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Purpose: To develop a weakly supervised deep learning (WSDL) method that could utilize incomplete/missing survival data to predict the prognosis of extranodal natural killer/T cell lymphoma, nasal type (ENKTL) based on pretreatment 18F-FDG PET/CT results. Methods: One hundred and sixty-seven patients with ENKTL who underwent pretreatment 18F-FDG PET/CT were retrospectively collected. Eighty-four patients were followed up for at least 2 years (training set = 64, test set = 20). A WSDL method was developed to enable the integration of the remaining 83 patients with incomplete/missing follow-up information in the training set. To test generalization, these data were derived from three types of scanners. Prediction similarity index (PSI) was derived from deep learning features of images. Its discriminative ability was calculated and compared with that of a conventional deep learning (CDL) method. Univariate and multivariate analyses helped explore the significance of PSI and clinical features. Results: PSI achieved area under the curve scores of 0.9858 and 0.9946 (training set) and 0.8750 and 0.7344 (test set) in the prediction of progression-free survival (PFS) with the WSDL and CDL methods, respectively. PSI threshold of 1.0 could significantly differentiate the prognosis. In the test set, WSDL and CDL achieved prediction sensitivity, specificity, and accuracy of 87.50% and 62.50%, 83.33% and 83.33%, and 85.00% and 75.00%, respectively. Multivariate analysis confirmed PSI to be an independent significant predictor of PFS in both the methods. Conclusion: The WSDL-based framework was more effective for extracting 18F-FDG PET/CT features and predicting the prognosis of ENKTL than the CDL method. [ABSTRACT FROM AUTHOR]