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Note that this is not due to bad tests, just a counter-intuitive probabilistic result happening when one tries to detect an a priori very rare condition. It fo

Note that this is not due to bad tests, just a counter-intuitive probabilistic result happening when one tries to detect an a priori very rare condition. It follows from a straightforward application of Bayes formula: - Suppose a person has 1% chance of getting cancer, so p(cancer) = 0.01 - Suppose that the test has 99% sensitivity and specificity, i.e., p(positive | cancer) = p(negative | no cancer) = 0.99 - To use Bayes we first need the probability of a positive result regardless of disease status, i.e. p(positive) = p(positive | cancer) * p(cancer) + p(positive | no cancer) * p(no cancer) = 0.99 * 0.01 + 0.01 * 0.99 = 0.0198 - Then by Bayes we have p(cancer | positive) = p(positive | cancer) * p(cancer) / p(positive) = 0.99 * 0.01 / 0.0198 = 0.5 And things get worse the rarer the condition is. When p(cancer) = 0.5 the computations above give p(cancer | positive) = 0.99, and when p(cancer) = 0.001 then p(cancer | positive) = 0.09. In other words, the rarer the condition, the more precise tests have to be.

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hackernewds 5y ago
So in summary, it is a bad test for a rare case? Am I missing anything?
- ceras 5y ago
  I think there's one nuance to add: the test is based on your base rate expectation for how likely the given individual is to have the rare disease. The more evidence you have that this person is more likely to have the disease, the more useful the test becomes. Some examples: - if the disease is more common among people over age 65, it's more useful on people in that age group - if the person displays more symptoms associated with the disease, and not also associated with more common diseases, then it's more useful for someone with those symptoms - if a disease is common in an area of the world, and the person has traveled there, the test is more useful The more factors you have, the less likely a false positive. This is why it's often better to avoid medical tests unless there's a reason to suspect someone is at elevated risk for a disease: a positive result is more likely to be a false positive.

deleted 5y ago

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hackernewds 5y ago

So in summary, it is a bad test for a rare case? Am I missing anything?

ceras 5y ago
I think there's one nuance to add: the test is based on your base rate expectation for how likely the given individual is to have the rare disease. The more evidence you have that this person is more likely to have the disease, the more useful the test becomes. Some examples: - if the disease is more common among people over age 65, it's more useful on people in that age group - if the person displays more symptoms associated with the disease, and not also associated with more common diseases, then it's more useful for someone with those symptoms - if a disease is common in an area of the world, and the person has traveled there, the test is more useful The more factors you have, the less likely a false positive. This is why it's often better to avoid medical tests unless there's a reason to suspect someone is at elevated risk for a disease: a positive result is more likely to be a false positive.