HIV Testing Not As Accurate As You'd Think

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    Jan 10, 2011 9:18 PM GMT
    So modern HIV Testing claims to be over 98% accurate. What this actually means is that if you have HIV, there is a 98% chance that the test will actually show up positive. The opposite of that however is not the case. In other words, it is not true that if your test shows up positive, you have a 98 percent chance of having HIV. This is often assumed to be the case though.

    If we use Bayes' Theorem [url][/url] we can determine the probability of having HIV if your test shows up positive.

    Baye's Theorem looks like this:

    P(F|E) = ( P(E|F) x P(F) ) / ( P(E|F) x P(F) + P(E|F^c) x P(F^c) )

    Here's a key for what the terms mean (in regard to this scenario):

    E & F are events that respectively refer to testing positive and actually being positive. P stands for "probability).

    P(F) = You Actually Have HIV (0.5% of the US population has HIV)
    P(F|E) = Probability of actually having HIV if you test positive for HIV (this is what we're solving for)
    P(E|F) = Probability of testing positive if you have HIV (98% as mentioned above)
    P(E|F^c) = Probability of getting a false positive (roughly 1%).
    P(F^c) = Probability of not having HIV (99.5%).

    So if you plug in all those numbers into the original equation:

    P(F|E) = ( 0.98 x 0.005) / ( .98 x .005 + 0.01 x 0.995 ) = (roughly) 0.330

    This means that if you test positive for HIV, there is only roughly a 33% chance that you actually have HIV.

    What accounts for this very counter-intuitive phenomenon?

    Basically what happens is that even though the rate of false positives is extremely low (1%), SO MANY people get tested that all of those false positives start to add up and eventually outnumber the true positives, since the percentage of people who actually have HIV is very very small.

    On the flip-side however, if you test negative, the probability of getting a false-negative are so low they are almost non-existent. Without writing out all the math here, the chance of getting a false-negative is 0.01%.
    This is why its still good to get tested, because if you test negative, its pretty much a sure bet that you are in fact negative (assuming that you waited the appropriate amount of time after getting infected that doctors recommend).

    Just thought I'd share this.

  • metta

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    Jan 10, 2011 11:33 PM GMT
    Where is your source?
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    Jan 10, 2011 11:37 PM GMT
    also, are you referring to the buccal swab test, the 20-minute blood drop test or the full assay done in the lab?
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    Jan 11, 2011 12:59 AM GMT
    metta8 saidWhere is your source?

    The proof is in the mathematics, not in any source online. But you can verify the data that I put into the equation if you want. There's a plethora of information on the web.

    According to this site, between 800,000 and 900,000 Americans have HIV. The US population is roughly 300,000,000. So less than half of a percentage of Americans have HIV, which I stated before.

    According to this, HIV tests are around 99% effective. I originally said 98%. Replacing 0.98 with 0.99 in my above equation will barely affect the result.

    All the data I used in my proof is correct, and the theorem I used is a widely accepted tool to access statistical probability and has many real-world applications. It's simply been applied here to access the accuracy of HIV tests.
  • metta

    Posts: 38625

    Jan 11, 2011 1:36 AM GMT

    Accuracy of HIV testing
    Modern HIV testing is highly accurate. The evidence regarding the risks and benefits of HIV screening was reviewed in July 2005 by the U.S. Preventive Services Task Force.[21] The authors concluded that:
    ...the use of repeatedly reactive enzyme immunoassay followed by confirmatory Western blot or immunofluorescent assay remains the standard method for diagnosing HIV-1 infection. A large study of HIV testing in 752 U.S. laboratories reported a sensitivity of 99.7% and specificity of 98.5% for enzyme immunoassay, and studies in U.S. blood donors reported specificities of 99.8% and greater than 99.99%. With confirmatory Western blot, the chance of a false-positive identification in a low-prevalence setting is about 1 in 250 000 (95% CI, 1 in 173 000 to 1 in 379 000).

    The specificity rate given here for the inexpensive enzyme immunoassay screening tests indicates that, in 1,000 positive HIV test results, about 15 of these results will be a false positive. Confirming the test result (i.e., by repeating the test, if this option is available) could reduce the ultimate likelihood of a false positive to about 1 result in 250,000 tests given. The sensitivity rating, likewise, indicates that, in 1,000 negative HIV test results, 3 will actually be a false negative result. However, based upon the HIV prevalence rates at most testing centers within the United States, the negative predictive value of these tests is extremely high, meaning that a negative test result will be correct more than 9,997 times in 10,000 (99.97% of the time). The very high negative predictive value of these tests is why the CDC recommends that a negative test result be considered conclusive evidence that an individual does not have HIV.


    I think that your numbers are way off.
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    Jan 11, 2011 1:56 AM GMT
    I think you're misunderstanding what I tried to show in the OP. Your source says that 15/1000 HIV Test positive results are false. That's 1.5%. I stated in my OP that HIV Positive results are roughly 98% effective (100-1.5 = 98.5). Your source also says that tests are around 99.9% effective, but that's including negative results as well. You'll see that in my OP I said that negative results were extremely accurate. That's not what I'm disputing here.

    There are many different probabilities here to measure and it's easy to mix them up.

    The probability of testing positive if you have HIV is 98-99.99% effective. That's not in question.

    The probability of getting a false positive if you are HIV negative is around 1%-ish. This is also not in question.

    What my original proof shows is that the probability of having HIV if you test positive (essentially the opposite of the above figure) is surprisingly low. It is very counter-intuitive and that's essentially the point.

    Basically just because "If A, then B" has a very high probability, that does not mean that "If B, then A" has to have an equally high probability. That is what Bayes' theorem shows here.
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    Jan 11, 2011 1:58 AM GMT
    Metta, I think you're both saying the same thing about the rate of false negatives being very low.

    What differs between you and cardinal is
    1. the quoted sensitivities and specificities of the various tests (as you pointed out, technology has advanced so that what used to be 98% is now 99.99%). However, the final result doesn't really depend as much on these numbers as

    2. the pretest probabilities (to use 0.5% if you're not in an at-risk population is fine, but it's probably higher for people who voluntarily get tested, e.g. gay males).

    Here's a nice online calculator:

    Vary the prevalence from 0.005 to 0.2 (supposedly 1 in 5 gay males have HIV?!), and you'll see the odds change dramatically from 20% to 93% for a true positive.
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    Jan 11, 2011 2:10 AM GMT
    Cardinal is right...what he is describing is the positive predictive value of a test. This value boils down to a truly positive result out of ALL positive results. This is highly dependent on the PREVALENCE of a disease in the group being tested. So, a test may have a high sensitivity and specificity (as the HIV test does), if the prevalence is very low, the the positive predictive value goes down. Conversely, if the prevalence is very high, the PPV goes up! This is also why if the initial HIV test is positive (+ antibodies via ELISA) they must do a confirmatory westernblot. When done in sequence, the post test probability that you are + or - are very accurate.
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    Jan 11, 2011 2:15 AM GMT
    Cardinal is perfectly right when he's describing a person randomly picked from the US population for an HIV test. (Prevalence =0.5%)

    Metta is right when you're talking about the audience of this site (gay males, prevalence = 20%)

    Either way, a single ELISA test is always confirmed with a WB if it's positive.