Optimal times of transfer between therapies: a mathematical framework

This paper develops a mathematical framework for identifying optimal transfer times from a low-intensity, watchful waiting therapy to direct intervention. It allows for the probability that patients discharged from watchful waiting will suffer disease recurrence. Two specific functional forms for the resolution of the relevant medical condition are modeled (modified exponential and logistic). Initially structured as an expected cost minimisation problem, the analysis is extended to include the possibilities of differential benefits of the therapies and discounted cost and benefit valuations. The framework demonstrates the existence of non-synchronous transfer optima.