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The main applications of Data Envelopment Analysis (DEA) to medicine focus on evaluating the efficiency of different health structures, hospitals and departments within them. The evolution of patients after undergoing a medical procedure or their response to a given treatment are not generally studied through this programming technique. In addition to the difficulty inherent to the collection of this type of data, the use of a technique that is mainly applied to evaluate the efficiency of decision making units representing industrial and production structures to analyze the evolution of human patients may seem inappropriate. In the current paper, we illustrate how this is not actually the case and implement a decision engineering approach to model kidney transplantation patients as decision making units. As such, patients undergo three different phases, each composed by specific as well as interrelated variables, determining the potential success of the transplantation process. DEA is applied to a set of 12 input and 6 output variables - retrieved over a 10-year period - describing the evolution of 485 patients undergoing kidney transplantation from living donors. The resulting analysis allows us to classify the set of patients in terms of the efficiency of the transplantation process and identify the specific characteristics across which potential improvements could be defined on a per patient basis.