Ask HN: Self hosted web analytics packages

I work in the pharmaceutical industry. Some of our customer facing systems contain patient data and so we cant take the risk of using something like google analytics which might leak info to an external service.

I have looked at mint (http://getamint.com) but that doesn't seem to collect much more than the basics, would be nice to be able to track usage paths through the site etc.

A huge bonus would be the ability to attach a custom piece of data (the username or customer account name for example) ... which would allow tracking of usage/browser info/workflow for an individual user of our system.

Budget is not too much of an issue, within reason. So it doesn't have to be free/open source. Can anyone recommend some solutions that allow this, or am I going to have to roll my own?