Nivolumab and Ipilimumab Treatment in Prostate Cancer With an Immunogenic Signature

This is a two-arm non-randomised, non-comparative phase II trial designed to assess the efficacy of nivolumab + ipilimumab in patients with metastatic castrate resistant prostate cancer that have progressed following at least 1 line of therapy and have an specified immunogenic signature. The immunogenic signature is defined by the presence of at least one of the following: * Mismatch repair deficiency by IHC * Defective DNA repair detected by a targeted sequencing panel * High inflammatory infiltrate defined on multiplexed IHC criteria. Treatment consists of : Cohort 1: * Nivolumab 1 mg/kg + ipilimumab 3 mg/kg every three weeks for a maximum of 4 doses * 6 week gap after last combination dose * 480 mg flat dose of nivolumab every 4 weeks for up to one year, or until progression, unacceptable toxicity or withdrawal of consent. Cohort 2: * Nivolumab 3 mg/kg + ipilimumab 1 mg/kg every three weeks for a maximum of 4 doses * 3 week gap after last combination dose * 480 mg flat dose of nivolumab every 4 weeks for up to one year, or until progression, unacceptable toxicity or withdrawal of consent. Patients must have ongoing androgen deprivation to maintain serum testosterone \< 1.73 nmol/L.