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Medical applications, such as medical diagnosis, can be understood as classification problems. While usual approaches try to minimize the number of errors, medical scenarios often require classifiers that face up with different types of costs. This paper analyzes the application of a particular class of Bregman divergences to design cost sensitive classifiers for medical applications. It has been shown that these divergence measures can be used to estimate posterior probabilities with maximal accuracy for the probability values that are close to the decision boundaries. Experimental results on various medical datasets support the efficacy of our method.