And as much or more than even the tire, all the other peripheral conditions that are too numerous and variable to control to be able to generalize.
My general feeling is that for local, low- to mid-speed driving, as long as the tire has been maintained at proper inflation, etc., and shows no visible signs of _extreme_ UV damage, etc., they're "safe enough". I would be somewhat nervous about taking that same tire and start cross-country on an interstate trip, especially in hot weather. Might be fine, but I'd far prefer to be safe than sorry. Before I started in a case like that, I'd put a new set on. Otherwise, I'd run them until something happened...
Obviously, ymmv... :)