We can sort discussions to see the ones with no replies. When the system is set to have all discussions start as a question, this measure is the true "unanswered" questions. In the analytic module how can we show the trend for this? Increasing engagement means that this number should be tracking down. Looking at the number of questions added in that time period, we can also calculate a good "engagement" number.
Another important metric which is related to engagement is the time to resolve the question. Not sure how to do this in the analytic module, though.