Let’s say you have a small n of randomly sampled testing from a population with x% positive and a larger N of non random testing of people who come into hospitals with a larger X% positive. Can you combine both samples to inform your estimate of the true population prevalence?
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What I’m wondering is if under different testing regimes we can make different inferences of how much ex ante we should expect X>x (ie, do we think someone who gets tested is one hundred or twice as likely to be positive as the general pop?)
Depends on your x% no? if x% is 100%, then equally likely. If x% is 1%, then they are much much much much more likely to be infected than the random person.
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It depends on how much more likely tested people are to be tested than the broader population, obviously, but obviously x|not tested is not zero, even if X does not equal x
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