arXiv:2609.01909v1 Announce Type: new
Abstract: Clinical prediction can saturate for two different reasons: a fitted learner may fail to extract available information, or the recorded variables may impose a population frontier. We separate these quantities through the \emph{learner gap} and the \emph{measurement-channel ceiling}. Optimal balanced accuracy is characterized by total-variation separation, yielding architecture invariance, a sharp partial-identification result under replacement contamination, a cross-fitted ceiling estimator, and exact conditions for multimodal decision improvement. We add two finite-sample diagnostics, namely a label-permutation optimism floor and an underfit curve, and validate the audit on three real cohorts: UCI readmission ($n=99{,}343$), BRFSS diabetes ($n=253{,}680$), and NHANES HbA1c ($n=10{,}219$). Well-tuned gradient boosting nearly reaches the estimated frontier in UCI and BRFSS, whereas deliberately or practically deficient learners retain large gaps. NHANES yields a null difference between questionnaire and measured marginal frontiers but a significant joint complementarity gain, refining the simplistic claim that an objective modality must dominate. Across all cohorts, modest AUROC gains coexist with substantially larger Bayes decision-flip rates, and several architectures estimate similar frontiers while their achieved balanced accuracy differs sharply. A PRISMA-guided synthesis of 104 clinical tasks then shows that the same channel-level regularities recur across more than 18 disease categories: a broad but non-universal structured-clinical region, diminishing same-channel gains across model families, and higher performance when measurement channels change. The framework converts saturation from an empirical observation into an auditable decision: improve the learner when headroom remains; improve measurement when it does not.
Abstract: Clinical prediction can saturate for two different reasons: a fitted learner may fail to extract available information, or the recorded variables may impose a population frontier. We separate these quantities through the \emph{learner gap} and the \emph{measurement-channel ceiling}. Optimal balanced accuracy is characterized by total-variation separation, yielding architecture invariance, a sharp partial-identification result under replacement contamination, a cross-fitted ceiling estimator, and exact conditions for multimodal decision improvement. We add two finite-sample diagnostics, namely a label-permutation optimism floor and an underfit curve, and validate the audit on three real cohorts: UCI readmission ($n=99{,}343$), BRFSS diabetes ($n=253{,}680$), and NHANES HbA1c ($n=10{,}219$). Well-tuned gradient boosting nearly reaches the estimated frontier in UCI and BRFSS, whereas deliberately or practically deficient learners retain large gaps. NHANES yields a null difference between questionnaire and measured marginal frontiers but a significant joint complementarity gain, refining the simplistic claim that an objective modality must dominate. Across all cohorts, modest AUROC gains coexist with substantially larger Bayes decision-flip rates, and several architectures estimate similar frontiers while their achieved balanced accuracy differs sharply. A PRISMA-guided synthesis of 104 clinical tasks then shows that the same channel-level regularities recur across more than 18 disease categories: a broad but non-universal structured-clinical region, diminishing same-channel gains across model families, and higher performance when measurement channels change. The framework converts saturation from an empirical observation into an auditable decision: improve the learner when headroom remains; improve measurement when it does not.
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