Finite-Sample Instability, Threshold Sensitivity, and Error Propagation in Early Anastomotic Leak Prediction

Abstract

Clinical prediction studies for postoperative complications often summarize performance by a small set of point estimates, even when the event is uncommon and the positive class in the test set is numerically small. In that setting, the apparent ranking of algorithms can be more fragile than it first appears. This paper presents an empirical uncertainty audit of early anastomotic leak prediction from structured perioperative records. The analysis reinterprets a reported held-out experiment not as a fixed leaderboard, but as a finite-resolution sample in which recall, precision, alert burden, and threshold choice are all subject to nontrivial instability. The paper examines three empirical questions. First, how much statistical resolution is actually available when only a small number of positive cases determine sensitivity estimates and thresholded comparisons? Second, how sharply can an F1-selected operating point distinguish between neighboring model families when one or two admissions can materially alter the observed metric balance? Third, how do these uncertainties scale when the model outputs are translated into service-level decisions such as alerts, workups, or intensified surveillance? The results indicate that the informative content of the experiment lies less in a simple declaration of the best model than in the geometry of uncertainty around the reported operating points. The stronger nonlinear configurations remain clinically interesting, but the observed gaps between several of them are narrower than their point estimates imply. At the same time, the differences in false-positive accumulation are large enough to matter under plausible error costs. The paper argues that rare-event surgical modeling should report interval structure, threshold volatility, and cost-ratio switching behavior alongside standard discrimination metrics, because these quantities better describe what the experiment actually establishes.