The problem
A single length-of-stay number can’t say whether a hospital stay ended in discharge or in death.
Two stays of identical length can end in completely different ways, and treating discharge and death as independent predictions doesn’t fix that: their probabilities could add to more than one, and once one outcome happens, the other becomes impossible for that patient.
The model instead tracks three mutually exclusive states after the day-3 assessment: still hospitalised, discharged alive, or died in hospital. These probabilities always sum to one, on every day of follow-up.
From 28 variables to 15
Two model families compete on equal terms: one additive, one free to learn interactions.
Logistic regression is the additive benchmark. Histogram gradient boosting (HGB) asks whether nonlinear structure and interactions improve the probability estimates. On validation, HGB wins by a margin large enough to justify the extra complexity, so HGB is selected.
HGB then gives up almost half its predictors for free: a simplified 15-feature version scores essentially the same as the full 28-feature one, while logistic regression still needs all 28 to match its own best result.
What the model actually learned
The single strongest predictor isn’t a lab value. It’s whether a form was filled in.
Patient-reported activities of daily living (ADL) outranks every other predictor for both model families. An ablation asks why: keep only a flag for whether the value was recorded, drop the value itself, and the model barely loses accuracy. Keep the value and drop the flag, and accuracy drops sharply.
Most of what makes this field useful is whether it was recorded, not what it says. A model trained on clinical data can learn something about the documentation process as well as about the patient. Why the field goes unrecorded, whether severity, workflow, or something else entirely, isn’t something this analysis can establish.
Held-out performance
On patients the model never touched during development, it still beats a population-only guess by a wide margin.
- 30.4%lower Brier · live discharge
- 22.3%lower Brier · in-hospital death
- 15predictors, down from 28
Relative reduction in mean daily Brier versus a patient-independent population reference, held-out test set.
Better predictions do not automatically mean trustworthy probabilities. At 30 days, death probabilities were reasonably well calibrated. Discharge probabilities were systematically overestimated. The model was confident about discharge more often than discharge actually happened.
Before this means anything clinically
This is an internally validated historical analysis, not a clinical tool.
SUPPORT2 is 1990s data from five US teaching hospitals, and the held-out test is a same-source split. It checks reproducibility within that historical population, not performance in a different hospital, healthcare system, or decade.