Route, Not Score: A Decision-Theoretic Basis for Pathway-Labelled Early Warning in Neonatal Cardiorespiratory Monitoring

This paper argues that a single risk score cannot tell clinicians what kind of concern they should have, because any continuous one-number summary of two or more features necessarily merges distinct physiological states. The author develops a decision-theoretic framework in which a display is a map from data to output, judged by the expected loss of the decisions it supports, and proves eleven propositions and two lemmas. The central result is that route information—naming which pathway is deteriorating—has value exactly when different routes call for different best responses at the same score; if every route leads to the same action, the route label adds nothing to decisions, though it may still support audit and trust. When routes do matter, the gain has an explicit formula. The paper then shows that an honest "uncertain" output is optimal below a threshold set by the relative costs of a wrong route and abstention, with calibration error imposing a bounded cost. Route sets calibrated by conformal prediction offer a coverage guarantee that does not assume the classifier is correct. Later results concern warning behaviour over time: stage labels carry per-window error guarantees; with a fixed alarm budget, combined evidence outperforms alerting on each route separately; persistence rules trade delay for fewer false alerts, less effectively when windows are correlated; a longer forecasting horizon buys lead time only at the price of more false alarms; label flicker near a boundary is predictable and reducible by hysteresis; attribution of a rising ratio is unique only in simple additive or multiplicative structures; adaptive baselines convert steady deterioration into a constant deviation; and rare endpoints make base rates unforgiving. Simulations of a synthetic route model illustrate every proposition. The author proposes a staged evaluation—retrospective, silent prospective, human-factors, then interventional—and a reporting checklist. No warning system is validated; all data are synthetic, and route labels describe observed associations, not established mechanisms.