Clinical prediction can saturate for two distinct reasons: the fitted learner fails to extract all available information, or the recorded variables impose a population‑level frontier. We formalize these as the learner gap and the measurement‑channel ceiling.
Using total‑variation separation, optimal balanced accuracy cleanly separates the two constraints, yielding architecture invariance and a sharp partial‑identification result under replacement contamination. A cross‑fitted ceiling estimator is introduced, together with exact conditions for multimodal decision improvement.
To diagnose finite‑sample scenarios we add two tools: a label‑permutation optimism floor and an underfit curve. The audit is validated 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 the UCI and BRFSS data, whereas deliberately or practically deficient learners retain large gaps. In NHANES the marginal frontiers of questionnaire and measured variables are statistically indistinguishable, yet their joint complementarity gain is significant, refuting the simplistic claim that an objective modality must dominate.
Across all cohorts, AUROC gains are modest but Bayes decision‑flip rates improve substantially; different architectures often estimate similar frontiers while their achieved balanced accuracy diverges sharply. A PRISMA‑guided synthesis of 104 clinical tasks 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 turns saturation from an empirical observation into an auditable decision: improve the learner when headroom remains; improve measurement when it does not.
Review