Optimal scheduling of examinations for the early detection of disease

The general theory of scheduling examinations for the diagnosis of disease is formulated with respect to the optimal spacing between examinations. This same theory is also applicable, with a change in language, to the inspection of equipment and the scheduling of patients under surveillance with disease. Optimal scheduling programmes are investigated using a weighted utility function which is linear in the probabilities both of finding a case at examination and of being clinically incident between examinations. If disease incidence is independent of time, then a necessary and sufficient condition for the intervals to be equally spaced is that the sensitivity of the examination be unity. The equations for finding the optimal intervals are derived and depend on the distribution of the pre-clinical sojourn times and the sensitivity of the test. If the sojourn distribution is exponential, the optimal intervals are equal except for the first and last intervals.