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As you discovered in your quiz. section discussion exercise about medical tests, medical tests rarely refer directly to the presence or absence of the condition

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As you discovered in your quiz. section discussion exercise about medical tests, medical tests rarely refer directly to the presence or absence of the condition of interest in the patient, so it is possible for someone without a condition to yield a positive result, and it is also possible for someone with the condition to yield a negative result. In such situations, arriving at a diagnosis about the patient's health status requires us to combine the test result with epidemiological information about the general prevalence of the condition in the population. Bayesl Rule provides a principled rule for how to combine such information and arrive at a valid diagnosis. In the case of a positive test, Bayesl Rule has the following form: PlCJxPlTVC] va= P c] xP TV Ci+P(C\"]X PiTVCCl Many of the pieces of this equation have technical names in clinical medicine and epidemiology. The meaning of each piece and its technical name (if any) are given below: 1. P [C] : In epidemiology, this probability is known as the prevalence, the proportion of a given population that has the health condition of interest. The closer this probabity is to 1, the stronger the belief that a patient drawn at random from the population will have the condition. In Bayesian terms, this marginal probability is known as a prior probability that a patient has the condition of interest rior to observing the result of a medical test. The complementary probability, Pic: , is the belief that a patient drawn at random from the population does not have the condition, once again prior to the medical test. As is true of complementary probabilities in general, P C" = 1 P [C] . 2. The set of the next four probabilities constitute a kind of probability known as a likelihood, which represents the probability of observing evidence (in this case the test result) conditional on a particular value of an unknown quantity (in this case the presence/absence of the health condition): a. PiTV C] : Clinicians refer to this probability as the sensitivity of a test or as the probability of a true positive. It answers the question, how probable is it that someone with the condition will yield a positive test? b. PiTC VCi : This is the probability of a false negative. It answers the question, how probable is it that someone with the condition will yield a negative test? c. Sensitivity PlT VC] and the probability of a false negative PiTCVCi are com lemenmry probabilities; subtracting one of these from 1 will give the other. d. P T VCC : This is the probability of a false positive. It answers the question, how probable is it that someone who does not have the condition will yield a positive test

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