How to analyze data with restricted range proportions

I have a dataset where one variable is a proportion with a restricted range (say 4%). I would like to use this variable to predict a death rate. Running a simple correlation I'm guessing would underestimate the relationship (?). I also have raw counts for both variables. What analysis do I do here? I'm stuck. Binomial regression? Below is an excerpt of my early attempts....

Firearm denial proportion and firearm suicide rate are positively correlated (r = .25, p < .01). There is a range restriction problem with using denials as a proportion (R = 4.13), but that should only result in underestimating the correlation.

Thanks!

• Is the range you have restricted relative to the population, or relative to the possible range? (i.e. do you say that the range is restricted because it's so low, and it could go to 100%, or because in the population it's likely to be 20%). – Jeremy Miles Sep 4 '14 at 23:51
• Relative to the possible range it is on the low end between 0% and 4%. – Joe Sep 5 '14 at 13:18