Connected medicine, using smart (software based and networked) medical devices is frequently presented as the major disruptive trend in health care. Such devices will however be broadly used only if they are "prescribed" by the hospitals as a part of a therapy and are reimbursed by the insurances. For this we need the proof of their safety, medical efficacy and economic efficiency. Aside of obligatory clinical trials we need an extensive system of post-market surveillance, because: a medical device is a part of a complex cyber-physical system, with humans in the loop / the environment cannot be sufficiently defined / humans react differently to the therapy, they also behave differently / after every software upgrade the device is not the same as before In their operation such devices generate huge amounts of data that can be reused for such analysis. Technically oriented people believe it can be done using a Big Data Analytics system without a deeper understanding of the underlying processes. It is doubtful if such approach can deliver useful results. The main problems seem to be: unbalanced cohort / various patient groups with various preferences / multiple quality parameters (basic algorithm, signal propagation, battery, security and privacy, obtrusiveness, etc.) / multiple variants (operating modes, device settings) / variability of the device and of the environment. When we transform data into "actionable knowledge", especially if the generated decisions influence human health, utmost care has to be applied. The goal of this paper is to present the complexity of the problem, warn against hasty, purely technical solutions, raise interest among specialists in health statistics and ignite an interdisciplinary cooperation to solve it.