JAK Inhibitor Treatment in AGS

Inclusion Criteria: * Clinical or molecular identification of Aicardi Goutières Syndrome including the following features * Cerebrospinal fluid (CSF) or blood markers suggesting elevations of markers of interferon activation including CSF pleocytosis, elevation of interferon, and/or neopterin and tetrahydrobiopterin elevations * Evidence of neurologic disease on neuroimaging including intracranial calcifications and or a leukoencephalopathy * Clinical features of disease including features such as microcephaly, subacute encephalopathy, myopathy, spastic diplegia, skin involvement, autoimmune hepatitis, hematologic abnormalities * OR have documented mutations felt to be pathogenic in an AGS associated gene. * Are ≥1 month of age. * Are ≥4.5 kg in body weight. * Females after menarche must have a negative urine/serum pregnancy test and must use an acceptable method of contraception, including abstinence, a barrier method (diaphragm or condom), Depo-Provera, or an oral contraceptive, for the duration of the study. * Parental/guardian permission (informed consent). Exclusion Criteria: * Are pregnant or nursing at the time of entry or unable to use contraception as detailed below * Are females of childbearing potential (women \>12 or who have had at least one menstrual period regardless of age) who are sexually active and who do not agree to use 2 forms of highly effective methods of birth control (see below) or remain abstinent during the study and for at least 28 days following the last dose of investigational product * Are sexually active males who do not agree to use 2 forms of highly effective birth control (see below) with female partners of childbearing potential or remain abstinent during the study and for at least 28 days following the last dose of investigational product. * Each of the following is considered a single highly effective method of birth control (the patient should choose 2): * oral, injectable, or implanted hormonal contraceptives * condom with spermicidal foam/gel/film/cream/suppository * occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository * intrauterine device * intrauterine system (for example, progestin releasing coil) * vasectomized male (with the appropriate post-vasectomy documentation of the absence of sperm in the ejaculate) * Overall health status that in the opinion of the investigator limits the safety of the use of bariticinib * Have been exposed to a live vaccine within 12 weeks prior to entry or are expected to need/receive a live vaccine (including herpes zoster vaccination) during the course of the study, with the exception of oral rotavirus vaccinations for which the time period is 2 weeks. Young patients who are not yet vaccinated and will be unable to receive live vaccines while they are receiving the program drug (baricitinib) may be included after a documented conversation by a physician not affiliated with the study or the medical monitor with the parents to ensure parental consent and understanding of the risk/benefit ratio of not receiving scheduled vaccinations. These subjects will only be included in the study after a physician obtaining consent also describes the risk/benefit ratio of not receiving scheduled vaccinations. * Have the following evidence of renal insufficiency: * An estimated glomerular filtration rate (eGFR) based on the most recent available serum creatinine of \<40 mL/min/1.73 m2 if greater than 2 year of age. eGFR will be calculated using the Bedside Schwartz Equation: eGFR (mL/min/1.73 m2) = (0.413 x height) / SCr, with height measured in cm, and serum creatinine (SCr) in units of mg/dL. * Children with an eGFR of \<40 mL/min/1.73 m2 will not be enrolled, unless \<24 months of age in which case a cut off of \<30 ml/min/1.73 m2 will be used due to age-based differences in normal eGFR. Normal eGFR of \<60 ml/min/1.73 m2 is common in children \<12 months, and a normal eGFR \<40 ml/min/1.73 m2 is common in infants \<3-6 months. * The creatinine should be measured using the Isotopic Dilution Mass Spectrometry (IDMS) technique to monitor the eGFR if available. Other methods are allowed but are not preferred. Laboratory testing using other methods will not be used to monitor the eGFR. * Have any of the following specific Hematologic abnormalities on screening laboratory tests: * Hemoglobin \<7 mg/dL (70 g/L). In infants \<2 mo of age, 8 mg/dL will be used as a threshold * Neutropenia \[absolute neutrophil count (ANC) \<500 cells/µL\] * CD4 \<250 cell/µl on lymphocyte subset testing (where Absolute CD4 count=Absolute cluster of differentiation 3/ cluster of differentiation 4 (CD3/CD4) count=CD3/CD4 count=CD4 count=Absolute CD3+CD4+ cells) * Thrombocytopenia (platelets \<30,000/µL). Patients who are on anticoagulation or having a history of life-threatening bleeding should be excluded if platelet count is \<50,000/µL * Have any of the following infectious risks: * Evidence of active infection, at the time of entry or during the screening period, that in the opinion of the investigator, would pose an unacceptable risk for participating in the study * Ongoing or incompletely treated severe or systemic infection, excluding cellulitis/osteomyelitis that is felt to be attributable to AGS * Have had symptomatic herpes zoster infection within 12 weeks prior to entry or during the screening period * Have a history of disseminated/complicated herpes zoster (for example, multidermatomal involvement, central nervous system involvement or systemic involvement including hepatitis or pneumonitis) * Have a history of active hepatitis B, hepatitis C, or human immunodeficiency virus (HIV) * Have had household contact with a person with active tuberculosis (TB) and did not receive appropriate and documented prophylaxis for TB * Have or have had a history of lymphoproliferative disease; or signs or symptoms suggestive of possible lymphoproliferative disease, or active primary or recurrent malignant disease; or been in remission from clinically significant malignancy for \<5 years * Have liver abnormalities consistent with severe, chronic liver disease * Have ECG or echocardiogram results that include an arrhythmia unamenable to standard treatment, severe pulmonary hypertension, severe heart valvular (greater than mild insufficiency or stenosis), or significant left heart failure \[per American Heart Association (AHA) guidelines, an left ventricle ejection factor (LVEF) \<50% is considered impaired\] or right heart failure (RV function described as qualitatively more than mildly diminished systolic function), that in the consideration of the investigator places them at greater risk for participation in the study; have screening electrocardiogram (ECG) abnormalities that, in the opinion of the investigator, are clinically significant and indicate an unacceptable risk for the patient's participation in the study (for example, Bazett's corrected QT interval \>450 msec for males and \>470 msec for females); have echocardiogram results that, in the opinion of the investigator, places them at greater risk if included in the study. * Are unable or unwilling to make themselves available for the duration of the study and/or are unwilling to follow study restrictions/procedures * Have received an immunosuppressive biologic agent/monoclonal antibody within 4 half-lives prior to entry, for example, anakinra (4 half- lives=18 hours); etanercept (4 half-lives=18 days); infliximab; or adalimumab (4 half-lives=36 days). Use is not indicated in subjects receiving Natalizumab, Nivolumab, Trastuzumab, Denosumab, and Belimumab. Use of intravenous immune globulin (IVIg) is permitted. * Have received or be currently treated with Bacillus Calmette-Guerin (BCG) (Intravesical), Cladribine, Dipyrone, Pimecrolimus, and Tacrolimus (Topical). * Are currently enrolled in, or discontinued within the last 30 days from, a clinical trial involving an investigational product or non-approved use of a drug or device (other than the investigational product used in this study), or concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study. * Have screening laboratory test values outside the reference range for the population or investigative site that, in the opinion of the investigator, pose an unacceptable risk for the patient's participation in the study and are not attributable to AGS. * Have screening thyroid-stimulating hormone and/or thyroxine values outside of the laboratory's reference range and are assessed to be clinically significant. If results are available from testing within 1 month, then the patient will not have to be retested. Patients who are receiving thyroxine as replacement therapy may participate in the study provided stable therapy has been administered. * Have evidence of active or latent TB as documented by a positive purified protein derivative (PPD) test (≥5 mm induration between approximately 2 and 3 days after application, regardless of vaccination history), medical history, and chest x-ray at screening. The patient may also have a QuantiFERON®-TB Gold test. If the test is positive or indeterminate, the patient may undergo evaluation including a chest x-ray (CXR) and PPD and assessed for likely risk of active tuberculosis infection. In infants \< 12 months of age, maternal and paternal testing can be used instead of testing the patient. Risk for TB will also be assessed using validated questions from The Red Book: Report of the Committee on Infectious Diseases (see below). Validated Questions for Determining Risk of latent tuberculosis infection (LTBI) in Children in the United States * Has a family member or contact had tuberculosis disease? * Has a family member had a positive tuberculin skin test result? * Was your child born in a high-risk country (countries other than the United States, Canada, Australia, New Zealand, or Western and North European countries)? * Has your child traveled to a high-risk country? How much contact did your child have with the resident population? * Have a positive test for hepatitis B defined as (1) positive for hepatitis B surface antigen, or (2) positive for anti-hepatitis B core antibody, but negative for hepatitis B surface antibody (unless the anti-hepatitis B core antibody is thought to be a false positive result). In the latter case, confirmation of the presence of hepatitis B virus (HBV) by DNA testing is required. An HBV DNA indeterminate result is considered HBV infection. If results are available from testing within the previous 3 months, then the patient will not have to be retested: If any of the hepatitis B tests have an indeterminate result, confirmatory testing will be performed by an alternate method. In infants \< 3 months of age, maternal testing can be used instead of testing the patient. * Have hepatitis C virus (positive for anti-hepatitis C antibody with confirmed presence of hepatitis C virus); * Have evidence of HIV infection and/or positive HIV antibodies. If results are available from testing within the previous 3 months, then the patient will not have to be retested. In infants \< 12 months of age, maternal testing can be used instead of testing the patient. * Have HIV virus. In infants \<12 months of age, maternal testing can be used instead of testing the patient. * Taking a concomitant medication on the list of exclusion criteria (please consult study team as needed).