A Study of Baricitinib (LY3009104) in Children From 6 Years to Less Than 18 Years of Age With Alopecia Areata

Inclusion Criteria: * Enrollment will be fully sequential by age group, with adolescents (12 to less than 18 years old) enrolling before children (6 to less than 12 years old). * Have severe areata alopecia (AA) for at least 1 year * Diagnosis for at least 1 year * Current AA episode of at least 6 months' duration * SALT score ≥50% at screening and baseline * History of trial and failure with at least 1 available treatment (topical or other) for AA * History of psychological counseling related to AA * Current episode of severe AA of less than 8 years. * Note: Participants who have severe AA for ≥8 years may be enrolled if episodes of regrowth, spontaneous or under treatment, have been observed on the affected areas over the past 8 years. Exclusion Criteria: * Primarily "diffuse" type of AA (characterized by diffuse hair shedding). * Are currently experiencing other forms of alopecia including, but not limited to trichotillomania, telogen effluvium, chemotherapy-induced hair loss, or any other concomitant conditions (for example, tinea capitis, psoriasis, lupus erythematosus, or secondary syphilis) that would interfere with evaluations of the effect of study medication on AA. * Are largely or wholly incapacitated permitting little or no self-care, such as being bedridden * Have uncontrolled arterial hypertension * Have had major surgery within 8 weeks prior to screening or will require major surgery during the study * Have a history or presence of cardiovascular, respiratory, hepatic, gastrointestinal, endocrine, hematological, neurological, or neuropsychiatric disorders or any other serious and/or unstable illness that, in the opinion of the investigator, could constitute an unacceptable risk when taking IP or interfere with the interpretation of data. * Have a positive test for hepatitis B virus (HBV) infection * Have hepatitis C virus (HCV) infection (positive for anti hepatitis C antibody with confirmed presence of HCV ribonucleic acid \[RNA\]). * Have evidence of human immunodeficiency virus (HIV) infection and/or positive HIV antibodies.