I change my tires, obsessively, way before it hits the wear-bars; like around 8,000 miles or so, give or take.
I've spun out in the rain before, so I play it safe, even if my tires still appears to have reasonable amount of meat on them.
Tires are the only part of the vehicle that actually touches the road, thus it's intricate to a said vehicle's performance and safety.
It's cheaper to replace them prematurely than having my insurance company charging me $1,000 collision deductible and then flooding my car with aftermarket Chinaman replacement parts.
I use this tire tread gauge to measure the remaining depth.