When Calibration Fails the Vulnerable Hospital: Federated Conformal Risk Control via Risk-Curve Shrinkage
Authors: Nafis Fuad Shahid
Organizations: Dhaka, Bangladesh
Abstract
Conformal risk control (CRC) provides distribution-free guarantees on segmentation quality by calibrating a prediction-set threshold on held-out data. In federated deployments, the standard approach pools calibration scores across sites into a single threshold. We provide the first quantification, on real multi-institutional brain tumor data (FeTS-2022, 1,251 subjects, 20 institutions), showing that this naive pooled CRC protects the average hospital but violates coverage at 40% of individual institutions, with the worst site exceeding the target false-negative rate by 7.8 percentage points. The naive alternative, per-site local CRC, largely restores coverage but inflates prediction sets by 83x, rendering them clinically useless. We propose a shrinkage-based federated CRC protocol: each site transmits only its empirical risk curve (G scalars) to a server, which computes a shrinkage-regularized threshold per site. A single hyperparameter n0 smoothly trades worst-case coverage for prediction-set efficiency; leave-one-site-out sensitivity analysis identifies n0=19, achieving 2.7/20 violations at 2.0x stretch. We further show that direct Lagrangian optimization of coverage budgets fails, concentrating risk on vulnerable hospitals, and that the finite-sample correction term is essential: removing it triples violations. The marginal CRC guarantee is preserved by construction under the stated site-mixture assumption; per-site coverage is validated across four targets with three seeds. No patient-level images, masks, or per-volume scores leave any site.
Federated learning enables hospitals to collaboratively train segmentation models without sharing patient data. However, current evaluation protocols report only average performance across clients, masking failures at individual sites. In clinical deployment, a model that fails consistently at one hospital is a real safety risk that a good mean score can hide entirely. We introduce MedFL-Stress, a controlled stress-testing framework that exposes exactly this failure mode. Using 2D axial slices from BraTS 2020 distributed across four simulated hospital clients, we apply graded MRI appearance shifts (gamma contrast, scale-shift, and noise-plus-blur) reflecting scanner and acquisition variability in real multi-site deployments. Three federated baselines are evaluated: FedAvg, FedProx, and FedBN. Worst-hospital Dice and inter-hospital disparity are treated as primary metrics, not supplementary observations. FedAvg achieves the highest global mean Dice (0.8159) but conceals a 0.0850 gap between its best and worst-performing hospital. FedBN closes that gap by 41% (0.0850 to 0.0503) while sacrificing less than half a Dice point in mean accuracy (0.8159 to 0.8109), and the weakest hospital gains 3.5 Dice points outright (0.7309 to 0.7656). These findings demonstrate that robustness-oriented evaluation protocols are essential for reliable federated medical imaging deployment.
Deploying trustworthy AI systems requires principled uncertainty quantification. Conformal prediction (CP) is a widely used framework for constructing prediction sets with distribution-free coverage guarantees. In many practical settings, including healthcare, finance, and mobile sensing, the calibration data required for CP are distributed across multiple clients, each with its own local data distribution. In this federated setting, data can often be partitioned into, potentially overlapping, groups, which may reflect client-specific strata or cross-cutting attributes such as demographic or semantic categories. We propose group-conditional federated conformal prediction (GC-FCP), a federated extension of conditional conformal calibration for a target mixture over prespecified groups. GC-FCP constructs mergeable, atom-stratified coresets from local calibration scores, enabling compact aggregation at the server when the number of active atoms is moderate. Experiments on synthetic and real-world datasets validate the performance of GC-FCP compared to centralized calibration baselines. The code of our work can be found at https://github.com/HaifengWen/GC-FCP.
Multi-center survival prediction can improve robustness and generalizability, yet privacy regulations and institutional governance often prevent pooling patient-level clinical and genomic data across institutions. In practice, deployment is further complicated by feature-space heterogeneity, in which sites collect different covariates or use different sequencing panels, resulting in only partially overlapping feature sets. We present FederatedRSF, a Python package that implements federated random survival forests, aggregating locally trained survival trees and redistributing only feature-compatible trees to each site, enabling inference with partial overlap without sharing raw data. We evaluate FederatedRSF on the GBSG2 breast cancer cohort distributed with the scikit-survival package, simulating feature heterogeneity across clients by withholding subsets of features, and assessing discrimination using Harrell's concordance index (C-Index) under repeated cross-validation and site-splits. The results demonstrated that the federated model can achieve performance comparable to that of the centralized training setting.
Maryam Moradpour, Jonas Harriehausen, Amirreza Aleyasin +3