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A reliable locoregional recurrence (LRR) prediction model is important for the personalized management of head and neck cancers (HNC) patients. This work aims to develop a delta-radiomics feature-based multi-classifier, multi-objective, and multi-modality (Delta-mCOM) model for post-treatment HNC LRR prediction and adopting a learning with rejection option (LRO) strategy to boost the prediction reliability by rejecting samples with high prediction uncertainties. In this retrospective study, we collected PET/CT image and clinical data from 224 HNC patients. We calculated the differences between radiomics features extracted from PET/CT images acquired before and after radiotherapy as the input features. Using clinical parameters, PET and CT radiomics features, we built and optimized three separate single-modality models. We used multiple classifiers for model construction and employed sensitivity and specificity simultaneously as the training objectives. For testing samples, we fused the output probabilities from all these single-modality models to obtain the final output probabilities of the Delta-mCOM model. In the LRO strategy, we estimated the epistemic and aleatoric uncertainties when predicting with Delta-mCOM model and identified patients associated with prediction of higher reliability. Predictions with higher epistemic uncertainty or higher aleatoric uncertainty than given thresholds were deemed unreliable, and they were rejected before providing a final prediction. Different thresholds corresponding to different low-reliability prediction rejection ratios were applied. The inclusion of the delta-radiomics feature improved the accuracy of HNC LRR prediction, and the proposed Delta-mCOM model can give more reliable predictions by rejecting predictions for samples of high uncertainty using the LRO strategy.