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The sensitivity of a screening test is the proportion of individuals who have the disease who test positive: a/(a+c). This is also known as the true positive rate.
The specificity is the proportion who don’t have the disease that test negative: d/(b+d). This is the complement of the false negative rate. That is the false negative rate is 1-specificity or b/(b+d).
The positive predictive value is the proportion of individuals who test positive who actually have the disease, a/(a+b).
The negative predictive value is the proportion who test negative who don’t have disease d/(c+d).
Note that the sensitivity and specificity are based on the columns of the table and thus are independent of disease prevalence, (a+c)/N, while the predictive values, which are based on the rows, are not.