• Percentage of Participants Achieving Investigator's Global Assessment (IGA) of 0 or 1 with a ≥2 Point Improvement [ Time Frame: 16 Weeks ]
  Percentage of participants achieving IGA of 0 or 1 with a ≥2 point improvement
• Open Label Pharmacokinetics (PK): Maximum Concentration (Cmax) of LY3009104 [ Time Frame: Baseline through 2 Weeks ]
  PK: Cmax of LY3009104
• Open Label PK: Area Under the Concentration Time Curve (AUC) of LY3009104 [ Time Frame: Baseline through 2 Weeks ]
  PK: AUC of LY3009104

• Percentage of Participants Achieving Eczema Area and Severity Index 75 (EASI75) [ Time Frame: 16 Weeks ]
  Percentage of participants achieving EASI75
• Percentage of Participants Achieving EASI90 [ Time Frame: 16 Weeks ]
  Percentage of participants achieving EASI90
• Change from Baseline on EASI Score [ Time Frame: Baseline, 16 Weeks ]
  Change from baseline on EASI Score
• Percentage of Participants Achieving SCORing Atopic Dermatitis 75 (SCORAD75) [ Time Frame: 16 Weeks ]
  Percentage of participants achieving SCORAD75
• Percentage of Participants Achieving a 4-Point Improvement in Itch Numeric Rating Scale (NRS) for Participants ≥10 Years Old [ Time Frame: 16 Weeks ]
  Percentage of participants achieving a 4-point improvement in Itch NRS for participants ≥10 years old
• Percentage of Participants Achieving EASI50 [ Time Frame: 16 Weeks ]
  Percentage of participants achieving EASI50
• Percentage of Participants Achieving IGA of 0 [ Time Frame: 16 Weeks ]
  Percentage of participants achieving IGA of 0
• Change from Baseline in SCORAD [ Time Frame: Baseline, 16 Weeks ]
  Change from baseline in SCORAD
• Percentage of Participants Achieving SCORAD90 [ Time Frame: 16 Weeks ]
  Percentage of participants achieving SCORAD90
• Change from Baseline in Body Surface Area (BSA) Affected [ Time Frame: Baseline, 16 Weeks ]
  Change from baseline in BSA affected
• Percentage of Participants Developing Skin Infections Requiring Antibiotic Treatment [ Time Frame: 16 Weeks ]
  Percentage of participants developing skin infections requiring antibiotic treatment
• Mean Number of Days without Use of Background Topical Corticosteroid (TCS) [ Time Frame: Baseline through 16 Weeks ]
  Mean number of days without use of background TCS
• Mean Gram Quantity of TCS Use (Tube Weights) [ Time Frame: Baseline through 16 Weeks ]
  Mean gram quantity of TCS use (tube weights)
• Change from Baseline in Itch NRS [ Time Frame: Baseline, 16 Weeks ]
  Change from baseline in itch NRS
• Change from Baseline in the Parent-Reported Itch Severity Measure (PRISM) for Participants <10 years old [ Time Frame: Baseline, 16 Weeks ]
  Change from baseline in the PRISM for participants <10 years old
• Change from Baseline on the Patient-Oriented Eczema Measure (POEM) Total Score [ Time Frame: Baseline, 16 Weeks ]
  Change from baseline on the POEM total score
• Change from Baseline in Patient Global Impression of Severity-Atopic Dermatitis (PGI-S-AD) Score [ Time Frame: Baseline, 16 Weeks ]
  Change from baseline in PGI-S-AD score
• Change from Baseline in the Patient-Reported Outcomes Measurement Information System (PROMIS)-Pediatric Depression [ Time Frame: Baseline, 16 Weeks ]
  Change from baseline in the PROMIS-pediatric depression
• Change from Baseline in the PROMIS-Pediatric Anxiety [ Time Frame: Baseline, 16 Weeks ]
  Change from baseline in the PROMIS-pediatric anxiety
• Change from Baseline in the Children's/Infants's Dermatology Life Quality Index (CDLQI/IDQOL) [ Time Frame: Baseline, 16 Weeks ]
  Change from baseline in the CDLQI/IDQOL
• Change from Baseline on the Work Productivity and Activity Impairment: Atopic Dermatitis - Caregiver (WPAI-AD-CG) Score [ Time Frame: Baseline, 16 Weeks ]
  Change from baseline on the WPAI-AD-CG score
• Change from Baseline on the European Quality of Life-5 Dimensions-Youth (EQ-5D-Y) [ Time Frame: Baseline, 16 Weeks ]
  Change from baseline on the EQ-5D-Y
• Change from Baseline in the Score of Item 2 of the Atopic Dermatitis Sleep Scale (ADSS) for Participants ≥10 Years Old [ Time Frame: Baseline, 16 Weeks ]
  Change from baseline in the score of item 2 of the ADSS for participants ≥10 years old
• Change from Baseline in Skin Pain NRS for Participants ≥10 Years Old [ Time Frame: Baseline, 16 Weeks ]
  Change from baseline in Skin Pain NRS for participants ≥10 years old
• Acceptability Assessment (PK Lead-In) [ Time Frame: 2 Weeks ]
  Participants were evaluated for baricitinib acceptability using a 5-category questionnaire. Participants were asked to answer one of the following to describe the ease of use of baricitinib: Very difficult (or hard), difficult (or hard), neither easy nor hard, easy, or very easy.
• Palatability Assessment (PK Lead-In) [ Time Frame: 2 Weeks ]
  Participants were evaluated for baricitinib palatability using a 5-category questionnaire. Participants were asked to answer one of the following to describe the taste and smell of baricitinib: Disliked very much, disliked, neither liked nor disliked, liked, or like very much.
• Change of Immunoglobulin G (IgG) Titers [ Time Frame: Pre-Vaccination to 12 Weeks Post-Vaccination ]
  Change of IgG titers
• Height Growth Rate (in Centimeters/Year) [ Time Frame: 124 Weeks ]
  Height growth rate (in centimeters/year)
• PK: Cmax of LY3009104 [ Time Frame: Baseline through 16 Weeks ]
  PK: Cmax of LY3009104
• PK: AUC of LY3009104 [ Time Frame: Baseline through 16 Weeks ]
  PK: AUC of LY3009104

• Drug: Baricitinib
  Administered orally
  Other Name: LY3009104
• Drug: Placebo
  Administered orally
• Drug: Topical corticosteroid
  Administered as standard-of-care

• Experimental: Baricitinib Open Label High Dose
  Baricitinib administered orally.
  Intervention: Drug: Baricitinib
• Experimental: Baricitinib High Dose
  Baricitinib administered orally. Placebo administered orally to maintain the blind.
  Interventions:

  • Drug: Baricitinib
  • Drug: Topical corticosteroid
• Experimental: Baricitinib Mid Dose
  Baricitinib administered orally. Placebo administered orally to maintain the blind.
  Interventions:

  • Drug: Baricitinib
  • Drug: Topical corticosteroid
• Experimental: Baricitinib Low Dose
  Baricitinib administered orally. Placebo administered orally to maintain the blind.
  Interventions:

  • Drug: Baricitinib
  • Drug: Topical corticosteroid
• Placebo Comparator: Placebo
  Placebo administered orally. Matching placebo administered orally to maintain the blind.
  Interventions:

  • Drug: Placebo
  • Drug: Topical corticosteroid

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.