assumed per positive test result but seems it's per all tests. That's right, right?

[–] • 0 pt

It seems they’re generally bad at math (x.com).