A Study of Baricitinib (LY3009104) in Children and Adolescents With Atopic Dermatitis

The reason for this study is to see if the study drug called baricitinib works and is safe in children and teenage participants with atopic dermatitis.

Inclusion Criteria: * At or above the 5th percentile of weight for age. * Have been diagnosed with moderate to severe atopic dermatitis for at least 12 months (if 6 years old or older) or at least 6 months (if 2 up to 6 years old). * Have had inadequate response or intolerance to existing topical (applied to the skin) medications within 6 months preceding screening. * Are willing to discontinue certain treatments for eczema (such as systemic and topical treatments during a washout period). * Agree to use emollients daily. Exclusion Criteria: * Are currently experiencing or have a history of other concomitant skin conditions (e.g., psoriasis or lupus erythematosus), or a history of erythrodermic, refractory, or unstable skin disease that requires frequent hospitalizations and/or intravenous treatment for skin infections. * A history of eczema herpeticum within 12 months, and/or a history of 2 or more episode of eczema herpeticum in the past. * Participants who are currently experiencing a skin infection that requires treatment, or is currently being treated, with topical or systemic antibiotics. * Have any serious illness that is anticipated to require the use of systemic corticosteroids or otherwise interfere with study participation or require active frequent monitoring (e.g., unstable chronic asthma). * Have been treated with the following therapies: * Monoclonal antibody for less than 5 half-lives prior to beginning study treatment. * Received prior treatment with any oral Janus kinase (JAK) inhibitor. * Received any parenteral corticosteroids administered by intramuscular or intravenous (IV) injection within 2 weeks prior to study entry or within 6 weeks prior to planned initiation of study drug or are anticipated to require parenteral injection of corticosteroids during the study. * Have had an intra-articular corticosteroid injection within 2 weeks prior to study entry or within 6 weeks prior to planned initiation of study drug. * Have high blood pressure characterized by a repeated systolic or diastolic blood pressure \>95th percentile based on age, sex and height. * Have had major surgery within the past eight weeks or are planning major surgery during the study. * Have experienced any of the following within 12 weeks of screening: venous thromboembolic event (VTE), myocardial infarction (MI), unstable ischemic heart disease, stroke, or New York Heart Association Stage III/IV heart failure. * Have a history of VTE or are considered at high risk of VTE as deemed by the investigator. * Have a history or presence of cardiovascular, respiratory, hepatic, chronic liver disease gastrointestinal, endocrine, hematological, neurological, lymphoproliferative disease or neuropsychiatric disorders or any other serious and/or unstable illness. * Have a current or recent clinically serious viral, bacterial, fungal, or parasitic infection including herpes zoster (shingles or chicken pox), tuberculosis. * Have specific laboratory abnormalities. * Have received certain treatments that are contraindicated. * Pregnant or breastfeeding.