Discrete strategies of cancer posttreatment surveillance-Estimation and optimization problems

The authors 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, they obtain parametric estimates of both the time-to-recurrence distribution and the probability of false-negative diagnosis. Then assuming the false-negarive rate known, the authors give a nonparametric maximum likelihood estimator for the tumor latency time distribution. When designing an optimal strategy of post-treatment surveillance, they proceed from the minimum of the expected delay in detecting tumor recurrence as a pertinent criterion of optimality. To solve this problem the authors give a dynamic programming algorithm. They illustrate the methods by analyzing data on breast cancer recurrence.