Although migraine headaches are believed to be caused by food allergies, putting patients on diets that eliminate those foods to which the patients have been demonstrated to have allergic migraine reactions frequently does not stop headaches. Obviously, some other cause of migraine headaches besides food allergies much exist.

Which of the following, if true, would most weaken the conclusion above?

(A) Many common foods elicit an allergic response only after several days, making it very difficult to observe links between specific foods patients eat and headaches they develop.
(B) Food allergies affect many people who never develop the symptom of migraine headaches.
(C) Many patients report that the foods that cause them migraine headaches are among the foods that they most enjoy eating.
(D) Very few patients have allergic migraine reactions as children live migraine-free adult lives once they have eliminated from their diets foods to which they have been demonstrated to be allergic.
(E) Very rarely do food allergies cause patients to suffer a symptom more severe than that of migraine