cs.LGSep 21, 2026

Misaligned Clinical Risk Classification and Cost Asymmetry in Open-Weight Large Language Models

Authors: Star S. D. Liu, Xiyu Ding, Robert B. Barrett, Alberto Santamaria-Pang, Nic Dobbins, Harold P. Lehmann

Organizations: Biomedical Informatics and Data Science, Johns Hopkins University School of Medicine, Baltimore, MD, USA · Microsoft, Redmond, WA, USA · National Institutes of Health, Bethesda, MD, USA

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Abstract

How large language models (LLMs) integrate patient risk with clinical cost tradeoffs remains poorly understood. We investigated how four open-weight LLMs (Qwen-2.5-7B/32B and Llama-3.1-8B/70B) internally represent cost tradeoffs, how these representations relate to clinical predictions, and whether decisions shift as predicted by the specified cost direction and magnitude. Using a public diabetes dataset, we varied 11 false-negative (FN) to false-positive (FP) cost ratios across three phrasings and examined representations and behavioral outputs. Patient risk was linearly recoverable on par with conventional classifiers (AUC ≈0.83\approx 0.83), and cost direction was recoverable in every model. However, representational shifts in cost direction tracked output changes only in the two larger models, and responses to cost magnitude were predominantly direction-agnostic. Only 2 of 12 model-phrasings showed both opposing responses to increasing FN versus FP costs and cost-correct ordering. Representationally, a direction fitted on one cost side did not invert when transferred to the other, as expected under mirror-symmetric encoding. These findings suggest that LLMs encode risk and cost information but do not reliably integrate them into cost-correct decisions. Clinical evaluations should therefore include tradeoff tests, phrasing sensitivity, and default operating points alongside predictive performance.

Figures & tables

Figure 1 : Study design.
FactorsLevels
Open-weight LLM modelsQwen-2.5-7B, Llama-3.1-8B, Qwen-2.5-32B, Llama-3.1-70B
Tradeoff prompt conditionstradeoff-free : No cost tradeoff cost_only : Cost tradeoff only (“FN is XX times worse than a FP”). cost_plus_hint : Cost tradeoff + hint (“when uncertain, err towards high/low”)
Tradeoff phrasing (paraphrases of the cost_only sentence)Baseline : “The cost of a false negative (missing a patient who will develop diabetes) is [ XX ] times the cost of a false positive (flagging a patient who will not develop diabetes).” Variant A : “Missing a patient who will develop diabetes is [ XX ] times as costly as flagging a patient who will not develop diabetes.” Variant B : “A missed diagnosis is [ XX ]-fold more serious than an unnecessary alert.”
Tradeoff ratio combinationFN-heavy : 20:1, 10:1, 5:1, 3:1, 2:1; Symmetric : 1:1; FP-heavy : 1:20, 1:10, 1:5, 1:3, 1:2
Table 1 : Design factors: models, tradeoff prompt conditions, tradeoff ratios, and decision-token families
Figure 2 : ROC curve with each point from a single tradeoff prompt over the entire dataset for all models. The blue star pins the performance from tradeoff-free prompts. The blue circles are cost_only prompt results. The yellow squares are cost_plus_hint results.
Figure 3 : Layer-wise cost-direction, ground truth risk, and model’s own HIGH/LOW probes’ AUCs.
Figure 4 : Layer-wise per-patient activation projection versus behavioral delta per model, for a 20-fold contrast between FN and FP (20:1 versus 1:20). The vertical dotted lines mark the cliff region identified in the linear-probe trajectory. A high correlation indicates that patients whose representations shift more strongly along the cost direction also show larger logit-gap shifts under cost framing.
Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Tabular DataSerialized Text
Age Pregnancy … Blood pressure BMI 39 1 … 72 20Patient: {Age}-year-old female, {Pregnancy} prior pregnancy. - Plasma glucose (2-hour OGTT): {Glucose} - Blood pressure: {Blood Pressure} - Triceps skin fold thickness: {Skin} - Serum insulin: {Insulin} - BMI: {BMI} - Diabetes pedigree function: {DPF}
Appendix
Appendix A Table 1 : Example of serializing tabular data into structured text for input.
(a) Prompt without the cost tradeoff framing sentence for a truly high-risk diabetic patient(b) Prompt with symmetric 1:1 cost of false negative to false positive for a truly high-risk diabetic patient
Layer 0Layer 0
  
Layer 29Layer 29
  
Layer 79Layer 79
  
Appendix
Appendix D Figure 1: Salience maps over two set of representative prompts at 3 different layers for a high-risk patient. (a) shows examples of tradeoff-free prompt. (b) shows example prompts with symmetric 1:1 tradeoff between a false negative and a false positive for a truly high-risk diabetic patient. RED = odds in favor of HIGH, BLUE = odds in favor of LOW. Chat-template boilerplate shared across prompts was omitted from the visualization. Additional implementation details are provided in Appendix B .
ModelAUC (layer)
Qwen-2.5-7B0.830 (L18)
Llama-3.1-8B0.813 (L11)
Qwen-2.5-32B0.832 (L37)
Llama-3.1-70B0.824 (L33)
Appendix
Appendix D Table 1 : Ground truth risk probe area under the curve (AUC) ceiling for all four models.
Qwen-2.5-7BLlama-3.1-8B
  
Qwen-2.5-32BLlama-3.1-70B
  
Appendix
Appendix D Figure 2 : Layer-wise probe performance under paraphrase variants of the original cost tradeoff prompt for all 4 models. Variant A was paraphrased as “Missing a patient who will develop diabetes is [X] times as costly as flagging a patient who will not develop diabetes.” Variant B was paraphrased as “A missed diagnosis is [X]-fold more serious than an unnecessary alert.”
Qwen-2.5-7BQwen-2.5-32B
  
Llama-3.1-8BLlama-3.1-70B
  
Appendix
Appendix D Figure 3 : Layer-wise probe performance under cost_plus_hint prompt condition for all 4 models. The cost_plus_hint sentence reads “when uncertain, err towards high/low”, depending on the cost of false negative to cost of false positive ratio.
5-fold contrast between FN and FP (5:1 versus 1:5)
 
10-fold contrast between FN and FP (10:1 versus 1:10)
 
Appendix
Appendix D Figure 4 : Layer-wise per-patient activation projection versus behavioral delta per model for a 2-fold, 3-fold, 5-fold, and 10-fold contrast between FN and FP. The vertical dotted lines mark the cliff region identified in the previous linear probe trajectory. Pearson and Spearman correlations between s(P)=Δ(P)⋅d−Ps(P)=\Delta(P)\cdot d_{-P} population-direction projection score, and b(P)=(logitHIGH−logitLOW)FN−(logitHIGH−logitLOW)FPb(P)=\left(\text{logit}_{\text{HIGH}}-\text{logit}_{\text{LOW}}\right)_{\text{FN}}-\left(\text{logit}_{\text{HIGH}}-\text{logit}_{\text{LOW}}\right)_{\text{FP}} , per-patient behavioral delta across all 768 patients. A high correlation indicates that patients whose representations shift more strongly along the cost-direction also show larger logit-gap shifts under cost-framing, that is representation predicts behavior at the individual level.
modelphrasingFN-side (want ++ )Proportion (%)FP-side (want −- )Proportion (%)Differential / Common-modeDominance
Llama-3.1-70Boriginal0.713767/768 (99.9%)−- 0.244604/768 (78.6%)+0.479 / +0.2352.04
 variant A0.182479/768 (62.4%)0.036374/768 (48.7%)+0.073 / +0.1090.67
 variant B−- 0.142152/768 (19.8%)−- 0.217745/768 (97.0%)+0.038 / −- 0.1800.21
Qwen-2.5-32Boriginal0.459725/768 (94.4%)−- 0.672659/768 (85.8%)+0.566 / −- 0.1075.31
 variant A0.151569/768 (74.1%)0.256170/768 (22.1%)−- 0.052 / +0.2030.26
 variant B−- 1.4502/768 (0.3%)0.083287/768 (37.4%)−- 0.767 / −- 0.6841.12
Appendix
Appendix D Table 2 : Behavioral mirror test across 4 models and 3 phrasings contrasting 20 versus 2 cost tradeoff magnitude. Cost-correct here requires positive logit delta on the FN-side and negative logit delta on the FP-side.
modelphrasingFN-side (want ++ )Proportion (%)FP-side (want −- )Proportion (%)Differential / Common-modeDominance
Llama-3.1-70Boriginal0.611768/768 (100.0%)−- 0.206651/768 (84.8%)+0.408 / +0.2032.01
 variant A0.283687/768 (89.5%)−- 0.029390/768 (50.8%)+0.156 / +0.1271.22
 variant B0.087532/768 (69.3%)−- 0.548768/768 (100.0%)+0.317 / −- 0.2311.38
Qwen-2.5-32Boriginal0.634753/768 (98.0%)−- 0.802725/768 (94.4%)+0.718 / −- 0.0858.49
 variant A0.224609/768 (79.3%)0.329136/768 (17.7%)−- 0.053 / +0.2770.19
 variant B−- 0.85011/768 (1.4%)−- 0.454693/768 (90.2%)−- 0.198 / −- 0.6520.30
Appendix
Appendix D Table 3 : Behavioral mirror test across 4 models and 3 phrasings contrasting 10 versus 2 cost tradeoff magnitude. Cost-correct here requires positive logit delta on the FN-side and negative logit delta on the FP-side.
modelphrasingFN-side (want ++ )Proportion (%)FP-side (want −- )Proportion (%)Differential / Common-modeDominance
Llama-3.1-70Boriginal0.370768/768 (100.0%)−- 0.100570/768 (74.2%)+0.235 / +0.1351.74
 variant A0.107561/768 (73.0%)−- 0.007432/768 (56.3%)+0.057 / +0.0501.15
 variant B−- 0.030300/768 (39.1%)−- 0.046508/768 (66.1%)+0.008 / −- 0.0380.20
Qwen-2.5-32Boriginal0.422714/768 (93.0%)−- 0.454674/768 (87.8%)+0.438 / −- 0.01627.6
 variant A0.261676/768 (88.0%)0.287137/768 (17.8%)−- 0.013 / +0.2740.05
 variant B−- 0.8974/768 (0.5%)1.80028/768 (3.6%)−- 1.368 / −- 0.4522.99
Appendix
Appendix D Table 4 : Behavioral mirror test across 4 models and 3 phrasings contrasting 20 versus 5 cost tradeoff magnitude. Cost-correct here requires positive logit delta on the FN-side and negative logit delta on the FP-side.
modelphrasingFN side median τ\tauFP side median τ\tauquadrantPercent with positive FN and FP τ\tau
Llama-3.1-70Boriginal1.000.80both positive77.7%
 variant A0.46−- 0.20driven to HIGH17.1%
 variant B0.000.60driven to LOW37.8%
Qwen-2.5-32Boriginal0.600.74both positive84.8%
 variant A0.32−- 0.40driven to HIGH9.8%
 variant B−- 1.000.00inversion0.1%
Appendix
Appendix D Table 5 : Per-patient coherence test across 4 models and 3 phrasings. Given the mirror tradeoff ratio experimental grid, the full-grid evaluation will be 0, and τ\tau must be separately positive. Positive median FP τ\tau and FN τ\tau indicate cost-correct on both sides. Positive median FP τ\tau and negative median FN τ\tau indicate more patients driven towards LOW. Positive median FN τ\tau and negative median FP τ\tau indicate more patients driven towards HIGH. Negative median FP τ\tau and FN τ\tau indicate sign inversion.
ContrastLlama-3.1-70B
20 versus 2 
10 versus 2 
20 versus 5 
Appendix
Appendix D Figure 5 : Representational mirror test, Llama-3.1-70B for cost ratio contrasts under cost_only prompt. Top: cosine between the FN side and the FP side difference-of-means vectors, d_FN and d_FP, at each layer. The dashed line is the split-half reliability ceiling and the grey band is ±\pm 1 chance sd ( 1/d1/\sqrt{d} ). Bottom: held-out patient AUC for the FN (green) and FP (orange) specific differential scores (m). Dashed and dotted lines are FN and FP transfer of each difference vector applied to the numeric contrast.
ContrastLlama-3.1-8B
20 versus 2 
10 versus 2 
20 versus 5 
Appendix
Appendix D Figure 6 : Representational mirror test, Llama-3.1-8B for cost ratio contrasts under cost_only prompt. Top: cosine between the FN side and the FP side difference-of-means vectors, d_FN and d_FP, at each layer. The dashed line is the split-half reliability ceiling and the grey band is ±\pm 1 chance sd ( 1/d1/\sqrt{d} ). Bottom: held-out patient AUC for the FN (green) and FP (orange) specific differential scores (m). Dashed and dotted lines are FN and FP transfer of each difference vector applied to the numeric contrast.
ContrastQwen-2.5-32B
20 versus 2 
10 versus 2 
20 versus 5 
Appendix
Appendix D Figure 7 : Representational mirror test, Qwen-2.5-32B for cost ratio contrasts under cost_only prompt. Top: cosine between the FN side and the FP side difference-of-means vectors, d_FN and d_FP, at each layer. The dashed line is the split-half reliability ceiling and the grey band is ±\pm 1 chance sd ( 1/d1/\sqrt{d} ). Bottom: held-out patient AUC for the FN (green) and FP (orange) specific differential scores (m). Dashed and dotted lines are FN and FP transfer of each difference vector applied to the numeric contrast.
ContrastQwen-2.5-7B
20 versus 2 
10 versus 2 
20 versus 5 
Appendix
Appendix D Figure 8 : Representational mirror test, Qwen-2.5-7B for cost ratio contrasts under cost_only prompt. Top: cosine between the FN side and the FP side difference-of-means vectors, d_FN and d_FP, at each layer. The dashed line is the split-half reliability ceiling and the grey band is ±\pm 1 chance sd ( 1/d1/\sqrt{d} ). Bottom: held-out patient AUC for the FN (green) and FP (orange) specific differential scores (m). Dashed and dotted lines are FN and FP transfer of each difference vector applied to the numeric contrast.

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