A Long-term Study of Baricitinib (LY3009104) With Topical Corticosteroids in Adults With Moderate to Severe Atopic Dermatitis That Are Not Controlled With Cyclosporine or for Those Who Cannot Take Oral Cyclosporine Because it is Not Medically Advisable (BREEZE-AD4)

Participants must have been diagnosed with moderate to severe eczema for at least 12 months

Participants must be willing to stop taking certain eczema treatments

Participants must agree to use a lotion or cream that softens the skin daily

Participants must not have had satisfactory results with existing medications applied to the skin

Participants must not be candidates for cyclosporine treatment because of one of the following: 1. They are not able to take it for medical reasons, 2. They are intolerant to it or developed toxicity from it, or 3. They had unsatisfactory results with it

Participants must not have other skin conditions (such as psoriasis or lupus) or a history of skin diseases or infections that did not respond to treatment or require frequent hospitalization and/or IV treatment

Participants must not have a skin infection that requires antibiotics or are currently taking antibiotics that affect the whole body or are applied to the skin

Participants must not have been treated with corticosteroids taken by mouth four weeks before treatment assignment or corticosteroids given by injection within 6 weeks prior to treatment assignment and are not expected to need corticosteroid injections during the study

Participants must not have uncontrolled high blood pressure, major surgery (within the last two months or planned to take place during the study), or recent blood clot, heart attack, chest pain, stroke, heart failure or any other serious or unstable disease or infection

Female participants must not be pregnant or breastfeeding and must agree to use 2 forms of birth control