Treatment of Atopic Dermatitis and Alopecia Areata With Abrocitinib in Individuals With Down Syndrome

Inclusion Criteria: Participants must meet all of the following criteria to be eligible as study participants: * Male or female participants who are at least 12 years old, for whom signed informed consent can be provided by parent or legal guardian/LAR prior to participation in any study assessments or procedures. * Diagnosis of Trisomy 21 or translocation Down Syndrome. * Participant is able to adhere to the study visit schedule and other protocol requirements. * Females of childbearing potential (FCBP) must have a negative pregnancy test at Screening and Week 0/Baseline. While on investigational product and for at least 28 days after taking the last dose of investigational product (IP), FCBP who engage in activity in which conception is possible must use one of the approved contraceptive options described below: a. Any one of the following highly effective methods: hormonal contraception (oral, injection, implant, transdermal patch, vaginal ring); intrauterine device (IUD); tubal ligation; or partner's vasectomy; or b. Male or female condom (latex condom or non-latex condom NOT made out of natural \[animal\] membrane \[for example, polyurethane\]). * Participant has a history of ≥6 months AD (≥7%BSA) or AA (≥25% scalp involvement). If the participant presents with both conditions, but only one meets the inclusion criteria, then the participant can only be enrolled under that category. If a participant meets inclusion criteria for both conditions at the Baseline visit, then the participant will be enrolled under the AA category as this disease is less prevalent. If the AA category has fulfilled its enrollment target, then the participant will be enrolled in the AD category. * Participant is judged to be in otherwise good overall health following a detailed medical and medication history, physical examination, and laboratory testing. Exclusion Criteria: Participants who meet any of the following criteria are not eligible for randomization as study participants: * Inability or unwillingness of a participant's parent or legal guardian/LAR to give written informed consent or comply with study protocol. * Participant is pregnant or breastfeeding. * Participants with AA: A. cause of hair loss is indeterminable and/or they have concomitant causes of alopecia, such as traction, cicatricial, pregnancy-related, druginduced, telogen effluvium, or advanced androgenetic alopecia (i.e. Ludwig Type III or Norwood-Hamilton Stage ≥ V). B. Participant has a history of AA with no evidence of hair regrowth for ≥7 years since the last episode of hair loss * Participant has increased risk of developing venous thromboembolism, e.g. deep vein thrombosis or pulmonary embolism (history of venous thromboembolism, or first-degree relative with unprovoked venous thromboembolism (i.e. without known underlying cause such as trauma, surgery, immobilization, prolonged travel, pregnancy, hormone use, or plaster cast), that would suggest participant is at increased risk of inherited coagulation disorder (e.g. Factor V Leiden). * Participant currently has active forms of other inflammatory skin diseases (eg, psoriasis, seborrheic dermatitis, lupus) at the time of Day 1 that would interfere with evaluation of AD or AA. * Participant was vaccinated or exposed to a live or attenuated vaccine within the 6 weeks prior to Baseline visit, or is expected to be vaccinated or to have household exposure to these vaccines during treatment. * Participant has a suspected or active lymphoproliferative disorder or malignancy; OR a history of malignancy within 5 years before the Week 0/Baseline assessment, except for completely treated in situ non-melanoma skin and cervical cancers without evidence of metastasis. * Infection History: • Participant has an active bacterial, viral, or helminth parasitic infection; OR a history of ongoing, recurrent severe infections requiring systemic antibiotics. • Participant has active chronic or acute skin infection requiring treatment with systemic antibiotics, antivirals, antiparasitics, antiprotozoals, or antifungals within 2 weeks prior to Baseline or superficial skin infections within 1 week prior to Baseline. • Participant has a history (single episode) of disseminated herpes zoster or disseminated herpes simplex, or a recurrent (more than one episode of) localized, dermatomal herpes zoster. * Participant has a history of alcohol or substance abuse within 6 months prior to Day 1 that in the opinion of the investigator will preclude participation in the study. * Participant with a known or suspected underlying immunodeficiency or immune-compromised state as determined by the investigator. * Participant has a concurrent or recent history of severe, progressive, or uncontrolled renal, hepatic, hematological, intestinal, metabolic, endocrine, pulmonary, cardiovascular, or neurological disease. ANY of the following abnormalities in renal or hepatic tests at screening are exclusionary: Estimated creatinine clearance \<40 mL/min based on the age appropriate calculation, or serum creatinine \>1.5 times the upper limit of normal (ULN); • Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) values \>2 times the ULN; • Total bilirubin ≥1.5 times the ULN; participants with a history of Gilbert's syndrome may have a direct bilirubin measured and would be eligible for this study provided the direct bilirubin is ≤ ULN. * Participant has active hepatitis B, hepatitis C, or human immunodeficiency virus (HIV) prior to Baseline. * Participant has positive or indeterminable PPD or QFT result including participants that completed standard tuberculosis therapy prior to Baseline. * Past or current medical problems or findings from physical examination or laboratory testing that are not listed above, which, in the opinion of the investigator, may pose additional risks from participation in the study, may interfere with the participant's ability to comply with study requirements or that may impact the quality or interpretation of the data obtained from the study. * Participant has history of adverse systemic or allergic reactions to any component of the study drug or any safety event deemed "related" to a JAK inhibitor. * Participant has used systemic immunosuppressive medications, including, but not limited to, cyclosporine, systemic or intralesional corticosteroids, mycophenolate mofetil, azathioprine, methotrexate, tacrolimus, oral JAK inhibitor (tofacitinib, ruxolitinib, baricitinib, ritlecitinib, or investigational oral JAK Inhibitors) or ultraviolet (UV) phototherapy with/without Psoralen Ultraviolet A (PUVA) therapy, within 4 weeks prior to the Week 0/Baseline visit. * Participant has used systemic monoclonal antibody treatments (such as the IL-4R antagonist dupilumab) within 12 weeks of Baseline visit. * Participant has used topical corticosteroids, and/or tacrolimus, and/or pimecrolimus within 1 week prior to the Week 0/Baseline visit. * Participant with Translocation or Mosaic Downs Syndrome.