Bound-Aware Per-Organ Recall Risk Control for Multi-Organ CT Segmentation under Clinical Domain Shift

Souraj Adhikary; Negar Chabi; Andre Mastmeyer

cs.CVAug 18, 2026

Bound-Aware Per-Organ Recall Risk Control for Multi-Organ CT Segmentation under Clinical Domain Shift

Authors: Souraj Adhikary, Negar Chabi, Andre Mastmeyer

Organizations: Department of Engineering Sciences, Jade Hochschule Wilhelmshaven, Germany

Abstract

Distribution-free risk control adds organ-specific recall guarantees to frozen segmentation. We calibrate per-organ thresholds for an AMOS-trained nnU-Net, audit transfer to RAOS, and estimate local re-certification cost using case-level voxel false-negative rate (FNR). The AMOS control passes, but $7/12$ organs exceed $α{=}0.10$ after transfer; smaller calibration sets can mask exceedances with conservative or vacuous thresholds. Risk-Controlling Prediction Sets (RCPS) give high-probability control of population-mean risk, whereas Conformal Risk Control (CRC) gives weaker expectation control. Both require exchangeability; fixed and global thresholds give no per-organ guarantee. The Waudby--Smith--Ramdas (WSR) betting bound re-certifies six Tier-1 organs with 25 local cases, versus 30--40 for Hoeffding--Bentkus (HB). CRC needs 10--15 but has a heavier individual-case tail. No Tier-2 organ meets our illustrative precision criterion with 25 cases.

Figures & tables

Figure 1: Frozen AMOS thresholds often fail on RAOS. Centre: one RAOS case at the duodenum threshold $\tau{=}0.024$ ; red marks missed ground-truth voxels, teal recalled ones (case FNR $0.29$ , cohort mean $0.30$ ). With pooled AMOS out-of-fold calibration, $7/12$ organs exceed $\alpha{=}0.10$ on RAOS; only three of the other five have a non-vacuous threshold. Here, re-certification varies with the bound and budget ( Section 5.3 ).

Figure 2: Transfer audit ( $\alpha{=}0.10$ ). Per-organ FNR for AMOS in-distribution vs. frozen-threshold transfer to RAOS, with 95% CIs; highlighted organs exceed $\alpha$ on RAOS.

Organ	$\lambda_{k}$	AMOS FNR	RAOS FNR (95% CI)	$n_{\text{AMOS}}$	$n_{\text{RAOS}}$
Bladder	0.277	0.061	0.088 [0.074, 0.105]	233	163
Duodenum	0.024	0.063	0.297 [0.264, 0.330]	236	163
Esophagus	0.050	0.064	0.152 [0.139, 0.166]	235	161
Gallbladder	0.051	0.063	0.161 [0.131, 0.196]	222	123
L adrenal	0.000	0.000	0.000 [0.000, 0.000]	236	163
L kidney	0.690	0.064	0.130 [0.124, 0.137]	235	160

Table 1: Frozen AMOS thresholds

\lambda_{k}

and realized voxel FNR at

\alpha{=}0.10

on AMOS and the clinically shifted RAOS cohort, with 95% CI. Boldface marks RAOS FNR exceeding

\alpha

; both adrenals’

\lambda_{k}{=}0.000

is vacuous;

n_{\text{AMOS}}/n_{\text{RAOS}}

are present-organ case counts.

Figure 3: Re-certification analysis ( $\alpha{=}0.10$ ). (a) Precision at a fixed 25-case budget, HB vs. WSR. (b) False-positive cost vs. in-domain calibration cases.

High-probability control: $\mathbb{P}(R_{k}\leq\alpha)\geq 1-\delta$
	Usable budget $n$			Held-out loss, column-wise worst
Rule	$\alpha{=}.10$	$\alpha{=}.05$	simult.	mean	$p_{95}$	$p_{99}$	max	% ${>}\alpha$
WSR	25	50–80	50–60	.012	.043	.092	.64	1.0
HB	30–40	60–100	60–100	.002	.010	.020	.29	0.0
Expectation control: $\mathbb{E}[L_{k}]\leq\alpha$
CRC	10–15	25	—	.066	.175	.922	1.00	17.4

Table 2: Within high-probability control, WSR needs fewer cases than HB. Left: usable local RAOS budgets for the six Tier-1 organs; ranges span organs. A usable threshold controls held-out FNR and has precision

{\geq}0.5

; “simult.” uses Bonferroni

\delta/12

over all 12 at

\alpha{=}0.10

. HB and WSR provide high-probability control; CRC provides expectation control, so their counts are not equivalent. Right: held-out case loss at

n{=}25

\alpha{=}0.10

. Each column reports the worst statistic among organs with a non-vacuous threshold (CRC 9, WSR 6, HB 2); columns can refer to different organs. At

\alpha{=}0.05

, HB never certifies the right kidney within our grid.

Figure 4: (a) Surgical-shift ladder is nearly flat. (b) Contrast/sex decomposition with $\alpha$ and 95% CIs.

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ReCIRC: Rectified Conformal Risk Control

Bruno Marcondes e Resende, Helton Graziadei, Thiago Rodrigo Ramos, Rafael Izbicki

Department of Statistics, Federal University of São Carlos

Conformal Prediction Conformal Risk Control

Open paper AskPDF arXiv

Many applications of black-box predictive models require controlling task-relevant error rates, such as missed lesion pixels in segmentation or missed labels in multilabel classification. Conformal risk control (CRC; Angelopoulos et al., arXiv:2208.02814) gives distribution-free guarantees for such losses, but it calibrates a single threshold shared by all inputs. Because conditional risk varies with the input, this marginal guarantee often overprotects easy cases and underprotects hard ones. We propose ReCIRC (Rectified Conformal Risk Control), which inverts each input's estimated local risk curve to reparameterize the calibrated threshold as a risk budget

a

representing a common target conditional risk, and then applies CRC unchanged to the resulting family. ReCIRC retains CRC's finite-sample marginal guarantee regardless of the accuracy of the estimated curves, while accurate curves yield approximate conditional risk control and, under additional conditions, asymptotically exact conditional risk control; they also support a risk-calibration diagnostic. Across three synthetic and five real-data settings spanning segmentation, multilabel and multiclass classification, and regression, ReCIRC attained the lowest average worst-group risk and mean positive group excess in every setting, while maintaining marginal risk close to the target, whereas changes in prediction size were application-dependent.

Abstract

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