Use of the Hazard Rate to Schedule Follow-Up Exams Efficiently

Abstract

The problem of surveillance for metastasis in a cancer patient is modeled as an allocation problem. The hazard rate of metastasis appearing determines the efficient scheduling of follow-up exams. An optimal schedule of follow-up exams is shown to be dependent on the hazard rate, K, and D. K relates the cost of testing to the benefit of early detection. It diminishes as benefit increases or cost diminishes. D is the time by which a metastasis' detection by testing precedes its clinical presentation. Hence it is a direct measure of the effectiveness of testing. The optimal testing frequency = (hazard rate/2K)1/2. Testing may be stopped when the hazard rate drops below 2K/D2. Tests need never be routinely scheduled if the intervals between tests exceed D in length.