We developed deep learning models for predicting Total Knee Replacement (TKR) need within various time horizons in knee osteoarthritis patients, with a novel capability: the models can perform TKR prediction using a single scan, and furthermore when a previous scan is available, they leverage a progressive risk formulation to improve their predictions. Unlike conventional approaches that treat each scan of a patient independently, our method incorporates a constraint based on disease's progressive nature, ensuring that predicted TKR risk either increases or remains stable over time when multiple scans of a knee are available. This was achieved by enforcing a progressive risk formulation constraint during training with patients who have more than one available scan in the studies. Knee radiographs and MRIs from the Osteoarthritis Initiative (OAI) and Multicenter Osteoarthritis Study (MOST) were used in this work and deep learning models were trained to predict TKR within 1, 2, and 4-year time periods. The proposed approach, utilizing a dual-model risk constraint architecture, demonstrated superior performance compared to baseline - conventional models trained with standard binary cross entropy loss. It achieved an AUROC of 0.87 and AUPRC of 0.47 for 1-year TKR prediction on the OAI radiograph test set, considerably improving over the baseline AUROC of 0.79 and AUPRC of 0.34. For the MOST radiograph test set, the proposed approach achieved an AUROC of 0.77 and AUPRC of 0.25 for 1-year predictions, outperforming the baseline AUROC of 0.71 and AUPRC of 0.19. Similar trends were observed in the MRI testsets

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