A Study of Ruxolitinib vs Best Available Therapy (BAT) in Patients With Steroid-refractory Chronic Graft vs. Host Disease (GvHD) After Bone Marrow Transplantation (REACH3)

Inclusion Criteria: * Have undergone allogeneic stem cell transplantation (alloSCT) from any donor source (matched unrelated donor, sibling, haplo-identical) using bone marrow, peripheral blood stem cells, or cord blood. Recipients of non-myeloablative, myeloablative, and reduced intensity conditioning are eligible * Evident myeloid and platelet engraftment: Absolute neutrophil count (ANC) \> 1000/mm\^3 and platelet count \> 25,000/ mm\^3 * Participants with clinically diagnosed moderate to severe cGvHD according to NIH Consensus Criteria prior to randomization: * Moderate cGvHD: At least one organ (not lung) with a score of 2, 3 or more organs involved with a score of 1 in each organ, or lung score of 1 * Severe cGvHD: at least 1 organ with a score of 3, or lung score of 2 or 3 * Participants currently receiving systemic or topical corticosteroids for the treatment of cGvHD for a duration of \< 12 months prior to Cycle 1 Day 1 (if applicable), and have a confirmed diagnosis of steroid-refractory cGvHD defined per 2014 NIH consensus criteria irrespective of the concomitant use of a calcineurin inhibitor (CNI), as follows: * A lack of response or disease progression after administration of minimum prednisone 1 mg/kg/day for at least 1 week, OR * Disease persistence without improvement despite continued treatment with prednisone at \> 0.5 mg/kg/day or 1 mg/kg/every other day for at least 4 weeks, OR * Increase to prednisolone dose to \> 0.25 mg/kg/day after 2 unsuc…