I don't think they do. Which is much better than correcting for variables and doing it badly.

Anecdotally, I am the only healthy person I know of in my group who voluntarily uses artificial sweetener. It seems to me that the use of artificial sweetener is strongly associated with health problems such as morbid obesity and diabetes: people who don't have to don't use them.

Regarding artificial sweetener itself being causal there is very little reliable data to support that. There does seem to be a link between Aspartame and (bladder) cancer but it has so far only been shown in animal models.