Optimal Stopping in Sequential Clinical Prediction

TL;DR

This paper models the timing of clinical decisions as an optimal stopping problem, showing that the best model isn't always the best moment to act, with implications for staged medical testing.

Contribution

It introduces a sequential prediction framework using optimal stopping theory, tailored for clinical settings with staged information, and demonstrates its application across multiple datasets.

Findings

Stopping decisions vary by setting, sometimes favoring more information, other times earlier action.

Patient-specific risk trajectories inform optimal stopping points.

Model performance does not always align with the best timing for clinical decisions.

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.