Enzalutamide and Cabazitaxel in Treating Patients With Metastatic, Castration-Resistant Prostate Cancer

PRIMARY OBJECTIVES: I. To determine the safety and tolerability of combination treatment with enzalutamide and cabazitaxel (as determined by percent dose limiting toxicities \[DLT\], where DLT \< 17% is consistent with it being a tolerable combination). II. To determine the efficacy of treatment with the hormonal agent enzalutamide and the chemotherapy cabazitaxel in combination in men with metastatic castration-resistant prostate cancer (CRPC) (as determined by percent of patients achieving \>= 90% prostate specific antigen \[PSA\] declines following initiation of treatment). SECONDARY OBJECTIVES: I. To further define the anticancer effect and safety profile of the combination of enzalutamide and cabazitaxel. Ia. Collect toxicity data (description of adverse events). Ib. Determine PSA response (percent of patients who achieve \>= 50% PSA decline and \>= 30% PSA decline). Ic. Examine pharmacokinetic (PK) data of cabazitaxel to characterize enzalutamide and cabazitaxel pharmacokinetic blood levels. Id. Determine tumor response by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 for measurable disease and Prostate Cancer Working Group 2 criteria for non-measurable (bone) disease. Ie. Determine overall survival. EXPLORATORY OBJECTIVES: I. To determine baseline (and at progression) biological tumor characteristics to evaluate for possible biomarkers indicative or predictive of response: apoptosis by cleaved caspase 3; androgen signaling axis (including but not limited to: androgen receptor expression, androgen receptor splice variants, and intratumoral androgen levels), and glucocorticoid receptor. II. To collect circulating tumor cells (CTCs) and determine the degree to which tumor characteristics (delineated above) are shared by the CTCs. III. To collect plasma and serum pre-treatment and at progression for assessment of circulating micro-ribonucleic acid (RNA)s and other circulating markers. IV. To collect buffy coat to evaluate for steroid transporters. OUTLINE: This is a dose de-escalation study of cabazitaxel. Patients receive cabazitaxel intravenously (IV) over 1 hour on day 1 and enzalutamide orally (PO) once daily (QD) on days 1-21 (days 2-21 of cycle 1). Patients also receive prednisone PO twice daily (BID) as standard of care with cabazitaxel. Cycles repeat every 21 days for 6-10 cycles in the absence of disease progression or unacceptable toxicity. Patients may continue enzalutamide PO QD on days 1-28 in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up at 28 days and then every 6 months for up to 5 years.