Inclusion Criteria:  Confirmed diagnosis of OI Types I, III, or IV as confirmed by identification of genetic mutation in collagen, type I, alpha 1 (COL1A1) or collagen, type I, alpha 2 (COLA2) ≥ 1 fracture in the past 12 months or ≥ 2 fractures in the past 24 months Serum 25 hydroxyvitamin D (25[OH]D) above the lower limit of normal (≥ 30 ng/mL) at the Screening Visit. If 25(OH)D levels are below the normal range, 25(OH)D supplementation may be prescribed at the discretion of the treating physician. Assuming a subject meets all other eligibility requirements, the subject may be rescreened after a minimum of 14 days of supplementation. Willing to not receive bisphosphonate therapy during the study From the period following informed consent to 60 days after the last dose of the study drug, females of childbearing potential and fertile males must consent to use highly effective contraception. If female, agree not to become pregnant. If male, agree not to father a child or donate sperm Willing and able to provide informed consent for subjects greater than or equal to 18 years of age, or provide assent (if possible) and have a legally authorized representative provide informed consent, after the nature of the study has been explained and prior to any research-related procedures Willing to provide access to prior medical records for the collection of historical radiographic data, fracture data, growth data, and disease history Must, in the opinion of the Investigator, be willing and able to complete all aspects of the study, adhere to the study visit schedule, and comply with the assessments  Exclusion Criteria:  Cohort A only: Body weight > 60 kg A history of bone surgery within the previous 6 months prior to Screening or planned bone surgery for new hardware placement for next 18 months History of skeletal malignancies or bone metastases at any time History of neural foraminal stenosis (except if due to scoliosis) History of or uncontrolled concomitant diseases such as hypo/hyperparathyroidism, Paget's disease, abnormal thyroid function, thyroid disease or other endocrine disorders or conditions that could affect bone metabolism such as Stage IV/V renal disease Rickets or any skeletal condition (other than OI) leading to long-bone deformities and/or increased risk of fractures History of stroke, myocardial infarction, transient ischemic attack or angina. Hypocalcemia, defined as serum calcium levels below the age-adjusted normal limits determined based on overnight fasting (≥ 4 hours) Estimated glomerular filtration rate ≤ 29 mL/min/1.73 m2  Prior treatment with the following:  Bisphosphonates within 3 months of Screening Teriparatide, growth hormone, or other anabolic or anti-resorptive medications within 6 months of Screening Denosumab within 24 months of Screening Documented alcohol and/or drug abuse within 12 months prior to dosing or evidence of such abuse as indicated by the laboratory results during the Screening assessments Presence or history of any condition that, in the view of the Investigator, would interfere with participation, pose undue risk, or would confound interpretation of results Known hypersensitivity to setrusumab or their excipients that, in the judgment of the Investigator, places the subject at increased risk for adverse effects History of external radiation Pregnant or breastfeeding or planning to become pregnant (self or partner) at any time during the study Use of any investigational product or investigational medical device within 4 weeks or 5 half-lives of investigational drug (whichever is longer) prior to Screening, or during the study (per discretion of the Investigator in consultation with the Medical Monitor) Concurrent participation in another clinical study without prior approval from the Investigator in consultation with the Medical Monitor