Docetaxel and PROSTVAC for Metastatic Castration-Sensitive Prostate Cancer

* INCLUSION CRITERIA:
* Documented histopathological confirmation of prostate cancer-from a Clinical Laboratory Improvement Amendments (CLIA) certified laboratory.
* Patients must have metastatic disease, defined as at least one lesion on bone scan or at least one lesion that are measurable per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. (Patients who have metastatic disease by these criteria prior to ADT, but then have changes after androgen deprivation therapy (ADT) that diminish the size of these lesions or changes on bone scan are still eligible.)
* Patients must have a performance status of 0 to 2 according to the Eastern Cooperative Oncology Group (ECOG) criteria
* Patients must have adequate bone marrow, hepatic, and renal function with:

  * Absolute neutrophil count (ANC) greater than or equal to 1500/microL, without cerebrospinal fluid (CSF) support
  * Platelets greater than or equal to 100,000/microL
  * Aspartate aminotransferase (AST)/Serum glutamic-oxaloacetic transaminase (SGOT) less than or equal to 2.5 times upper limit of normal (ULN);
  * Alanine aminotransferase (ALT)/Serum glutamic-pyruvic transaminase (SGPT) less than or equal to 2.5 times upper limit of normal (ULN);
  * Total serum bilirubin less than or equal to 1.5 times upper limit of normal (ULN), OR in patients with Gilbert's syndrome, a total bilirubin less than or equal to 3.0)
  * Serum albumin greater than or equal to 2.8 g/dL
  * Lipase \< 2.0 times the upper limit of normal and no radiologic or clinical evidence of pancreatitis
  * Creatinine less than or equal to 1.5 times institutional upper limits of normal

OR

Creatinine clearance of greater than or equal to 50 ml/min/1.73 m(2) for patients with creatinine levels above institutional normal by 24-hour urine.

* Willing to travel to the National Institutes of Health (NIH) for follow-up visits
* 18 years of age or older.
* Able to understand and sign informed consent.
* May have had up to 24 months of ADT (testosterone suppression therapy in the nonmetastatic setting) and are at least 12 months removed from treatment
* Men treated or enrolled on this protocol must also agree to use adequate contraception, prior to the study, for the duration of study participation, and 4 months after completion. Sexually active subjects and their female partners must agree to use medically accepted barrier methods of contraception (e.g., male or female condom) during the course of the study and for 4 months after the last dose of study drug(s), even if oral contraceptives are also used. All subjects of reproductive potential must also agree to use both a barrier method and a second method of birth control during the course on the study and for 4 months after the last dose of study drug(s). Should a woman become pregnant or suspect she is pregnant while her partner is participating in this study, she should inform her treating physician immediately.
* Must have started ADT for metastatic disease within 134 days (for Arm A and B) or within 28 days (for Arm C).

EXCLUSION CRITERIA:

* Immunocompromised status due to:

  * Human immunodeficiency virus (HIV) positivity.
  * Active autoimmune diseases such as Addison's disease, Hashimoto's thyroiditis, systemic lupus erythematosus, Sjogren's syndrome, scleroderma, myasthenia gravis, Goodpasture syndrome or active Grave's disease. Patients with a history of autoimmunity that has not required systemic immunosuppressive therapy or does not threaten vital organ function including central nervous system (CNS), heart, lungs, kidneys, skin, and gastrointestinal (GI) tract will be allowed.
  * Other immunodeficiency diseases
* Chronic administration (defined as daily or every other day for continued use \> 14 days) of corticosteroids deemed systemic by investigator within 28 days before the first planned dose of PROSTVAC. Use of inhaled steroids, nasal sprays, and topical creams for small body areas is allowed.
* Evidence of rising prostate-specific antigen (PSA) on ADT
* Serious intercurrent medical illness that, in the judgment of the investigator, would interfere with patient's ability to carry out the treatment program.
* Other medications used for urinary symptoms including 5-alpha reductase inhibitors (finasteride and dutasteride) and alternative medications known to alter PSA (e.g. phytoestrogens and saw palmetto)
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to poxviral vaccines (e.g., vaccinia vaccine)
* Known allergy to eggs, egg products, aminoglycoside antibiotics (for example, gentamicin or tobramycin).
* History of atopic dermatitis or active skin condition (acute, chronic, exfoliative) that disrupts the epidermis
* Previous serious adverse reactions to smallpox vaccination
* Unable to avoid close contact or household contact with the following high-risk individuals for three weeks after the Day 1 vaccination: (a) children less than or equal to 3 years of age, (b) pregnant or nursing women, (c) individuals with prior or concurrent extensive eczema or other eczemoid skin disorders, or (d) immunocompromised individuals, such as those with human immunodeficiency virus (HIV).
* Receipt of an investigational agent within 28 days (or 60 days for an antibody-based therapy) before the first planned dose of study drugs.
* Patients who test positive for hepatitis B virus (HBV) or hepatitis C virus (HCV)
* Uncontrolled hypertension (systolic blood pressure (SBP)\>170/ diastolic blood pressure (DBP)\>105)
* Patients who have had prior chemotherapy for prostate cancer.
* The subject has had evidence within 2 years of the start of study treatment of another malignancy which required systemic treatment (with the exception of nonmelanoma skin cancers or carcinoma in situ of the bladder).
* The subject has active brain metastases or epidural disease.
* Patients with greater than or equal to grade 2 peripheral neuropathy at baseline.
* Patients with history of splenectomy