This sounds like a problem with file permissions. Please try the following:
1. Open Finder and go to:
Please note that this path is NOT the same as the similar path in your user directory (<username>/Library/Application Support/).
2. Right click or CTRL click on the Addictive Drums folder and choose "Get Info".
3. In the bottom of the window that pops up, make sure that the drop down boxes says "Read & Write". You might need to click the icon with a lock on it and type your password to be able to change the permissions.
4. Check out the picture in this link make sure that it looks right:
http://www.xlnaudio.com/graphics/suppor ... ssions.jpg
5. Click "Apply to enclosed items..."
6. Also repair disk permissions:
Go to Applications -> Utilities -> Disk Utility
Select the hard drive that Addictive Drums is installed on and click "Repair disk permissions". Restart your computer and try starting Addictive Drums again.