A Study of Ibrutinib With Rituximab in People With Untreated Marginal Zone Lymphoma

Inclusion Criteria: * Histologically documented marginal zone lymphoma, including splenic, nodal, and extranodal sub-types at the enrolling institution. * No prior systemic therapy for MZL with the exception of the following: * Prior antibiotic therapy for H. pylori, C. psittaci, and B. burgdorferi * Prior antiviral therapy for HCV Note: Subjects are eligible if they had prior splenectomy or other local surgical treatment or local radiation therapy without systemic therapy and now require their first ever systemic therapy. * Men and women ≥18 years of age * Patients with gastric MALT lymphoma must be H. pylori negative or have failed a trial of H. pylori eradication * Patients with gastric MALT lymphoma who are H. pylori negative or who have relapsed/refractory disease after H. pylori eradication must be ineligible for, have refused or failed gastric radiation therapy * Eastern Cooperative Oncology Group (ECOG) performance status of ≤2 * ≥1 measurable lesion on computed tomography (CT) scan (\>1.5 cm in longest dimension) unless bone marrow disease only including those with hemolytic anemia. Lesions in anatomical locations (such as extremities or soft tissue lesions) that are not well visualized by CT may be measured by magnetic resonance imaging (MRI) instead. Patients with splenomegaly without other measurable disease must have splenomegaly of \>15 cm in the craniocaudal direction * Life expectancy of \>3 months, in the opinion of the investigator * Female subjects mu…