Optimal schedules of cancer surveillance and tumor size at detection

The paper explores methodological and mathematical aspects of a new approach to constructing optimal schedules of cancer screening. This approach consists of systematic use of tumor size at detection, combining stochastic models of tumor latency, tumor growth and tumor detection, and employing a new biologically natural screening efficiency criterion defined as the Kantorovich distance between the tumor size at spontaneous detection in the absence of screening and the tumor size at detecton when both spontaneous and screening based mechanisms are in place. An explicit formula for the efficiency functional is obtained. Sample calculations suggest that in the case of exponential tumor growth, the optimal screening schedules with a fixed number of exams have a trend to uniformity.