In this paper, the problem of intra-operative hypotension (IOH) prediction is addressed. Recent studies on the Hypotension Prediction Index have demonstrated a gap between the results presented during model development and clinical evaluation. Thus, there is a need for better collaboration between data scientists and clinicians, who need to agree on a common basis. In this contribution, we propose a comprehensive framework for IOH prediction: to address several issues inherent to the commonly used fixed-time-to-onset approach in the literature, a sliding window approach is suggested. The risk prediction problem is formalized with consistent precision-recall metrics rather than the receiver-operator characteristic. For illustration, a standard machine learning method is applied using two different datasets from non-cardiac and cardiac surgery. Training is done on a part of the non-cardiac surgery dataset, and tests are performed separately on the rest of the non-cardiac dataset and cardiac dataset. Compared to a realistic clinical baseline, the proposed method achieves a significant improvement on the non-cardiac surgeries (precision of 42% compared to 28% for a recall of 24%). For cardiac surgery, this improvement is less significant but still demonstrate the generalization of the model.