Quantifying Volumetric Risk: Class-Aware Asymmetric Weighted Conformal Prediction for 3D Medical Image Segmentation

Shadi Alijani; Fereshteh Aghaee Meibodi; Homayoun Najjaran

cs.CVOct 7, 2026

Quantifying Volumetric Risk: Class-Aware Asymmetric Weighted Conformal Prediction for 3D Medical Image Segmentation

Authors: Shadi Alijani, Fereshteh Aghaee Meibodi, Homayoun Najjaran

Organizations: University of Victoria, 800 Finnerty Road, Victoria, BC, Canada

Abstract

Reliable volumetric segmentation is critical for clinical diagnostics, yet foundation models such as MedSAM remain deterministic and lack calibrated uncertainty under distribution shift. Existing conformal prediction methods offer statistical guarantees but are frequently applied in 2D and assume symmetric error distributions, so they do not capture the class-specific biases that arise in 3D multi-class segmentation. We propose Class-Aware Asymmetric Weighted Conformal Prediction (CA-WCP), which combines latent-space density-ratio weighting for covariate shift with directional quantiles for the lower and upper volume bounds, and scales each bound by a class-specific asymmetry factor derived from validation-set false-positive and false-negative rates. We prove that CA-WCP retains the weighted-exchangeability marginal coverage guarantee for every class, and we evaluate it on 3D brain tumor segmentation (BraTS 2020) and on a synthetic multi-organ CT benchmark constructed under covariate shift. On both benchmarks the 95% Clopper--Pearson interval for the observed coverage of CA-WCP contains the nominal 90% level for every semantic class, while interval width is reduced by 8--14% relative to symmetric weighted conformal prediction. We further encode the calibrated intervals into structured prompts for a multimodal large language model to produce uncertainty-conditioned radiology reports, linking distribution-shift-aware uncertainty quantification to interpretable clinical communication.

Figures & tables

Figure 1: Class-specific error patterns revealing asymmetric biases in brain tumor segmentation, measured on the validation split. (Left) False positive versus false negative rates. Rates are normalized by ground-truth volume $v^{*}$ (Eq. ( 5 )), so values above 100% are well defined and indicate severe over-segmentation. Necrotic core shows a false-negative bias, edema a large false-positive bias, and enhancing tumor a moderate false-positive bias. (Right) Distribution of volume errors across classes, showing the skew that motivates asymmetric interval design.

Figure 2: Overview of the proposed CA-WCP pipeline: feature extraction, multi-threshold segmentation, and weighted asymmetric conformal prediction.

Backbone Dice (identical for all rows): necrosis 0.63, edema 0.81, enhancing 0.88
	Necrosis		Edema		Enhancing
Method	Cov (%) [95% CI]	Wid.	Cov (%) [95% CI]	Wid.	Cov (%) [95% CI]	Wid.
Unweighted CP	84.9 [74.6–92.2]	4.2	78.1 [66.9–86.9]	21.5	97.3 [90.5–99.7]	6.8
Symmetric WCP	90.4 [81.2–96.1]	3.9	86.3 [76.2–93.2]	19.2	100.0 [95.1–100.0]	5.9
Directional WCP ( $\gamma\equiv 1$ )	87.7 [77.9–94.2]	2.8	84.9 [74.6–92.2]	12.5	89.0 [79.5–95.1]	4.8
Ours (CA-WCP)	90.4 [81.2–96.1]	3.6	90.4 [81.2–96.1]	16.8	90.4 [81.2–96.1]	5.1

Table 1: Per-class results on BraTS 2020 (target coverage 90%,

n=73

). Coverage is an exact

k/73

fraction with a 95% Clopper–Pearson interval. Width in mL.

Method	Dice	Cov. (%)	Wid. (mL)	Dir. $q$	Class $\gamma$	Shift
MedSAM [ 27 ] (no CP)	0.77	–	–	–	–	–
+ Unweighted CP	0.77	86.8	10.8	No	No	No
+ Symmetric WCP [ 23 ]	0.77	92.2	9.7	No	No	Yes
+ Directional WCP ( $\gamma\equiv 1$ )	0.77	87.2	6.7	Yes	No	Yes
+ Ours (CA-WCP)	0.77	90.4	8.5	Yes	Yes	Yes

Table 2: Aggregate results on BraTS 2020 with a fixed MedSAM backbone. Coverage and width are the unweighted mean of the three per-class values in Table 1 . Dir.

q

: directional quantiles; Class

\gamma

: asymmetry factors; Shift: density-ratio weighting. Bold coverage denotes the value closest to the nominal 90% target; coverage above the target reflects over-conservatism, and a smaller width obtained at coverage below the target is not a like-for-like efficiency gain.

Backbone Dice: liver 0.92, kidneys 0.88, spleen 0.85
	Symmetric WCP		Ours (CA-WCP)
Organ (Scale)	Cov (%) [95% CI]	Wid.	Cov (%) [95% CI]	Wid.
Liver (large)	98.0 [93.0–99.8]	145.2	91.0 [83.6–95.8]	128.4
Kidneys (medium)	89.0 [81.2–94.4]	32.1	90.0 [82.4–95.1]	29.5
Spleen (small)	84.0 [75.3–90.6]	18.5	90.0 [82.4–95.1]	16.8

Table 3: Synthetic multi-organ CT benchmark under induced conditioning shift (target coverage 90%,

n=100

). Coverage is an exact

k/100

fraction with a 95% Clopper–Pearson interval. Width in mL.

Prompt configuration	BLEU-4	Factual Acc.	Uncert. Concord.
Image+Seg	0.28	3.8 / 5.0	2.1 / 5.0
Ours (Image+Seg+UQ)	0.42	4.8 / 5.0	4.6 / 5.0

Table 4: Assessment of uncertainty-conditioned report generation on 10 BraTS test cases. BLEU-4 is computed against the templated reference reports; factual accuracy and uncertainty concordance are rated on a 1–5 scale by an independent radiologist blinded to the prompt configuration.

Figure 3: Representative patient: ground-truth and predicted tumor subregions overlaid on the T1-weighted MR anatomy, with the uncertainty-conditioned report generated from the calibrated volumetric intervals.

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