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

The purpose of this study is to evaluate the safety of the combination of cetrelimab, with apalutamide and to define a population of participants with metastatic castration-resistant prostate cancer (mCRPC) who respond to treatment with the combination of cetrelimab and apalutamide.

This study is of participants originally diagnosed with adenocarcinoma of the prostate who have now developed mCRPC and who have progressed on therapy with abiraterone acetate plus prednisone/prednisolone (AA-P), apalutamide, darolutamide, or enzalutamide. Participants with treatment-emergent small-cell neuroendocrine prostate cancer (t-SCNC) assessed by the screening biopsy may be considered for this study. Participants must have confirmed prostate-specific antigen (PSA) progression per Prostate Cancer Clinical Trials Working Group (PCWG3) criteria. The primary hypothesis is that treatment with cetrelimab and apalutamide is safe and leads to improvement in the 12-week PSA response rate. The study consists of an Optional Pre-screening Period, Screening period (28 days prior to Cycle 1 Day 1), Treatment Period, End-of-Treatment Visit (performed after the last dose of study drug is administered), and Follow-up Period (participants will have Follow-up assessment every 12 weeks after the End-of-Treatment Visit). The efficacy, safety, and pharmacokinetics of cetrelimab in combination with apalutamide will be evaluated.

Eligibility Criteria:
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