Stochastic-Process Representations for Informative Missingness in Multimodal ICU Forecasting under Distribution Shift and Causal Masking Constraints

Abstract

This paper develops a framework for risk forecasting that treats irregular sampling and missingness as first-class stochastic objects rather than as artifacts to be imputed away. We formalize electronic health record inputs as marked point processes and derive a risk estimator that conditions on both observed values and the endogenous measurement policy. The model couples a latent continuous-time state space for patient dynamics with a separately parameterized observation-intensity model, enabling explicit reasoning about informative missingness, temporal uncertainty, and asynchrony between numeric streams and text-derived context. We propose modality-stable fusion operators that remain well-defined when notes are absent or temporally ambiguous, and we analyze learning objectives that preserve discrimination under extreme class imbalance while allowing post-hoc calibration to recover probability semantics. Finally, we outline evaluation protocols that separate gains due to physiologic signal from gains due to measurement-policy shortcuts, including stratified testing across missingness regimes, shift-sensitive calibration checks, and event-level operational metrics. The resulting treatment provides a principled path from irregular clinical logs to reliable probabilistic forecasting models that are compatible with streaming deployment and retrospective auditing