JAK 1/2 Inhibitor, Baricitinib, in the Treatment of Adult IIM

Inclusion Criteria: 1. Participant meets EULAR/ACR classification criteria for polymyositis (PM) or dermatomyositis (DM) (at least 55% probability). 2. Persisting disease activity as defined in (3), after a minimum of 12 weeks treatment with prednisolone or equal drug. The history of treatment with prednisolone (or equal) should include the dose of ≥ 20mg/day for at least 4 weeks. Prednisolone should be at a stable dose of ≤ 20 mg/day for at least 4 weeks prior to the baseline visit. 3. Inflammatory active disease based on persisting or worsening muscle weakness; MMT \< 150 or low endurance (FI-3 \< 20% of upper value), together with at least one other sign of active disease: elevated serum levels of at least one muscle enzyme (CK, LDH, AST, ALT) above upper limit of normal and being explained by muscle involvement and no other cause e.g. liver disease, inflammation in recent muscle biopsy or on MRI scans (\<12 weeks), or active extra muscular disease: dermatomyositis-specific skin rash, arthritis or interstitial lung disease (ILD) (as suggested by chest x-ray/ high resolution computerised tomography (HRCT) or pulmonary function test (reduction of TLCO by 15% and/or FVC by 10% from baseline)) and on the treating physicians' judgement. In particular, patients who meet the inclusion criteria but with less than moderate disease activity should only be included at the discretion of the PI. 4. If criteria in (2) not met, then to fulfil sum of Physician global assessment, participant global assessment and extra muscular global assessment visual analogue scale (VAS) score ≥ 10 cm (all scales individually on 0-10 cm scale). 5. For polymyositis, a participant can be included if they are positive for myositis specific (anti-synthetase, NXP2, SAE1, TIF1g, Mi2, MDA5,) or myositis-associated autoantibodies (Ro52, Ro60, PmScl, RNP). Polymyositis will be included after a judicial process by the three PIs. 6. Are receiving at least one of the following standard of care medications within the required timeframe: * A single antimalarial (e.g. hydroxychloroquine) for 3 months and at a stable therapeutic dose for at least 8 weeks prior to the screening visit * A single immunosuppressant (such as methotrexate (MTX), azathioprine, mycophenolate) for 3 months and at a stable therapeutic dose for at least 4 weeks prior to the screening visit * An oral corticosteroid, at a stable dose ≤ 20 mg/day prednisone (or equivalent), for at least 4 weeks prior to baseline (visit 1) 7. Age ≥18 years. 8. Full capability of providing informed consent. Exclusion criteria 1. Participants with other types of inflammatory myopathies including: * Drug induced myositis * Inclusion body myositis * Malignancy-associated myositis * Immune-mediated necrotizing myopathy 2. Participants unable to participate in clinical assessments or provide biological specimens as per the study protocol 3. Participants where the use of bariticinib would be contraindicated 4. Participants with known allergies to IMP or excipients 5. Women with a positive pregnancy test on enrolment or prior to start of study drug administration 6. Women who are known to be pregnant or breastfeeding 7. Women of child bearing potential (WOCBP) who are unwilling or unable to use an acceptable method to avoid pregnancy for the entire study period and for at least 1 week after treatment (Please see Appendix 3 for definitions and acceptable methods of contraception). 8. Current symptoms of severe, progressive, or uncontrolled renal, hepatic, haematological, gastrointestinal, pulmonary, cardiac, neurological, ophthalmologic or cerebral disease with the exception of those symptoms that are a manifestation of polymyositis or dermatomyositis. 9. Concomitant medical conditions that in the opinion of the investigator might place the subject at unacceptable risk for participation in this study. 10. Participants with a history of venous thromboembolism including deep vein thrombosis and pulmonary embolism. 11. Participants with a history of cancer within the last five years (other than non-melanoma skin cell cancers cured by local resection), including carcinoma-in-situ. Existing non-melanoma skin cell cancers must be removed prior to IMP dosing. Participants with dermatomyositis need to be screened for malignancies according to routine procedures. 12. Participants who have a history of clinically significant drug or alcohol abuse. Subjects currently taking MTX who admit to consumption of more than an average of 1 alcoholic drink per day. 13. Participants with any serious bacterial infection (such as pneumonia, other renal infection and sinusitis), unless treated and resolved with antibiotics. 14. Participants with any chronic bacterial infection (such as pyelonephritis and chest infection with bronchiectasis) in the previous 12 weeks before screening. 15. Participants with active tuberculosis (TB) requiring treatment within the previous 3 years. Subjects with a positive PPD and/or Quantiferon assay at screening will not be eligible for the study unless they have completed at least 4 weeks of treatment for latent TB, have a negative chest x-ray at enrolment, and commit to completing the course during the study. Such cases should be discussed with a respiratory physician as per local guidelines. A PPD response that is equal to or greater than 10 mm should be considered a positive test, although more conservative criteria may be applied as determined by the clinical circumstance and investigator according to published guidelines and/or local standards endorsed by the medical society. PPD and/or Quantiferon positive participants who have previously completed treatment for latent tuberculosis according to the local guidelines may be considered for enrolment. Equivocal Quantiferon results will need to be discussed with a local respiratory physician. 16. Participants with herpes zoster that resolved less than 8 weeks prior to the screening visit. 17. Participants with evidence (as assessed by the Investigator) of active or latent bacterial or viral infections at the screening visit, including subjects with evidence of Human Immunodeficiency Virus (HIV) infection, positive HepBsAg, HepBcAb or hepatitis C antibody. 18. Significant toxicities associated with concomitant or previous immunosuppressive/biologic therapy that would preclude subjects from participating and completing the study. 19. Participants with clinically apparent immunodeficiency syndrome, (IgA deficiency alone is not an exclusion criterion). 20. Participants with any of the following laboratory values at screening: * Haemoglobin (Hb) \< 80 g/litre * Absolute lymphocyte count (ALC) \< 500 cells/mm3 * Absolute neutrophil count (ANC) \< 1000 cells/mm3 * Platelets \<100,000/mm3 (100 x 109/L) * Creatinine clearance \<30ml/min. Note: participants with creatinine clearance between 30-60mL/min should receive a reduced oral dose of 2mg baricitinib OD. * Any other laboratory test results that, in the opinion of the investigator, might place the subject at unacceptable risk for participation in this study. 21. For participants previously treated with rituximab: B cell levels less than lower limit of normal as measured by Fluorescent Activated Cell Sorting (FACS) analysis. 22. For all participants who have received prior rituximab, a normal CD19 B cell count must be documented at the time of screening for this study. 23. Participants who have received treatment with any investigational drug within 28 days of the first dose of IMP. 24. Participants who have at any time received treatment with JAK/STAT inhibitors. 25. Administration of live/ attenuated vaccines in the 4 weeks prior to screening and during the study. Effect on vaccine efficacy or the risk of infection transmission is unknown. In addition, clinical safety has not been established. 26. Concomitant use of targeted biologic therapies at any time during the study.