• Bayes
• specificity
• probability
• likelihood ratio
• sensitivity

The most common measures of diagnostic test performance, sensitivity and specificity, involve two simplifying assumptions: that disease status is binary (present or absent), and test results are binary (positive or negative). Bayes’ theorem tells us that these features must be combined with a third ingredient, the prior or pretest probability (PreTP) of disease, to update the disease probability following the observed test result. As we1 2 and others3 4 have written, readers and authors of medical literature often interpret test results in ways that violate Bayes’ rule. Publications celebrating diagnostic tests that on close inspection perform near-chance level represent an important example of this interpretation risk.5 6 In some cases, even frankly paradoxical combinations of sensitivity and specificity are reported, for example, with certain physical examination findings,7 in which a ‘positive’ result lowers the disease probability, and ‘negative’ result increases it.

We recently pointed out a simple litmus test that can be used at a glance to recognise the potential for chance or paradoxical performance, which we term the ‘rule of 100’.6 Any test for which the sensitivity and specificity add to 100% does not modify the PreTP of disease, that is, the result (positive or negative) provides a post-test probability (PostTP), identical to the PreTP. Such tests therefore provide no information. Here is a three-line proof:

The second line of the proof makes use of the fact that when For those comfortable with combining sensitivity and specificity into the likelihood ratio (LR) value, …