We track patient flows through various departments in a large university hospital using data collected from over 100,000 visits during a three year period. By linking congestion crisis messages issued by the hospital management to variables describing patient length-of-stay, movements, bed occupancy rates, and labour hours we develop a statistical model to anticipate bottlenecks in the system to show that it is possible to predict congestion two to five days in advance. The developed method shows which variables are the most useful for explaining congestion and other patient flow issues in the case hospital. This advanced warning can be sufficient to avoid the congestion, since hospitals show an inherent capability to stretch their capacity, and vice versa, should it be needed. We compile our results into practical guidelines to complement existing patient flow management systems in hospitals.