An HIV test has a sensitivity of 99.7% and a specificity of 98.5%. A subject from a population of prevalence 0.1% receives a positive test result. What is the precision of the test (i.e the probability he is HIV positive)?

An HIV test has a sensitivity of 99.7% and a specificity of 98.5%. A subject from a population of prevalence 0.1% receives a positive test result. What is the precision of the test (i.e the probability he is HIV positive)?



Bayes rule: P(Actu+|Pred+)=P(Pred+|Actu+)×P(Actu+)P(Pred+|Actu+)×P(Actu+)+P(Pred+|Actu−)P(Actu−)P(Actu+|Pred+)=P(Pred+|Actu+)×P(Actu+)P(Pred+|Actu+)×P(Actu+)+P(Pred+|Actu−)P(Actu−)

We have: sensitivity×prevalencesensitivity×prevalence+(1−specificity)×(1−prevalence)=0.997×0.0010.997×0.001+0.15×0.999=0.62

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