- For the first phase, participants will have infusions (under their skin) of either omalizumab or a placebo. They will have an overnight hospital stay for the first infusion and then an outpatient safety monitor visit 2 weeks after. If subjects safety measures are good they will return in 2 weeks and receive the second dose. They will then get three more doses every 4 weeks which will be given during outpatient visits to the NIH.