A Study of Cetrelimab (JNJ-63723283), a Programmed Cell Death Receptor-1 (PD-1) Inhibitor, Administered in Combination With Apalutamide in Participants With Metastatic Castration-Resistant Prostate Cancer

Inclusion Criteria: * Pathologically confirmed adenocarcinoma of the prostate. Treatment-emergent small-cell neuroendocrine prostate cancer (t-SCNC) on screening biopsy may be eligible for cohort 5 * Metastatic disease as documented by technetium-99m (99mTc) bone scan or metastatic lesions by computed tomography (CT) or magnetic resonance imaging (MRI) scans (visceral or lymph node disease). CT-portion of positron emission tomography (PET)/CT scan may be used for eligibility. If lymph node metastasis is the only evidence of metastatic disease, it must be greater than (\>=) 1.0 centimeter (cm) in the short axis and above the level of the iliac bifurcation * Progressed while on therapy with abiraterone acetate plus prednisone/prednisolone (AA-P), enzalutamide, darolutamide, or apalutamide for mCRPC. No washout is required and no additional therapy may have been administered between discontinuation of AR-targeted the agent and study treatment. Participants will be assigned to cohorts based on the results of the biomarker panel. Cohort 1: Biomarker-negative or biomarker-unknown participants with adenocarcinoma (and not t-SCNC) who progressed on abiraterone acetate plus prednisone/prednisolone (AA-P); Cohort 2: Biomarker-negative or biomarker-unknown participants with adenocarcinoma (and not t-SCNC) who progressed on apalutamide, darolutamide, or enzalutamide; Cohort 3: Biomarker-positive participants who progressed on AA-P; Cohort 4: Biomarker-positive participants who progressed on apalutamide, darolutamide, or enzalutamide; Cohort 5: Biomarker-negative participants with t-SCNC who progressed on treatment with AA-P, apalutamide, darolutamide, or enzalutamide * Surgical or medical castration, with testosterone levels of less than (\<)50 nanogram per deciliter (ng/dL). If the participant is being treated with gonadotropin-releasing hormone (GnRH) analogs (participant who has not undergone bilateral orchiectomy), this therapy must have been initiated at least 4 weeks prior to first dose of study drug and must be continued throughout the study * Eastern Cooperative Oncology Group Performance Status (ECOG) prostate-specific (PS) grade of 0 or 1 Exclusion Criteria: * Initial diagnosis of primary prostatic neuroendocrine or small cell carcinoma * Brain metastases * Prior treatment with an anti-programmed cell death receptor-1 (PD-1), anti-programmed cell death ligand 1 (PD-L1), or anti-cytotoxic T-lymphocyte antigen 4 (CTLA-4) antibody * Prior chemotherapy, except for docetaxel for hormone-sensitive prostate cancer (HSPC) * Prior therapy with poly adenosine diphosphate (ADP)-ribose polymerase (PARP) inhibitors