Severe peanut allergy is different from other allergic reactions because it can lead to fatal reactions and is an invisible disability. There is no cure today. The purpose of this study is to treat children and adolescents with severe peanut allergy with oral immunotherapy with peanuts under the protection of anti-IgE (immunoglobulin E) antibodies (omalizumab), and thereby inducing tolerance to peanuts. The treatment will be monitored by basophil cell stimulation (CD-sens).