Discrete strategies of cancer post-treatment surveillance. Estimation and optimization problems

We consider the cancer post-treatment surveillance to be represented by a discrete observation process with a non-zero false-negative rate. Using a simple stochastic model of cancer recurrence derived within the random minima framework, we obtain parametric estimates of both the time-to-recurrence distribution and the probability of false-negative diagnosis. Then assuming the false-negative rate known, we give a nonparametric maximum likelihood estimator for the tumor latency time distribution. When designing an optimal strategy of post-treatment surveillance, we proceed from the minimum of the expected delay in detecting tumor recurrence as a pertinent criterion of optimality. To solve this problem we give a dynamic programming algorithm. We illustrate the methods by analyzing data on breast cancer recurrence.