This study compares 2 methods of treating infants who were born prematurely with a patent ductus arteriosus (PDA). A PDA is a blood vessel connecting the lungs and the heart. All infants have a PDA when they are born, and most PDAs close shortly after birth. In premature infants, the PDA can stay open, which may cause breathing problems. Infants born early (more than 12 weeks before the planned delivery date) who need help breathing using a machine (ventilator) and who have an open PDA may qualify for this study. Both widely used treatment approaches in this study are considered standard of care. Researchers aim to determine which method is most effective to treat infants with open PDAs within the first weeks of life for best possible health outcomes. Specifically, the study will compare catheter closure to responsive management. In catheter closure, the PDA will be closed with a device called Piccolo (approved by the U.S. Food and Drug Administration) that is inserted with a small flexible tube (catheter). Responsive management would manage the symptoms caused by the PDA, which may include medications and changes in fluid amounts given to the infant, allowing more time for the PDA to possibly close on its own. Participants will be randomly assigned to either the catheter closure group or the responsive management group.