An Entropy-Weighted Biological Energy Index for Decomposable Mortality Prediction and Patient-Specific Tipping Dimension Identification in Sepsis: A Hypothesis-Generating Methodological Study

Sepsis remains a leading cause of global mortality, yet current severity scores provide only aggregate risk estimates without identifying the specific biological systems driving individual deterioration. This limits precision triage and mechanism-guided intervention. To develop and evaluate the entropy-weighted Biological Energy Index (BEI), an explainable AI framework that quantifies a composite biomarker reserve and identifies the dominant “tipping dimension” responsible for mortality risk in individual patients. Here “energy” is an information-theoretic construct derived from biomarker values; it is not a metabolic (ATP) or physical measurement. We analyzed 17 biomarkers from the Davoudian et al. (2022) sepsis cohort (N=135 from 178 enrolled; 34.3% 90-day mortality among 105 patients with confirmed outcome). Entropy-based weights were derived from the geometric mean of Shannon information gain, mutual information, and Spearman |ρ|, each computed on quintile-binned energy scores, with normalization to unit sum applied once after the geometric mean. BEI was computed as a weighted energy score with per-patient tipping-contribution decomposition. SHAP analysis examined independent prognostic signals. Discrimination was assessed out-of-fold under 5-fold stratified cross-validation with the entropy weights recomputed inside each training fold; bootstrap confidence intervals, leave-one-out cross-validation, calibration, decision-curve and survival analyses were also performed. A complete-case sensitivity analysis was restricted to the 45 patients with all 17 markers observed, of whom 33 had a confirmed 90-day outcome (13 deaths). BEI achieved an out-of-fold AUC=0.793, comparable to the equal-weighted BEI (AUC=0.799) — entropy weighting conferred no discriminative advantage under leakage-free cross-validation — and to standard classifiers trained on the same 17 markers: logistic regression (AUC 0.787), random forest (0.819) and XGBoost (0.797), while retaining full interpretability. In the complete-case sensitivity analysis the out-of-fold AUC was 0.885 (95% CI 0.752–0.981), an imprecise estimate that overlaps the primary result. Mortality exhibited a sharp nonlinear gradient: 86% in the lowest BEI quintile versus 19% in the highest (n=21 per quintile). A four-tier tipping taxonomy (KILL, MODERATE, NOISE, BENIGN) identified PTX3 as the most frequent tipping dimension (17 of 105 patients), suggesting endothelial collapse as a candidate early failure mode warranting prospective investigation. Any consciousness impairment (GCS ≤14) was associated with 67% mortality (16/24). sIL-1R2 outperformed IL-18 for inflammasome-related mortality prediction (AUC 0.726 vs 0.610). BEI provides a transparent, decomposable framework for identifying per-patient biological failure modes in sepsis. Its contribution is interpretive rather than discriminative. All findings are derived from a single-center retrospective cohort and require external validation before clinical application. The framework is presented as a hypothesis-generating methodological contribution.