"It's an imperfect world. People are imperfect. Tests are imperfect," last year's Sprint Cup runner-up said Friday before qualifying for Sunday's race at New Hampshire Motor Speedway.
"We need to have our own group that is paid by us, that works for us, to be here in tandem with the NASCAR drug testers and have them test us at the same time.
"I don't think it would be a contentious thing. I think that would remove almost all doubt in any situation of a positive test."
He called NASCAR's approach "very admirable" in trying to keep the sport clean but "there's one more layer that we could put on it. … You don't want to convict a guy of something he didn't do."
But Brad Keselowski, a teammate of Allmendinger, criticized Edwards' proposal.
"I don't think we need more politics involved in the sport and that's what (testing) groups like that bring in," Keselowski said.
He doesn't think drivers should be allowed to take any supplements, not even "Flintstone" vitamins. Permitting some of them leaves a gray area of what should and shouldn't be allowed, he said.
"I don't think there needs to be any committee that approves drugs or supplements or whatever it is," he said. "I just think you shouldn't be allowed to take anything. You should just man up and drive the damn race car." SI.com/AP