Prediction models are popular in medical research and practice. Many expect that by predicting patient-specific outcomes, these models have the potential to inform treatment decisions, and they are frequently lauded as instruments for personalized, data-driven healthcare. We show, however, that using prediction models for decision-making can lead to harm, even when the predictions exhibit good discrimination after deployment. These models are harmful self-fulfilling prophecies: their deployment harms a group of patients, but the worse outcome of these patients does not diminish the discrimination of the model. Our main result is a formal characterization of a set of such prediction models. Next, we show that models that are well calibrated before and after deployment are useless for decision-making, as they make no change in the data distribution. These results call for a reconsideration of standard practices for validation and deployment of prediction models that are used in medical decisions.@en