Machine learning applications hold promise to aid clinicians in a wide range of clinical tasks, from diagnosis to prognosis, treatment, and patient monitoring. These potential applications are accompanied by a surge of ethical concerns surrounding the use of Machine Learning (ML) models in healthcare, especially regarding fairness and non-discrimination. While there is an increasing number of regulatory policies to ensure the ethical and safe integration of such systems, the translation from policies to practices remains an open challenge. Algorithmic frameworks, aiming to bridge this gap, should be tailored to the application to enable the translation from fundamental human-right principles into accurate statistical analysis, capturing the inherent complexity and risks associated with the system. In this work, we propose a set of fairness impartial checks especially adapted to ML early-warning systems in the medical context, comprising on top of standard fairness metrics, an analysis of clinical outcomes, and a screening of potential sources of bias in the pipeline. Our analysis is further fortified by the inclusion of event-based and prevalence-corrected metrics, as well as statistical tests to measure biases. Additionally, we emphasize the importance of considering subgroups beyond the conventional demographic attributes. Finally, to facilitate operationalization, we present an open-source tool FAMEWS to generate comprehensive fairness reports. These reports address the diverse needs and interests of the stakeholders involved in integrating ML into medical practice. The use of FAMEWS has the potential to reveal critical insights that might otherwise remain obscured. This can lead to improved model design, which in turn may translate into enhanced health outcomes.