I think you'll find there tends to be a correlation between using [protection against bad thing] and being at risk for [bad thing]. As an example, I'm fairly certain you'll find a correlation between wearing a helmet while driving a car and being injured in car crashes because most people who wear helmets while driving are racing or doing stunts. I also suspect people with burglar alarms lose more money to burglary than people without if no other variables are taken in to account.

I don't think an unbiased study has been done that accurately identifies causes looking at gun ownership and crime. My suspicion is that it would be possible to do, as I described above.