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We developed and evaluated a novel inverse optimization (IO) model to estimate objective function weights from clinical dose-volume histograms (DVHs). These weights were used to solve a treatment planning problem to generate 'inverse plans' that had similar DVHs to the original clinical DVHs. Our methodology was applied to 217 clinical head and neck cancer treatment plans that were previously delivered at Princess Margaret Cancer Centre in Canada. Inverse plan DVHs were compared to the clinical DVHs using objective function values, dose-volume differences, and frequency of clinical planning criteria satisfaction. Median differences between the clinical and inverse DVHs were within 1.1 Gy. For most structures, the difference in clinical planning criteria satisfaction between the clinical and inverse plans was at most 1.4%. For structures where the two plans differed by more than 1.4% in planning criteria satisfaction, the difference in average criterion violation was less than 0.5 Gy. Overall, the inverse plans were very similar to the clinical plans. Compared with a previous inverse optimization method from the literature, our new inverse plans typically satisfied the same or more clinical criteria, and had consistently lower fluence heterogeneity. Overall, this paper demonstrates that DVHs, which are essentially summary statistics, provide sufficient information to estimate objective function weights that result in high quality treatment plans. However, as with any summary statistic that compresses three-dimensional dose information, care must be taken to avoid generating plans with undesirable features such as hotspots; our computational results suggest that such undesirable spatial features were uncommon. Our IO-based approach can be integrated into the current clinical planning paradigm to better initialize the planning process and improve planning efficiency. It could also be embedded in a knowledge-based planning or adaptive radiation therapy framework to automatically generate a new plan given a predicted or updated target DVH, respectively.