Some studies have reported a positive relationship, others have found no relationship. I encourage parents to follow a sugar-free diet for a week or two. This diet would be free of honey, corn syrup, maple syrup, and table sugar. In any event, I encourage parents to follow a low sugar diet because if a child fills up on sugary foods, he won't have room for other nutritious foods. So if you use aspartame, I would use a couple of packets a day, a very small amount.
Parents can also try saccharin.
They have just recently removed the cancer warning. Again, I would use small amounts. No one is sure what the effects of this will be on behavior. I encourage parents to use fruit as nature's answer to their child's sweet tooth. Delicious apple pie can be made without sweetener or any sugar.