Large artificial dataset
There is a large synthetic dataset of fake electronic health records available at Synthetic Mass. It's not a real dataset, but it's supposed to mirror many of the properties of a large health system in the US state of Massachusetts. You need to register for a free account to get an API key.
FHIR representations of publicly available de-identified datasets
The Medical Information Mart for Intensive Care (MIMIC) is a famously publicly available de-identified electronic health record (EHR) dataset. It may or may not have data for your purposes, but it is available. There has apparently been some work to provide a FHIR representation of MIMIC. Theoretically it was supposed to be available at fhir.mimic.mit.edu. However, that doesn't currently seem to work. The source code is available on GitHub, so you could attempt to host it yourself if you were so inclined.
Why aren't there real datasets?
- EHR data is highly sensitive private information. Very few people are going to agree to have their intensely personal information revealed to the public. Even if participants did provide informed consent, publicly releasing EHR data would pose a serious ethical risk for participants because it would place them at risk for identity theft (Kushida et al 2012. PMCID 6502465).
- De-identifying EHR data is extremely challenging. Computer scientists often suggest that you can just "de-identify" the EHR data. However, this is extremely challenging (Kushida et al 2012. PMCID 6502465). US law provides a "safe harbor" definition of what must be removed from private health information to render it de-identified. Trying to automatically remove these elements from unstructured clinical text, for example, is nearly impossible and is the subject of considerable ongoing research.
- Health systems have no incentives to provide the data. Comprehensive data sets contained in EHRs are highly valuable (monetarily) resources (Vezyridis et al 2017). Thus, large health systems have no incentive to give away their valuable data to the public when they can charge companies in the private sector.