A Study of Docetaxel + ARN-509 in Castration-Resistant Prostate Cancer

Inclusion Criteria: * Histologically confirmed adenocarcinoma of the prostate * Castration-resistant prostate cancer requires the following criteria: * A castrate level of testosterone (\< 50ng/dL) * Prostate cancer progression on or since last treatment as documented by PSA rise or bone progression according to PCWG2 or soft tissue radiographic progression according to RECIST criteria Version 1.1 * If on anti-androgen, will need to show no PSA decline after at least a 6 week withdrawal period from the last dose of bicalutamide or nilutamide or 4 weeks from last flutamide dose * Will require a 2 week washout period from last dose of ketoconazole, abiraterone acetate or radiation * Treatment with abiraterone acetate for CRPC in the past is required. Does not need to be the last treatment prior to enrollment. * There is no limit to number of prior therapies * Metastatic disease by bone scan or other nodal or visceral lesions on CT or MRI * Age ≥ 18 years * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 (See Appendix A) * Adequate organ function as evaluated by the following laboratory criteria: * Hemoglobin ≥ 9g/dL; no transfusions and erythropoietin supplementation permitted within the last 3 months * Absolute neutrophil count (ANC) ≥ 1500/µL * Platelet count ≥ 100 x 10\^9/L * Total bilirubin ≤ upper limit of normal (ULN, Note: In subjects with Gilbert's syndrome, if total bilirubin is ≥ 1.5 × ULN, measure direct and indirect bilirubin and if direct bilirubin is ≤ ULN, subject may be eligible) * AST and ALT \< 2.5 x ULN or \< 5x the ULN if liver metastasis * Serum creatinine \< 2.0 × ULN or creatinine clearance \> 30cc/min * Serum albumin ≥ 3.0 g/dL * Serum potassium ≥ 3.5 mmol/L (if \< 3.5, can be repleted and reassess for eligibility as long as stable off potassium supplementation for \> 48 hrs) * Ability to swallow the study drug as a whole tablet * The effects of apalutamide and docetaxel on the developing human fetus are unknown. For this reason and because chemotherapeutic agents are known to be teratogenic, men must agree to use adequate contraception. Specifically, they must agree 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 agree 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. They must also agree not to donate sperm during the study and for 3 months after receiving the last dose of study drug. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Pathology consistent with majority of specimen having small cell carcinoma of the prostate (prostate cancer with neuroendocrine features is acceptable). * Prior treatment with enzalutamide for CPRC; non-CRPC use allowed (e.g., neoadjuvant, combined with radiation for localized disease and didn't progress while on it in those settings) * Prior treatment with docetaxel chemotherapy except if \> 12 months since it was given in either the neoadjuvant or adjuvant setting or for hormone sensitive disease (e.g., CHAARTED population) * Presence of untreated brain metastasis * Seizure or known condition that may pre-dispose to seizure (including but not limited to prior stroke, transient ischemic attack within 1 year prior to randomization, brain arteriovenous malformation; or intracranial masses such as schwannomas and meningiomas that are causing edema or mass effect). Loss of consciousness within 12 months may be permitted upon discussion with study PI. * Medications known to lower the seizure threshold must be discontinued or substituted at least 4 weeks prior to study entry. * Current, recent (within 4 weeks of the first dose of this study), or planned participation in an experimental drug study * Persistent grade \> 1 (NCI CTCAE v4.0) AEs due to investigational drugs that were administered more than 14 days before study enrollment. * Radiation within 2 weeks prior to entering the study * Peripheral neuropathy ≥ Grade 2. * Current evidence of any of the following: * Uncontrolled hypertension * Gastrointestinal disorder affecting absorption * Active infection (e.g., human immunodeficiency virus \[HIV\] or viral hepatitis) or other medical condition that would make prednisone/prednisolone (corticosteroid) use contraindicated * Uncontrolled intercurrent illness including, but not limited to, severe or unstable angina, myocardial infarction, symptomatic congestive heart failure (defined as New York Heart Association Grade II or greater), arterial or venous thromboembolic events (e.g., pulmonary embolism), or clinically significant ventricular arrhythmias, significant vascular disease (e.g. aortic aneurysm, aortic dissection), or symptomatic peripheral vascular disease within 6 months prior to randomization. * Psychiatric illness/social situations that would limit compliance with study requirements. * Any condition that in the opinion of the investigator, would preclude participation in this study * History of allergic reactions or severe hypersensitivity reactions to drugs formulated with polysorbate 80 or antisense oligonucleotides. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to apalutamide or docetaxel * Participants receiving any medications or substances that are strong inhibitors or inducers of CYP3A4 are ineligible. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated list such as http://medicine.iupui.edu/clinpharm/ddis/table.aspx; medical reference texts such as the Physicians' Desk Reference may also provide this information. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product. * Inability to comply with study and/or follow-up procedures