- In the second phase, which begins at the 16th week of the study, all participants will receive omalizumab. This means that subjects who had been getting omalizumab will continue receiving it and subjects who had been receiving the placebo will now begin getting omalizumab. They will have an overnight hospital stay for this infusion and will return in 2 weeks for a safety monitor visit. If subjects safety measures are good they will return in 2 weeks and receive the next dose. They will then get three more doses every 4 weeks which will be given during outpatient visits to the NIH.