Optimal Stopping in Sequential Clinical Prediction

Abstract

Most clinical prediction studies are developed from retrospective cohorts and reported as if all patient information were observed at once. In practice, clinicians face a more consequential question: \emph{when is there already enough information to stop testing and act?} A later stage can produce a better-looking model and still fail to justify the added delay, burden, or invasiveness of further workup. We formulate sequential clinical prediction as an \emph{optimal-stopping} problem under staged information, and illustrate the framework across four retrospective clinical datasets. The preferred stopping stage differed substantially by setting: sometimes fuller information justified waiting, whereas in other cases early or intermediate action was preferable. The key object is the patient-specific conditional risk trajectory: forward martingale structure represents coherent risk updating across stages, while reverse-martingale ideas describe information loss when a richer predictor is replaced by a simpler score. The results demonstrate that the best-performing model is not always the best stage for clinical decision-making.