The channel capacity of a diagnostic test as a function of test sensitivity and test specificity

We apply the information theory concept of channel capacity to diagnostic test performance and derive an expression for channel capacity in terms of test sensitivity and test specificity. The expected value of the amount of information a diagnostic test will provide is equal to the mutual information between the test result and the disease state. For the case in which only two test results and two disease states are considered, mutual information, I(D;R), is a function of sensitivity, specificity, and the pretest probability of disease. The channel capacity of the test is the maximal value of I(D;R) for a given sensitivity and specificity. After deriving an expression for I(D;R) in terms of sensitivity, specificity, and pretest probability, we solve for the value of pretest probability that maximizes I(D;R). Channel capacity is obtained by using this value of pretest probability to calculate I(D;R). Channel capacity provides a convenient and meaningful single parameter measure of diagnostic test performance. It quantifies the upper limit of the amount of information a diagnostic test can be expected to provide about a patient's disease state.