Dynamic Risk-Set Geometry and Eligibility Drift in Hourly ICU Deterioration Forecasting Under Treatment and Discharge Censoring

Abstract

Intensive care warning systems are commonly evaluated as though they solve a straightforward repeated classification problem over patient-time windows. At each hour, the model reads the chart and estimates whether deterioration will occur within a future horizon. This setup is practical and has enabled broad methodological progress, yet it conceals a basic structural complication. The denominator of the task is moving. Patients enter and leave the set of clinically eligible windows through discharge, death, prior intervention, endpoint occurrence, and benchmark-specific exclusion rules. Consequently, a score assigned at one hour is not directly comparable to the same score assigned later in the stay unless the changing risk set is modeled explicitly. This paper develops a formal account of hourly deterioration forecasting as a dynamic risk-set problem rather than a static sequence of binary labels. The central argument is that much of the apparent difficulty, calibration drift, and transport instability of ICU warning systems arises from eligibility dynamics and policy-dependent censoring that are currently hidden inside benchmark construction. A multistate framework is introduced in which event onset, rescue intervention, ineligibility, and discharge are competing transitions over a latent severity trajectory. The paper then studies how repeated-window labeling distorts prevalence, how intervention-sensitive censoring reshapes observed risk, and how thresholding policies become unstable when the denominator contracts in a state-dependent manner. It concludes by arguing that warning models should be selected and interpreted through eligibility-aware likelihoods, risk-set-normalized ranking metrics, and counterfactual policy analyses rather than through pooled window-level discrimination alone