This phase II trial studies how well apalutamide, abiraterone acetate, prednisone, degarelix, and indomethacin work in treating patients with prostate cancer that has spread from where it started to nearby tissue or lymph nodes before surgery. Androgen can cause the growth of tumor cells. Hormone therapy using apalutamide, abiraterone acetate, prednisone, degarelix, and indomethacin may fight prostate cancer by lowering the amount of androgen the body makes and/or blocking the use of androgen by the tumor cells.

PRIMARY OBJECTIVES:

I. The rate of the pathologic complete response (pCR) (i.e. no evidence of residual tumor) as assessed on prostatectomy specimens following 3-months (12 weeks) of neoadjuvant apalutamide, abiraterone acetate, degarelix and indomethacin.

SECONDARY OBJECTIVES:

I. To determine the negative margin rate as assessed on prostatectomy specimens following 3-months (12 weeks) of neoadjuvant apalutamide, abiraterone acetate, degarelix and indomethacin.

II. To determine the rate of near pCR (i.e. =< 5 mm of residual tumor) as assessed on prostatectomy specimens following 3-months (12 weeks) of neoadjuvant apalutamide, abiraterone acetate, degarelix and indomethacin.

III. To determine the rate of pathologic T3 disease as assessed on prostatectomy specimens following 3-months (12 weeks) of neoadjuvant apalutamide, abiraterone acetate, degarelix and indomethacin.

IV. To determine the rate of nodal metastases as assessed on surgical lymph node specimens following 3-months (12 weeks) of neoadjuvant apalutamide, abiraterone acetate, degarelix and indomethacin.

V. To determine the apoptotic index (i.e. percentage of tumor cells undergoing apoptosis) as determined by cleaved caspase-3 immunohistochemistry following 3-months (12 weeks) of neoadjuvant apalutamide, abiraterone acetate, degarelix and indomethacin.

VI. To determine the proportion of men who receive adjuvant radiation therapy within 1-year of prostatectomy.

VII. To determine the biochemical (i.e. prostate-specific antigen [PSA]) progression free survival estimate two years after the last patient has accrued (i.e. confirmed PSA post-radical prostatectomy >= 0.2 ng/mL).

VIII. To determine the overall survival estimate two years after the last patient has accrued.

IX. Safety as assessed by the incidence and severity of adverse events and serious adverse events graded according to the National Cancer Institute - Common Terminology Criteria for Adverse Events (CTCAE) version 4.0.

X. Exploratory biomarker assessment.

OUTLINE:

Patients receive apalutamide and abiraterone acetate orally (PO) daily, prednisone PO twice per day (BID) and indomethacin PO three times per day (TID). Patients also receive degarelix subcutaneously (SC) on day 1 and every 4 weeks for 3 doses. Treatment continues for up to 12 weeks in the absence of disease progression or unacceptable toxicity. Patients undergo prostatectomy on day 85.

After completion of study treatment, patients are followed up at 28, 113, 450 and 815 days.

Inclusion Criteria:

• Willing and able to provide written informed consent
• Eastern Cooperative Oncology Group (ECOG) performance status =< 2
• Documented histologically confirmed adenocarcinoma of the prostate
• Willing to undergo prostatectomy as primary treatment for localized prostate cancer
• High risk prostate cancer (per National Comprehensive Cancer Network [NCCN] criteria): Gleason score 8-10 or T3a or PSA > 20 ng/mL or very-high risk prostate cancer (per NCCN criteria): T3b-T4
• Serum testosterone >= 150 ng/dL
• Able to swallow the study drugs whole
• Willing to take abiraterone acetate on an empty stomach (no food should be consumed at least two hours before and for one hour after dosing)
• Agrees to use a condom (even men with vasectomies) and another effective method of birth control if he is having sex with a woman of childbearing potential or agrees to use a condom if he is having sex with a woman who is pregnant while on study drug and for 3 months following the last dose of study drug; must also agree not to donate sperm during the study and for 3 months after receiving the last dose of study drug
• Medications known to lower the seizure threshold (see list under prohibited meds) must be discontinued or substituted at least 4 weeks prior to study entry

Exclusion Criteria:

• Prior local therapy to treat prostate cancer (e.g. radical prostatectomy, radiation therapy, brachytherapy)

• Prior use of apalutamide, abiraterone acetate or degarelix

• Prior or ongoing systemic therapy for prostate cancer including, but not limited to:

  • Hormonal therapy (for example [e.g.] leuprolide, goserelin, triptorelin, degarelix)
  • Cytochrome P450 (CYP)-17 inhibitors (e.g. ketoconazole)
  • Antiandrogens (e.g. bicalutamide, nilutamide)
  • Second generation antiandrogens (e.g. enzalutamide, apalutamide)
  • Immunotherapy (e.g. sipuleucel-T, ipilimumab)
  • Chemotherapy (e.g. docetaxel, cabazitaxel)

• Evidence of serious and/or unstable pre-existing medical, psychiatric or other condition (including laboratory abnormalities) that could interfere with patient safety or provision of informed consent to participate in this study

• Any psychological, familial, sociological, or geographical condition that could potentially interfere with compliance with the study protocol and follow-up schedule

• Absolute neutrophil count [ANC] < 1500/mm^3

• Platelet count < 100,000/mm^3

• Hemoglobin < 9 g/dL

• Total bilirubin > 1.5 x upper limit of normal (ULN)

• Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) >= 2.5 x ULN; Note: in subjects with Gilbert's syndrome, if total bilirubin is > 1.5 x ULN, measure direct and indirect bilirubin and if direct bilirubin is =< 1.5 x ULN, subject may be eligible

• Abnormal kidney function (glomerular filtration rate GFR < 45 mL/min)

• Serum albumin < 3 g/dL

• Serum potassium < 3.5 mmol/L

• Seizure or known condition that may pre-dispose to seizure (e.g. prior stroke within 1 year to randomization, brain arteriovenous malformation, schwannoma, meningioma, or other benign central nervous system [CNS] or meningeal disease which may require treatment with surgery or radiation therapy)

• Severe or unstable angina, myocardial infarction, symptomatic congestive heart failure, arterial or venous thromboembolic events (eg, pulmonary embolism, cerebrovascular accident including transient ischemic attacks), or clinically significant ventricular arrhythmias within 6 months prior to randomization

• History of stroke within the last 5-years

• History of gastrointestinal (GI) bleed requiring transfusion

• History of peptic ulcer disease requiring treatment within the last 5-years

• History of asthma that is nonsteroidal anti-inflammatory drug (NSAID)-induced or with asthma that is classified as 'mild-persistent' or worse (based on symptoms occurring more than 2 days per week)

• Uncontrolled hypertension

• Gastrointestinal disorder affecting absorption

• Active infection (eg, human immunodeficiency virus [HIV] or viral hepatitis)

• Any chronic medical condition requiring a higher dose of corticosteroid than 10 mg prednisone/ prednisolone once daily

• Any condition that in the opinion of the investigator, would preclude participation in this study

• Child Pugh class B & C

• Pre-existing viral hepatitis