Standard CRC enforces average-risk guarantees but fails silently on worst-group safety when radiology VLMs process display-recaptured smartphone images. We introduce FDV and WG-CRC — achieving 0/15 violations at 23.9% coverage, an 8.9× improvement over Bonferroni at matched safety.
Chest radiographs often reach clinicians in low-resource telemedicine settings as display-recaptured smartphone images rather than native digital studies. These images introduce structured acquisition artifacts that create clinically meaningful distribution shift for radiology vision-language models (VLMs). Standard Conformal Risk Control (CRC) enforces average-risk guarantees, but it can still violate worst-group safety on harder corruption subgroups — a failure that remains invisible under aggregate evaluation.
We trace this behavior to cross-modal decoupling: when visual evidence is degraded, the language decoder remains fluent and confident, producing disagreement across stochastic samples without correspondingly high token entropy. Motivated by this effect, we introduce Findings-Disagreement-Variance (FDV), an uncertainty score combining entropy and cross-sample disagreement, together with Worst-Group Conformal Risk Control (WG-CRC), a post-hoc calibration framework targeting subgroup-level safety without retraining.
On TeleRadShift, a structured 15-group benchmark, WG-CRC achieves 0/15 violations at 23.9% coverage, an 8.9× improvement over Bonferroni at matched safety. The method transfers without recalibration to 1,800 real smartphone captures (0/9 violations, worst-group risk 0.492) and remains stable across 30 random splits (worst-group risk 0.506 ± 0.022).
Standard CRC satisfies global risk guarantees while silently violating worst-group safety under structured telemedicine acquisition shift — an undetected deployment hazard invisible to conventional evaluation.
Post-hoc calibration combining disagreement-based uncertainty with group-conditional conformal bounds. Achieves 0/15 group violations at 23.9% coverage — an 8.9× improvement over Bonferroni at matched safety.
15 synthetic corruption groups (5 families × 3 severities) plus 1,800 real smartphone captures for systematic evaluation of VLM reliability under realistic telemedicine conditions.

A telemedicine chest X-ray undergoes structured acquisition corruptions (blur, brightness, JPEG, occlusion, screen). N=6 stochastic VLM samples are drawn, each parsed into binary findings. FDV uncertainty (entropy H and cross-modal disagreement D) is computed and used to calibrate a per-group abstention threshold τ̂g. At inference, FDV(x) < τ̂g delivers a risk-controlled report; otherwise the case is deferred to a radiologist.
15 groups: 5 families (Gaussian blur, brightness shift, JPEG compression, screen re-photography, occlusion) × 3 severity levels applied to 11,733 CheXpert chest X-rays.
CheXagent-8B generates N=6 stochastic reports per image at T=0.8 with nucleus sampling (top-p=0.9). Each report is parsed into binary pathology predictions ŷ ∈ {0,1}L.
Combines normalized entropy H̃(x) and pairwise disagreement D(x). Disagreement achieves Spearman ρ=0.606 — nearly 3× stronger than entropy alone (ρ=0.197).
Per-group thresholds calibrated at εcal = ε − Δ*, where Δ* adds base margin Δ and Hoeffding's finite-sample correction. For TeleRadShift: Δ=0.04, correction≈0.104, εcal=0.356.

As threshold τ increases, both worst-group risk and coverage rise. The safe zone (below ε=0.50) is entered at τ≈0.38. WG-CRC selects the coverage-maximising τ̂g per group calibrated at εcal=0.356.

Disagreement D dominates entropy H across all five corruption families (D: 0.57–0.67, H: 0.16–0.23). FDV combines both signals for calibration stability and coverage.
Evaluated on 5,333 test images across 15 corruption groups (ε=0.50). WG-CRC is the only method achieving zero violations with clinically meaningful coverage. Per-Group CRC without the buffer Δ fails 11/15 groups — showing Δ is structurally necessary, not a post-hoc tuning device. Bonferroni is safe but certifies only 2.7%; WG-CRC certifies 23.9% — an 8.9× improvement.
Table 1 — Main Results on TeleRadShift (n=5,333, 15 corruption groups, ε=0.50)
| Method | Avg. Risk ↓ | Worst-Group Risk ↓ | Coverage ↑ | Violations | Safe? |
|---|---|---|---|---|---|
| No Abstention | 0.635 | 0.696 | 100.0% | 15/15 | ✗ |
| Self-Consistency (H only) | 0.548 | 0.670 | 16.6% | 14/15 | ✗ |
| Per-Group CRC (no Δ) | 0.521 | 0.588 | 39.1% | 11/15 | ✗ |
| Bonferroni (Hoeffding) | 0.304 | 0.467 | 2.7% | 0/15 | ✓ |
| Worst-Group Tuned Global | 0.387 | 0.436 | 12.9% | 0/15 | ✓ |
| Minimax (cov ≥ 23.9%) | 0.464 | 0.516 | 30.6% | 3/15 | ✗ |
| Vanilla CRC | 0.472 | 0.528 | 33.6% | 3/15 | ✗ |
| WG-CRC + FDV (ours) | 0.450 | 0.500 | 23.9% | 0/15 | ✓ |

WG-CRC is the only method below ε=0.50 with clinically meaningful coverage. Points above the dashed line violate safety; lower-left methods are safe but unusable. The gap between Vanilla CRC and WG-CRC reveals the hidden failure of average-risk calibration.
Disagreement achieves Spearman ρ=0.606 with diagnostic risk (n=5,000, p < 10−100), while entropy achieves only ρ=0.197 — nearly three times weaker. FDV achieves ρ=0.492, capturing disagreement's predictive power while gaining coverage stability from entropy.
Table 2 — Spearman ρ between Uncertainty Signals and Diagnostic Risk
| Signal | ρ (corrupted) ↑ | ρ (clean) | Range |
|---|---|---|---|
| H (entropy) | 0.197 | 0.121 | 0.16–0.23 |
| D (disagreement) | 0.606 | 0.244 | 0.57–0.67 |
| FDV (α=0.5) | 0.492 | 0.171 | 0.47–0.51 |

Consistent positive correlation (ρ=0.47–0.51) across blur, brightness, JPEG, occlusion, and screen. This family-wise consistency confirms FDV as a reliable risk proxy under all tested acquisition artifacts.
200 real chest X-rays photographed on three consumer smartphones (iPhone 13 Pro Max, Samsung Galaxy S23, Google Pixel 7) under three lighting conditions → 1,800 total captures across G'=9 acquisition groups. WG-CRC thresholds applied directly from synthetic CheXpert calibration — no phone-specific tuning.

Naturalistic artifacts absent from synthetic calibration: (a) occlusion from hand placement, (b) display moiré from sensor-monitor interference, (c) perspective distortion from off-axis capture, (d) low-light sensor noise.
FDV achieves Spearman ρ=0.492 on real captures, consistent with the synthetic test-set range (0.471–0.514). WG-CRC maintains worst-group risk 0.492 ≤ ε=0.50 with 24.3% coverage; Vanilla CRC violates safety in 1/9 groups.
Table 3 — WG-CRC on Real Smartphone Captures (1,800 images, G'=9 groups)
| Method | Coverage ↑ | Violations ↓ | Worst Risk ↓ |
|---|---|---|---|
| Vanilla CRC | 21.2% | 1/9 | 0.531 |
| WG-CRC (ours) | 24.3% | 0/9 | 0.492 |

WG-CRC: mean 0.506±0.022, 17/30 seeds achieve zero violations, 27/30 at most one. Vanilla CRC violates ε=0.50 in all 30 runs, averaging 4.8 group violations per run.
Multi-seed stability. 17/30 seeds produce zero violations; 27/30 at most one. Four seeds exceed ε+Δ*=0.54, within the expected range under a 5% per-split failure probability (Proposition 1). α=0.5 is chosen over α=0.2 for a 2.1× reliability improvement despite modest coverage reduction.
Held-out corruption generalization. With screen family withheld from calibration, the global fallback τ̂min achieves worst-group risk 0.470 and 31.7% coverage — matching Vanilla CRC and only 0.8% below oracle assignment.
Table 4 — Held-Out Screen Corruption Family
| Calibration | Worst Risk ↓ | Coverage ↑ | Safe? |
|---|---|---|---|
| Vanilla CRC (4 families) | 0.470 | 31.7% | ✓ |
| WG-CRC (4f, fallback) | 0.470 | 31.7% | ✓ |
| WG-CRC (5f, oracle) | 0.464 | 30.9% | ✓ |
Cross-dataset transfer. On NIH ChestX-ray14 (zero-shot, n=15,000), FDV achieves Spearman ρ=0.513 — consistent across all five families (range 0.511–0.520). The disagreement signal generalizes across institutions, scanner types, and label schemas.

On NIH, disagreement D and entropy H achieve similar correlations (both ρ≈0.51) — contrasting with CheXpert where D substantially outperformed H. FDV's combined signal remains robust across institutions.
Using D alone (α=0) satisfies the constraint but yields only 12.7% coverage. α=0.2 gives higher single-split coverage (27.6%) but only 8/30 zero-violation seeds (27%) vs. 17/30 (57%) for α=0.5 — a 2.1× reliability improvement. Values α>0.5 progressively degrade safety.
Table 5 — WG-CRC Across α
| α | Worst Risk ↓ | Coverage ↑ | Violations |
|---|---|---|---|
| 0.0 (D only) | 0.577 | 12.7% | 1/15 |
| 0.2 | 0.498 | 27.6% | 0/15 |
| 0.5 (proposed) | 0.500 | 23.9% | 0/15 |
| 0.8 | 0.549 | 8.6% | 2/15 |
| 1.0 (H only) | 0.670 | 16.6% | 14/15 |
Zero violations hold for all Δ ∈ [0.04, 0.08] — confirming Δ=0.04 is the coverage-optimal value within a stable feasible range, not a cherry-picked optimum. Values Δ≤0.03 produce 1–3/15 violations; Δ≥0.05 reduces coverage unnecessarily.
Table 6 — WG-CRC Across Δ Values
| Δ | εcal | Violations | Worst Risk | Coverage |
|---|---|---|---|---|
| 0.00 | 0.50 | 3/15 | 0.519 | 30.7% |
| 0.01 | 0.49 | 3/15 | 0.519 | 27.7% |
| 0.02 | 0.48 | 1/15 | 0.516 | 25.7% |
| 0.03 | 0.47 | 1/15 | 0.505 | 25.3% |
| 0.04 | 0.46 | 0/15 | 0.500 | 23.9% |
| 0.05 | 0.45 | 0/15 | 0.471 | 16.2% |
| 0.06 | 0.44 | 0/15 | 0.460 | 13.4% |
| 0.07 | 0.43 | 0/15 | 0.423 | 11.9% |
| 0.08 | 0.42 | 0/15 | 0.427 | 10.9% |
WG-CRC effectiveness tracks ρ(D, risk). CheXagent (ρ=0.606) achieves 0/15 violations. LLaVA-Rad and MAIRA-2 (ρ≈0.49) also achieve 0/15 violations per minimum single-split result, but show higher multi-seed variability. Practical deployability criterion: estimate ρ(D, risk) on held-out calibration data before deployment.
Table 7 — Backbone Deployability Analysis (ε=0.50, δ=0.05, G=15)
| Backbone | Method | Coverage ↑ | Violations | Worst Risk ↓ | Multi-seed |
|---|---|---|---|---|---|
| CheXagent | Vanilla CRC | 33.6% | 3/15 | 0.528 | 0.551±0.013 |
| CheXagent | WG-CRC + FDV | 23.9% | 0/15 | 0.500 | 0.506±0.022 |
| LLaVA-Rad | Vanilla CRC | 33.6% | 2/15 | 0.534 | 0.568±0.037 |
| LLaVA-Rad | WG-CRC + FDV | 20.5% | 0/15 | 0.515 | 0.510±0.027 |
| MAIRA-2 | Vanilla CRC | 27.2% | 3/15 | 0.549 | 0.571±0.022 |
| MAIRA-2 | WG-CRC + FDV | 21.5% | 0/15 | 0.517 | 0.550±0.140 |
| Backbone | ρ(D, r) | ρ(FDV, r) | ρ(H, r) | Δ* | Min. viol. |
|---|---|---|---|---|---|
| CheXagent | 0.606 | 0.492 | 0.197 | 0.04 | 0/15 |
| LLaVA-Rad | 0.497 | 0.413 | 0.197 | 0.04 | 0/15 |
| MAIRA-2 | 0.489 | 0.397 | 0.157 | 0.05 | 0/15 |
BibTeX will be updated upon publication. The paper is currently under anonymous review.