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Deep learning models based on medical images play an increasingly important role for cancer outcome prediction. The standard approach involves usage of convolutional neural networks (CNNs) to automatically extract relevant features from the patient's image and perform a binary classification of the occurrence of a given clinical endpoint. In this work, a 2D-CNN and a 3D-CNN for the binary classification of distant metastasis (DM) occurrence in head and neck cancer patients were extended to perform time-to-event analysis. The newly built CNNs incorporate censoring information and output DM-free probability curves as a function of time for every patient. In total, 1037 patients were used to build and assess the performance of the time-to-event model. Training and validation was based on 294 patients also used in a previous benchmark classification study while for testing 743 patients from three independent cohorts were used. The best network could reproduce the good results from 3-fold cross validation [Harrell's concordance indices (HCIs) of 0.78, 0.74 and 0.80] in two out of three testing cohorts (HCIs of 0.88, 0.67 and 0.77). Additionally, the capability of the models for patient stratification into high and low-risk groups was investigated, the CNNs being able to significantly stratify all three testing cohorts. Results suggest that image-based deep learning models show good reliability for DM time-to-event analysis and could be used for treatment personalisation.