In modern e-healthcare systems, medical institutions can provide more reliable diagnoses by introducing Machine-Learning (ML)-based classifiers. These ML classifiers are frequently trained with huge numbers of patients’ data to keep updated with new diseases and changes in current disease patterns. To increase the accuracy in prediction process, Peer-to-Peer (P2P) learning systems have been explored by many studies by which medical institutions can share their data with others: the more data are available, the more accurate the predictions. However, the traditional P2P network system requires much time in which the training data are shared among the nodes in the network. The system also spends much time on learning from samples where the data labels are unknown. Moreover, some nodes may perform certain computations which had already been computed by other nodes, resulting in redundant computations. In this paper, in order to deal with samples having unknown data labels, we propose a Collaborative Extreme Learning Machine (CELM) with a Confidence Interval (CI), which is an enhanced version of the traditional Extreme Learning Machine (ELM). Our proposed model eliminates redundant calculations of the network nodes (the e-healthcare institutions) to improve the learning efficiency, and improves the prediction accuracy by considering where plausible predictions lie. The extensive experimental analysis shows that the proposed model is efficient and achieves high accuracy (up to 98%) in diagnosing clinical events by analyzing patients’ medical records.