I went to the ER for rapid/irregular feeling heart beat a couple years ago when I was 28. The doctors diagnosed it as Atrial Fibrillation. From what I have read the odds of having Atrial Fibrillation at that age are 1 in 10,000. According to a quick look into studies, the ECG has a 98% specificity for Atrial Fibrillation. Am I to then believe that it is much more likely I never had Atrial Fibrillation?

I think I'm thinking about it wrong, forgetting about symptoms changing the odds.

pretty sure the chance is still 99% you have the disease. If yours and everyone else's chance wasn't 99% why would it say 99%

The only thing that's breaking my brain (I'm quite tired) is that the probability that you have the disease plus the probability that you don't have the disease is more than 1.

The probability that you have the disease is about 0.98%. The probability that you don't have the disease is about 99.02%. Those sum to exactly 1. The 2 numbers that you quoted, 0.9999% and 0.0099%, sum to 1.0098% or 0.010098 which is less than 1, not more than 1. Those aren't supposed to sum to 1 since those are probabilities before the test was run. They sum to the total probability that the test will come out positive.

That part is actually important. If you are a hypochondriac and that's why you're worried the calculation he did is correct..... if you have a legitimate reason to be worried you can be well over 50/50 to have it.

" ...(in other words it will deliver a correct positive or negative result 99% of the time)."

This specific wording in the original problem seems crucial.

No, it is not the PPV/NPV, it is the sensitivity/specificity.

This example is how you teach medical students about the value of PPV/NPV.

Thats all comers. The chances of you having afib, at age 28, GIVEN THAT YOU HAVE AN IRREGULAR HEARTBEAT, are much higher than 1 in 10,000.

Correct. Though note that I made that post 2 years ago.

hahaha awesome sorry

The positive predictive value is the answer that we are computing in this problem. We are given that the sensitivity and the specificity are each 99%. We are also given the prevalence of the disease in the population as 1 in 10,000. This is all you need to compute positive predictive value. When this is done for a particular patient, it is often called the post-test probability rather than the positive predictive value. These are the same value as long as our patient has the same 1 in 10,000 pre-test probability of having the disease as the general population. If he has a different pre-test probability, then you would use his pre-test probability in place of the prevalence, but otherwise do the calculation the same way. This will give the same result as the method of likelihood ratios which may be familiar to doctors. In fact, when I did this problem from an odds perspective ITT, that was essentially the same as the method of likelihood ratios.

A study found that an appalling percentage of doctors did not know how to correctly use sensitivity, specificity, and prevalence to accurately compute the probability that a patient has a disease. One multiple choice question asked for the probability of disease when a screening test with a sensitivity and specificity of 95% returns a positive result in a population with a disease prevalence of 1%. The choices were <25%, about 50%, nearly 100%, and “Don't know”. The correct probability is about 16%, so the answer is <25%. Yet only 22% of the docs gave that answer, and 56% of them said that the answer was nearly 100%!

In case any of you are ACTUALLY surprised that doctors have no idea wtf they are talking about re: statistics, I have an informal test I give to all of my coworkers whenever the topic comes up. It is known, for example, that a patient on a ventilator has a risk of developing pneumonia of ~3% per day on the ventilator. So whenever this comes up, I ask them what is the chance of the guy getting a pneumonia for 10 days on the vent.

30% is the answer nearly 100% of the time.

Well, first, it seems to depend on the phrasing--3% per day versus (what I think you mean) 3% each day (if he hasn't already contracted pneumonia). The former phrasing, 3% per day, could be construed to mean what the doctors are answering.

Second, you're talking about the correct 27% versus 30%. Hardly a difference to be too worried about. Though they probably aren't thinking "the correction to the correct answer from the approximation is small, so the approximation of 3% times 10 is close enough".

30% is a great answer there imo

Yeah, that's what I figured. Symptoms change the odds greatly.

It's about as good an answer as they can give, without more information -- you didn't specify the relationship between the probability of getting it one day and getting it the next. The probabilities might just add (though that would be weird, and I don't think medicine works that way very often), they might be independent (giving 1 - 0.97¹⁰ = 26.3%, which I'm guessing is what you're looking for), and they might change in some way over time (for example, susceptible people catching it early more of the time) and we still might express it as "3% per day" as a shorthand in any of the cases.

Given that the independent-trials answer is still close to 30 it's not too bad. Though I don't doubt your conclusion that the doctors have no clue about statistics, and I suppose none of them think about it as I just did...

I will agree with vhawk that in my experience, most doctors are terrible at this sort of thing, and they almost surely answered 30% because they don't know any better. I mean, I can amaze my class with my ability to do arithmetic quickly in my head, something that's not supposed to be amazing to well-educated adults.

Right.

No its not, its much worse than "I dont know" or probably even 3%. Because it belies an ignorance of how probability works, and the fact that its "pretty close" allows them to make the same error. What if it was 12%? 40%?

Its approximately independent, but even if you didnt know that, it would be a bit odd to assume it WASNT independent, without knowing "more information" as you point out.

Well....that's the point. The problem is test giver. You can't ask somebody what Sin(.00001) and accuse them of not knowing what the function does if they say .00001.