[math-fun] cause and effect: eating more eggs ==> die from heart problems?

Consider egg consumption. Perhaps people with heart and circulatory problems get worried about cholesterol and hence reduce their egg consumption, because they are worried about the cause==>effect relation "more eggs==>heart disease." As a result of that behavior -- which is "heart disease risk==>eat fewer eggs," an opposite direction cause==>effect relation... the people with lower egg consumption, would die *more* often from heart disease... leading to exactly the wrong conclusion from any study assessing people's diets and counting up their deaths! (Or, perhaps it was the right conclusion. My point is: how can we tell?)