Constructing time-invariant dynamic surveillance rules for optimal monitoring schedules

Dynamic surveillance rules (DSRs) are sequential surveillance decision rules informing monitoring schedules in clinical practice, which can adapt over time according to a patient's evolving characteristics. In many clinical applications, it is desirable to identify and implement optimal time-invariant DSRs, where the parameters indexing the decision rules are shared across different decision points. We propose a new criterion for DSRs that accounts for benefit-cost tradeoff during the course of disease surveillance. We develop two methods to estimate the time-invariant DSRs optimizing the proposed criterion, and establish asymptotic properties for the estimated parameters of biomarkers indexing the DSRs. The first approach estimates the optimal decision rules for each individual at every stage via regression modeling, and then estimates the time-invariant DSRs via a classification procedure with the estimated time-varying decision rules as the response. The second approach proceeds by optimizing a relaxation of the empirical objective, where a surrogate function is utilized to facilitate computation. Extensive simulation studies are conducted to demonstrate the superior performances of the proposed methods. The methods are further applied to the Canary Prostate Active Surveillance Study (PASS).