Fig. 2
Cost‐sensitive triage performance and optimal ζ selection. (A) Fractions of patients assigned to regular ward (black), intermediate‐care unit (IMC; blue), or intensive care unit (ICU; red) as the cost‐sensitivity parameter ζ varies from -5 to + 5 in increments of 0.1. Solid lines denote the development cohort (n = 1072), and lighter markers with error bars denote the independent evaluation cohort (n = 81). When ζ is highly negative, prohibitive over‐triage costs drive almost all assignments to the ward; as ζ increases, IMC assignments peak in the shaded “tuning” region (ζ≈0.5–1.5), before ICU allocations dominate at high ζ. Error bars represent ± s.d. across 25 cross‐validation folds. (B) Histogram of ζ inflection points—defined as the ζ value at which the derivative of the total over‐triage rate reaches its maximum—across 50 bootstrapped cross‐validation runs. The median (green dashed line, 0.975) and mean (red dashed line, 0.833) are indicated. Clinically, this inflection point serves as an operating-point heuristic within the tuning range: it marks the region where further increases in ζ begin to yield diminishing reductions in under-triage while disproportionately increasing over-triage (i.e., escalation to higher-acuity care), reflecting a practical “diminishing returns” trade-off between under-triage risk and resource use. (C) Stacked plot of under‐triage (red), correct allocation (green), and over‐triage (yellow) rates as functions of ζ, illustrating how the balance of error types shifts smoothly across the tuning range. (D, E) Nine‐cell confusion matrices for representative ζ settings (–2.0, –1.5, –1.0, –0.5, 0.0, + 1.0, + 1.5, + 2.0) in (D) the development cohort and (E) the evaluation cohort. In each matrix, rows correspond to the true acuity class (ward, IMC, ICU), and columns correspond to the predicted class; cell shading reflects the proportion of patients in each category. At ζ = –2.0, under-triage (lower-left cells) is maximal, whereas at ζ = + 1.0, diagonal dominance indicates balanced, majority-correct triage in both datasets. Detailed confusion matrices for the main and evaluation cohorts are further supplied in supplementary Figures S1 and S2.
