As the world population ages, the patients per physician ratio keeps on increasing. This is even more important in the domain of chronic pathologies where people usually are monitored for years and need regular consultations. To address this problem, we propose an automated system to monitor a patient population, detecting anomalies in instantaneous data and in their temporal evolution, so that it could alert physicians. By handling autonomously the population of well-being patients and by drawing the physicians' attention to the patients-at-risk, the system allows physicians for spending comparatively more time with patients who need their services. In such a system, the interaction between the patients, the diagnosis module, and the physicians is very important. We based this system on a combination of stochastic models, fuzzy filters, and strong medical semantics. We particularly focused on a particular tele-medicine application: the Diatelic Project. Its objective is to monitor chronic kidney-insufficient patients and to detect hydration troubles. During two years, physicians from the ALTIR have conducted a prospective randomized study of the system. This experiment clearly shows that the proposed system is really beneficent to the patients' health.