I called back and it looks like they had the wrong number on file. It's probably something to do with medical billing/health insurance if they don't bother to leave a message. In that case, you wouldn't want to them disclosing that type of info in your mailbox for security purposes anyhow.
I have repeatedly gotten this caller but when I do finally answer they just hang up. They also never leave a message. I've finally just blocked the number.