Epidemiology probability question.
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  1. #1
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    Epidemiology probability question.

    Suppose a test for a disease is 99% accurate for positive results. This means there is a 1% false positive rate.

    Suppose 1% of the entire population has the disease.

    You get tested. The test is positive.

    What is the probability that you have the disease?
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    Quote Originally Posted by QuiQuaeQuod View Post
    Suppose a test for a disease is 99% accurate for positive results. This means there is a 1% false positive rate.

    Suppose 1% of the entire population has the disease.

    You get tested. The test is positive.

    What is the probability that you have the disease?
    .99. The number of people that have it is not relevant

  3. #3
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    Quote Originally Posted by QuiQuaeQuod View Post
    Suppose 1% of the entire population has the disease.


    What is the probability that you have the disease?
    Preposterous. Your supposition is flawed.

    Dr. Trump has ensured us the virus will magically disappear. Thus any percent of 0% =
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    Quote Originally Posted by DaveG View Post
    .99. The number of people that have it is not relevant
    Wrong, and wrong.

    Most people get it wrong, btw. And 99 is a very common answer. So are 98, and 1. Which are also wrong.
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    Quote Originally Posted by QuiQuaeQuod View Post
    Wrong, and wrong.

    Most people get it wrong, btw. And 99 is a very common answer. So are 98, and 1. Which are also wrong.
    can you show the math?

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    Quote Originally Posted by DaveG View Post
    can you show the math?
    Yes.

    And eventually I will.
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    .99 just got hit by a bus walking out of the clinic. Time to re-crunch the numbers.

    Where's my abacus?

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    Quote Originally Posted by QuiQuaeQuod View Post
    Yes.

    And eventually I will.
    Bayes's Theorem

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    Quote Originally Posted by DaveG View Post
    Bayes's Theorem
    I won't need to refer to that to show my math, but yes that will get you there.
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    50%, either you do, or you don't, same way I figure all my odds.

    Disclaimer: I am NOT good in math
    Of course I'm sure...that doesn't mean I'm right.....

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    Quote Originally Posted by QuiQuaeQuod View Post
    Wrong, and wrong.

    Most people get it wrong, btw. And 99 is a very common answer. So are 98, and 1. Which are also wrong.
    The only premise I can think of that would make his answers wrong is if "false positive" in not a confirmation of 'negative'.
    Is that why you say he's wrong?

    My understanding of the term is that it indeed is the same as negative.

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    Quote Originally Posted by Jay Strongbow View Post
    The only premise I can think of that would make his answers wrong is if "false positive" in not a confirmation of 'negative'.
    Is that why you say he's wrong?

    My understanding of the term is that it indeed is the same as negative.
    False positive = test says you have it, but you really don't.

    True negative = test says you don't have it, and you don't.

    Same disease status, different test results.
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    99%...
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    Quote Originally Posted by QuiQuaeQuod View Post
    Suppose a test for a disease is 99% accurate for positive results. This means there is a 1% false positive rate.

    Suppose 1% of the entire population has the disease.

    You get tested. The test is positive.

    What is the probability that you have the disease?
    Well, I'd think the probability of being infected is 50% (two possible outcomes, infected: Y/N) ...and the probability of your individual test result being correct is 25% (a further 2 outcomes, Test correct: Y/N).

    EDIT: And I'd be wrong...Interesting topic.
    Last edited by Marc; 3 Weeks Ago at 04:38 PM.
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    Quote Originally Posted by Marc View Post
    Interesting topic.
    I agree, of course. For many reasons. But mainly because what seems so obvious.... isn't.
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    Quote Originally Posted by QuiQuaeQuod View Post
    What is the probability that you have the disease?
    The math (barely math, so you'll have no problem) is below, Highlight or quote to see it.

    The math is easy to do percentages with if we think about 100 tests. Do 100, and you will find 1 case, a true positive. That's how many people have it, 1%. You will also have 1 false positive. So 100 tests, 2 will be positive.

    So your personal positive test? 50-50. Half of all positives will be false, half will be true. Under the specified conditions.
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    I'm going with my answer.
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    Quote Originally Posted by QuiQuaeQuod View Post
    The math (barely math, so you'll have no problem) is below, Highlight or quote to see it.

    The math is easy to do percentages with if we think about 100 tests. Do 100, and you will find 1 case, a true positive. That's how many people have it, 1%. You will also have 1 false positive. So 100 tests, 2 will be positive.

    So your personal positive test? 50-50. Half of all positives will be false, half will be true. Under the specified conditions.
    Huh, not where I thought that was going:

    https://brownmath.com/stat/falsepos.htm
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    So .... pretty much the tests are useless.
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    Quote Originally Posted by duriel View Post
    So .... pretty much the tests are useless.
    Not really,, A test is just way less predictive than people think for some things that are relatively rare. A single positive test does increase your probability from 1% up to X%, and that's a big jump.

    But you will still want a re-test to really confirm. Test-retest is very useful.
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    For all new tests, which have not went through a series of rigorous testing and evaluation (which is what we have), actually 50% of the population support that it's nothing more than the flu.

    A test > useless by its self.
    2 tests > maybe a little better.
    more tests > could be a little better, but basically useless.
    no pulse> pretty good test.

    This is what we have for Cov19 tests.
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    Quote Originally Posted by duriel View Post
    For all new tests,

    ...
    A test > useless by its self.
    2 tests > maybe a little better.
    I'm not talking about COVID, I am talking in general. But the risk of a false positive is a lot lower in NYC, given a much higher than 1% population prevalence. That's how the math works. The more that is out there, the less likely a given positive test is to be a false positive.

    A single positive test moves your chance of having it up by 49%. I think that is useful information for an individual to do something about. Like keep away from others until a re-test, be aware of even "minor" symptoms of the disease, etc.

    The chance of TWO false positives for the same person at the 1% (1/100) false positive rate is... 1/10,000. So double test 10,000 people, you get 101 double positives, one of which is false. 1/101 = very slightly over 99% sure any given double positive is a true positive.

    Not really a LITTLE better, imo.
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  23. #23
    tlg
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    Quote Originally Posted by QuiQuaeQuod View Post
    The math (barely math, so you'll have no problem) is below, Highlight or quote to see it.
    In my 'math' the 1 true positive person was given the 1 false positive test. Thus the result was 1 positive-false-positive.

    What's the probability of that?
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    Quote Originally Posted by tlg View Post
    In my 'math' the 1 true positive person was given the 1 false positive test. Thus the result was 1 positive-false-positive.

    What's the probability of that?
    What volume is your sky set on?

    IOW, that makes no sense. There is no such thing, by definition, as a person who is positive getting a false positive test result. False positives require a negative status to exist.
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    Quote Originally Posted by QuiQuaeQuod View Post
    I'm not talking about COVID,
    I am talking about cov19.
    And it you read the paper marc posted, without a thorough evaluation, many people give false results due to too many things not associated with the test. Like maybe if you had coffee that morning.
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