GWDRO-Lung: Gromov–Wasserstein distributionally robust learning for calibrated pulmonary nodule malignancy prediction across imaging cohorts

Low-dose chest computed tomography (CT) screening detects pulmonary nodules whose malignancy risk must be triaged, yet deep-learning risk models often lose both accuracy and calibration when transferred to a different scanner, protocol, or population. We developed GWDRO-Lung, a chest CT framework that treats cross-cohort transfer as a coupled problem of structural mismatch, distributional instability, and calibration. A weight-shared three-dimensional encoder with embedded acquisition metadata summarizes each cohort as a relation matrix over learned prototypes; cohort geometries are aligned to a shared Gromov–Wasserstein barycenter; and a distributionally robust, calibration-aware risk head estimates malignancy, with the residual alignment error setting a cohort-specific robustness radius. The model was developed on 1842 pulmonary nodules from LIDC-IDRI, organized into three acquisition-defined cohorts, and validated externally on 618 nodules from the independent LNDb cohort, with leave-one-cohort-out, protocol-shift, size-stratified, and decision-curve analyses. Relative to the strongest recent imaging baseline, external area under the receiver operating characteristic curve improved from 0.857 to 0.878, external expected calibration error fell from 0.106 to 0.066, worst-cohort AUC rose from 0.829 to 0.851, and net benefit was higher across triage-relevant thresholds. Prospective, pathology-confirmed validation is required before clinical use.