Accurate prognosis for an individual patient is a key component of precision oncology. Recent advances in machine learning have enabled the development of models using a wider range of data, including imaging. Radiomics aims to extract quantitative predictive and prognostic biomarkers from routine medical imaging, but evidence for computed tomography radiomics for prognosis remains inconclusive. We have conducted an institutional machine learning challenge to develop an accurate model for overall survival prediction in head and neck cancer using clinical data etxracted from electronic medical records and pre-treatment radiological images, as well as to evaluate the true added benefit of radiomics for head and neck cancer prognosis. Using a large, retrospective dataset of 2,552 patients and a rigorous evaluation framework, we compared 12 different submissions using imaging and clinical data, separately or in combination. The winning approach used non-linear, multitask learning on clinical data and tumour volume, achieving high prognostic accuracy for 2-year and lifetime survival prediction and outperforming models relying on clinical data only, engineered radiomics and deep learning. Combining all submissions in an ensemble model resulted in improved accuracy, with the highest gain from a image-based deep learning model. Our results show the potential of machine learning and simple, informative prognostic factors in combination with large datasets as a tool to guide personalized cancer care.