The link given by DonManfred is the idea from what you can start with (using PhoneStateChanged). I just would like to add that you should pay attention to Erel's advice on that post: you have to wait for some seconds before looking for the missed call. In another word, if you check the Call Log immediately during or right after the incoming call finishes, then you may not see the missed call. Erel said 20 seconds, but for my case I think I only need around 3 - 5 seconds.
In my earlier post, in the code snippet the missed call type is 3 (myitem.CallType = 3)