A Phase II Study of Androgen Deprivation Therapy With or Without Palbociclib in RB-Positive Metastatic Prostate Cancer

Inclusion Criteria: * Have pathologic diagnosis of prostate cancer. * Have hormone-sensitive metastatic disease (M1) as evidenced by soft tissue and/or bony metastases. * Patients may either be untreated for their newly diagnosed metastatic disease (preferred as much as possible) or have started androgen deprivation therapy. Patients who have started androgen deprivation therapy for the treatment of their newly diagnosed metastatic disease are eligible as long as the duration of treatment is less than or equal to 2 weeks (14days) prior to registration. The start date of androgen deprivation is considered the day the patient first received an injection of a LHRH agonist/antagonist (or orchiectomy), not the date when an oral antiandrogen started. * Patients must have a minimum PSA (Prostate-Specific Antigen) ≥ 5 ng/mL within 60 days of registration or prior to the initiation of androgen deprivation for patients who have started androgen deprivation therapy. * Agree to undergo a biopsy of at least one metastatic site for RB (Retinoblastoma Protein) status evaluation. Adequate metastatic tissue from prior biopsy/resection can be used if available in lieu of a biopsy. * ECOG performance status of 0-2 (Eastern Cooperative Oncology Group scoring system used to quantify general well-being and activities of daily life; scores range from 0 to 5 where 0 represents perfect health and 5 represents death). * Patients may have received prior neoadjuvant and/or adjuvant hormonal therapy, for non-metastatic disease but it must not have lasted for more than 36 months. At least 12 months must have elapsed since completion of androgen deprivation therapy in the neoadjuvant and/or adjuvant setting. * Within 14 days prior to registration patients must have adequate organ and marrow function: White Blood Cell (WBC) count ≥ 3,000/μl, Absolute Neutrophil Count (ANC) ≥ 1,500/μl, Platelet Count ≥ 100,000/μl, Serum Creatinine ≥1.5 x the institutional upper limits of normal or corrected creatinine clearance of ≥ 50 mg/ml/hr/1.73 m2 BSA (Body Surface Area), Bilirubin within the institutional limits of normal, AST (Aspartate Aminotransferase) ≤ 2 x upper limits of normal, ALT (Alanine Aminotransferase) ≤ 2 x upper limits of normal. * Patients must be able to take oral medication without crushing, dissolving or chewing tablets. * Patients may have received prior radiation therapy or surgery. However, at least 14 days must have elapsed since completion of radiation therapy or surgery and patient must have only grade 2 or less adverse effects at the time of registration. * Patients must agree to use highly effective contraception during treatment and for a period of 90 days after ending treatment with PD 0332991. * Ability to understand and the willingness to sign a written informed consent document that is approved by an institutional review board. Exclusion Criteria: * Patients who have received androgen deprivation therapy for greater than 14 days (LHRH-agonist or antagonist) for the treatment of their newly diagnosed metastatic disease prior to enrollment are not eligible for this study. * Patients who are currently being treated with strong CYP3A4 inhibitors (e.g., amprenavir, fosamprenavir, indinavir, itraconazole, ketoconazole, lopinavir, mibefradil, miconazole, nefazodone, nelfinavir, posaconazole, ritonavir, saquinavir, telaprevir, telithromycin, verapamil, voriconazole, and grapefruit) or strong inducers (e.g., carbamazepine, felbamate, nevirapine, phenobarbital, phenytoin, primidone, rifabutin, rifampin, rifapentine and St. John's wort) must either discontinue these drugs or are ineligible. * Patients must refrain from the use of proton pump inhibitors. If needed, alternative antacid therapies may be used including H2-receptor antagonists, and locally acting antacids. * Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure (New York Heart Association Class III and IV heart failure), unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Patients with a "currently active" second malignancy other than non-melanoma skin cancers are not eligible. Patients are not considered to have a "currently active" malignancy if they have completed all therapy and are now considered without evidence of disease for 1 year. * HIV-positive patients on combination antiretroviral therapy are ineligible .