Title:Missingness-Aware Conformal Prediction Under Cross-Hospital Distribution Shift

Abstract:Clinical measurements are recorded for some patients but not others, at rates that differ across hospitals, and marginal conformal coverage does not ensure coverage within groups defined by missingness. We propose a missingness-aware conformal calibration procedure for mortality prediction under cross-hospital distribution shift. It selects a measurement on an independent sample, groups patients by whether that measurement is recorded, and applies Mondrian calibration within each group, so no calibration outcome is reused. We evaluate the procedure across hospitals in eICU and across care units within one MIMIC-IV hospital, using three predictors. Relative to pooled calibration, it reduces the average worst-group coverage gap on its selected groups in all six settings, with a median reduction of 1.9 percentage points; paired site-bootstrap intervals exclude zero in five. These gains do not extend uniformly. Calibration by predicted risk achieves smaller gaps on a broader panel of missingness groups, and when eICU hospitals are evaluated separately, the gain shrinks for all three predictors and reverses in sign for one. We explain this discrepancy with a hospital-level decomposition. Pooling reweights hospitals through a covariance between group shares and coverage errors, and lets errors of opposite sign cancel: weighting explains the reversal, and cancellation accounts for most of the attenuation for the other two predictors. Constructed population distributions show that pooled and within-hospital evaluations can rank calibration methods oppositely even without sampling noise. Pooled improvement alone therefore cannot establish better coverage within hospitals, even when the calibration groups are fixed.

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