Healthcare systems have made a dramatic shift towards ubiquitous monitoring in the recent past. The reasons for such a change have been ease of timely diagnosis, convenience and comfort of clinical treatments. Wireless Body Area Networks (WBANs) are mainly characterized by deployment of biomedical sensors around human body which transmit vital signs measurements about the health status of the patient. Unfortunately, the huge traffic load of clinical data and limited resources of biomedical sensors make the efficiency of long-term operations almost impossible. Therefore, it is necessary to make significant advances in sensor's energy saving. Our idea is to reduce the activities of some sensors depending on the relevance between the data they measure and the diseases to detect. This paper shows how to extend the lifetime of medical WBANs by appropriately taking benefit of correlation between the knowledge about the disease and sensing data to drive the best scheduling of the medical sensors. For that, the theoretical framework of an economic approach, i.e., network utility maximization, is developed for sensor scheduling under operations cost constraint. It is shown that the compact subset of sensors can be found to provide necessary information for timely and correct diagnoses. Based on the theoretical framework, an algorithm combining sensor selection and information gain is then proposed. Simulation results show that the algorithm achieves high performance in terms of energy saving vs latency in disease detection.