This is an example of an industry vertical analytics solution. Our hypothesis is that analytics products will be created to support all kinds of use cases like this (insurance analytics, manufacturing analytics, distribution analytics, etc). We want Keen IO to be the platform on which people build those solutions.
The way we can help you is to first make it easy for you to reliably collect data from all your dentists (with client libraries). Then we expose all that data, and of our analytics capabilities (e.g. queries), by REST API. You can log into Keen IO and create a line chart, then copy and paste the javascript right into your site. Now you can build a completely white-labeled website for your dentists, while we take care of storing and querying your event data. Our scoped API keys will allow you to secure the data so a given dentist can only see data for her offices. You can also create an internal dashboard for your team so you'll able to do analysis across all the dentists. Hopefully you'll discover industry trends and benchmarks that you can use in marketing reports or to resell to the dental industry (assuming your dentists allow this!). I bet they would like to know how they compare to other dentists...
Anyway, this is too much fun. Let me know if you want to brainstorm more!