The aim of the study is to find out if patients with blood cancers receiving immunoglobulin (Ig) for the purpose of preventing infections can safety stop immunoglobulin after six months of therapy, and take oral antibiotics instead to prevent serious infections. Patients may be eligible to join this study if they are aged 18 years or above, have an acquired hypogammaglobulinaemia secondary to a haematological malignancy, and have been receiving intravenous or subcutaneous Ig for longer than 6 consecutive months. Participants will be randomised (allocated by chance) to one of three treatment groups, as follows: * Stop immunoglobulin (IVIg or SCIg) and be given oral antibiotics to take every day (ARM A) * Stop immunoglobulin (IVIg or SCIg) and be given oral antibiotics to keep at home to use as soon as symptoms of an infection develop (ARM B) * Continue receiving immunoglobulin (IVIg or SCIg) - this is the usual care group (ARM C) The duration of each treatment is for 12 months from study entry. Participants will be asked to attend a screening/baseline visit so that their treating clinician can assess their eligibility for the trial and collect baseline data. If eligible for the trial, participants will then be randomly allocated to one of the three treatment groups. Once randomised, active participation in the study will last for 13 months. During this period, participants will be asked to return to the hospital for a study visit every 3 months, with monthly telephone visits to check-in on your progress between each in-person visit. Participants will also be asked to complete a study diary, recording treatment compliance and signs/symptoms of infection experienced throughout the study period. Types of assessments and data collected will include: Medical history, demographics, physical examination, blood tests, stool sample, quality of life questionnaires, information about your general health, hospitalisations, medications and procedures. In order to assess and compare the cost-effectiveness of the treatment groups, the study team will also request authorisation from participants to access their Medicare Benefits Schedule (MBS), Pharmaceutical Benefits Scheme (PBS), and Australian Immunisation Register (AIR) data.