Optimal Stopping in Sequential Clinical Prediction

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.