This is a multi-center, randomized (treatment will be assigned by chance), placebo-controlled (an inactive substance will be compared with the test drug to see whether the drug has a real effect), parallel-group (two or more groups of patients will receive different treatments) study that will consist of two parts. Part 1 will be an open-label (all participants will know the identity of the treatment) proof-of-concept study. Part 2 will be contingent on the results of Part 1 and will be double-blind (investigators and patients will not know what treatment is being given) and will evaluate the efficacy and safety of ustekinumab in patients with primary biliary cirrhosis (PBC) who had an inadequate response to ursodeoxycholic acid. The duration of participation in the study for an individual participant may be up to 216 weeks. Patient safety will be monitored. Part 1: ustekinumab, 90mg subcutaneous (SC) at Weeks 0 and 4 and every 8 weeks through Week 20; Part 2: Depending on Part 1 results, either (ustekinumab 90mg or 45mg or placebo) or (ustekinumab 90mg or 180mg or placebo) SC at Weeks 0 and 4 and every 8 weeks through Week 20; Long-term Extension (including Part 1 and Part 2): beginning at Week 28, every 8 weeks with initially assigned dose until the extension dose has been selected; then every 8 weeks through Week 196 with the selected dose.