Pegtibatinase as a Treatment for Patients With Classical Homocystinuria (HCU) (Also Known as the COMPOSE Study)

Primary Objective - Cohorts 1-6 Researchers are performing this study to learn if pegtibatinase is safe and tolerable (how it makes participants feel). Researchers will use medical examination, blood tests, and urine tests to measure side effects (unwanted health problems that may or may not be related to the study treatment), changes in laboratory tests and in the electrical activity of the heart (as measured by electrocardiogram or "ECG"), and if the body makes antibodies to fight against pegtibatinase. Antibodies are proteins that the body makes that may stop pegtibatinase from working or may cause side effects. Secondary Objectives - Cohorts 1-6 Researchers also want to learn about: * What are the levels of pegtibatinase in the body after single and repeated doses? * How does pegtibatinase affect levels of certain substances that are produced when the body breaks down and creates homocysteine? * What are the effects of pegtibatinase on the eyes, bones, mental health, and cognitive function? Researchers will use blood tests, physical examinations, and questionnaires to answer these questions. Cohort 7 Objectives Group 7 is open to children aged 5 to 11 years old (or "pediatric participants") who meet the requirements for the study. Researchers are performing this part of the study with Group 7 to learn if pegtibatinase is safe and tolerable (how it makes participants feel) and if it increases antibody levels when it is given to children with HCU. Researchers will use blood tests and physical examinations to measure side effects that happen during the study, changes in laboratory tests, electrical activity of the heart, antibody levels, vital signs, and the number of pediatric participants that have too high or too low levels of methionine. Researchers will use questionnaires to measure the number of pediatric participants that need more protein in their diet. Researchers are performing this part of the study with Group 7 because they also want to learn about: * What are the levels of pegtibatinase in the pediatric participant's body after single and repeated doses? * How does pegtibatinase affect levels of total homocysteine and methionine in the pediatric participant's body? Researchers will use blood tests to answer these questions. Study Population and Treatments This study will include children and adults from 5 to 65 years old with HCU. Participants in Groups 1 to 6 were aged 12 to 65 years old, and Group 7 participants will be aged 5 to 11 years old. Participants in the study will take their standard of care treatment. Groups 1 to 6 have completed this study already. For these groups, 24 participants aged 12 to 65 years old who met the requirements of the study were split into 1 of the 6 groups. For each group, 3 participants were chosen to take pegtibatinase for every 1 participant chosen to take an injection that does not have any medicine in it (or "placebo"). Participants were assigned to pegtibatinase or placebo by chance, like the flip of a coin. This is called "randomization". Neither the researchers nor the participants knew which treatment they were getting until the study was completed. This is known as a "double-blind" approach. Group 7 is open and will be conducted globally. It will include 10 to 15 pediatric participants aged 5 to 11 years old who meet the requirements of the study. All participants in this group will receive pegtibatinase. All participants will know that this is the treatment that they receive. This is called an "open label" approach. The treatment period will be separated into 3 parts: Part A, Part B, and Part C. Each part will test a different dose of pegtibatinase. After each part, pediatric participants who meet specific requirements will move to the next part. If the pediatric participants do not meet specific requirements to move to the next part, they will have the option to join the ENSEMBLE study (NCT06431893) and continue taking that same dose. Pegtibatinase or placebo will be given as an injection under the skin (or "subcutaneous injection"). Doses for each group are shown below. * Group 1: 0.33 mg/kg pegtibatinase or placebo 1 time a week. * Group 2: 0.66 mg/kg pegtibatinase or placebo 1 time a week. * Group 3: 1.0 mg/kg pegtibatinase or placebo 1 time a week. * Group 4: 1.0 mg/kg pegtibatinase or placebo 2 times a week. * Group 5: 1.5 mg/kg pegtibatinase or placebo 2 times a week. * Group 6: 2.5 mg/kg pegtibatinase or placebo 2 times a week. * Group 7: * Part A: 1.0 mg/kg pegtibatinase 2 times a week for 8 weeks; * Part B: 1.5 mg/kg pegtibatinase 2 times a week for 8 weeks; * Part C: 2.5 mg/kg pegtibatinase 2 times a week for 4 weeks. Study Duration and Visits Participants in Groups 1 to 6 were in the study for up to 158 weeks, including the screening period of up to 8 weeks, a double-blind treatment period of up to 12 weeks, and an extension period of up to 138 weeks. A continuation study called ENSEMBLE was available to participants. Participants were offered to join the ENSEMBLE study before they finished the extension period of the COMPOSE study. Pediatric participants in Group 7 may be in the study for up to 42 weeks, including the screening period of up to 10 weeks, open-label treatment period of up to 20 weeks, and up to 12 weeks of additional treatment at the same dose if the ENSEMBLE study is not yet open. If participants in Group 7 meet all the requirements of the study, they will have up to 53 visits to a study center or at home. If the ENSEMBLE study is not yet open at their site, they can have up to 23 more visits to continue treatment. These visits can include: * Blood and urine tests * Physical examinations * Questionnaires * Injections * Questions about how they are feeling or any problems they are having Safety / Adverse Events Researchers will keep track of any medical problems that a participant has during a study (or "adverse event"). All participants in this study will have regular laboratory tests, health checkups, and site visits to watch for health risks and measure safety. Benefit-Risk Conclusion Researchers have worked to reduce risks to participants in this study. They believe the risks of taking pegtibatinase in this study are justified by the potential benefits that they think pegtibatinase may have for people with HCU.