That's not the same as controlling for vitamin d because people's blood levels vary wildly even with supplementation. To control for vitamin d level you would n

That's not the same as controlling for vitamin d because people's blood levels vary wildly even with supplementation. To control for vitamin d level you would need to blood test for it and supplement until the blood level is between 20 ng/ml and 50 ng/ml, ideally around 30. Depending on how they were supplementing blood levels could be way too low still (especially for obese people) or way too high with likely different effects on the outcome here.