Biostatistics and machine learning have been the cornerstone of a variety of recent developments in medicine. In order to gather large enough datasets, it is often necessary to set up multi-centric studies; yet, centralization of measurements can be difficult, either for practical, legal or ethical reasons. As an alternative, federated learning enables leveraging multiple centers' data without actually collating them. While existing works generally require a center to act as a leader and coordinate computations, we propose a fully decentralized framework where each center plays the same role. In this paper, we apply this framework to logistic regression, including confidence intervals computation. We test our algorithm on two distinct clinical datasets split among different centers, and show that it matches results from the centralized framework. In addition, we discuss possible privacy leaks and potential protection mechanisms, paving the way towards further research.