Cabazitaxel With or Without Carboplatin in Treating Patients With Previously Treated Metastatic Castration-Resistant Prostate Cancer

Inclusion Criteria

• Histologic evidence of prostate adenocarcinoma
• In addition to patients with adenocarcinoma, patients with "anaplastic" features are also eligible as defined by at least one of the following: a) histologic evidence of small cell prostate cancer (patients with small cell carcinoma on histology are not required to demonstrate castration-resistant progression); b) any of the following metastatic presentations: (i) exclusive visceral metastases; (ii) radiographically predominant lytic bone metastases identified by plain X-ray or computed tomography (CT) scan; (iii) bulky (>= 5 cm in longest dimension) lymphadenopathy (iv) bulky (>= 5 cm) tumor mass in the prostate/pelvis (v) low PSA (= = 20) bone metastases; (vi) elevated serum lactate dehydrogenase (LDH) (>= 2 x ULN) or elevated serum carcinoembryonic antigen (CEA) (>= 2 x upper limit of normal [ULN]) in the absence of other etiologies; (vii) short interval (= = 1.5 cm in diameter
• Patients may have received prior treatment with androgen ablative therapies (such as bicalutamide, ketoconazole, diethylstilbestrol [DES], abiraterone, Xtandi, ARN-509) and/or "targeted" therapies (such as tyrosine kinase inhibitors); androgen ablative therapies must be discontinued >= 3 days prior to initiation of study treatment with the exception of abiraterone and/or enzalutamide, which may be continued during study treatment per the practice preference of the treating physician; patients who are predicted to benefit from an antiandrogen withdrawal response should be tested for this possibility before being considered for eligibility to this study; targeted therapies must be discontinued >= 2 weeks before initiation of study treatment
• Both chemotherapy-naive and patients previously treated with chemotherapy are eligible; chemotherapy pretreated patients may have received a maximum of two prior systemic cytotoxic chemotherapies completed at least 3 weeks prior to initiation of study treatment
• Patients must have documented evidence of progressive disease as defined by any of the following: a) PSA progression: minimum of 2 rising values (3 measurements) obtained a minimum of 7 days apart with the last result being at least >= 2.0 ng/mL; b) new or increasing non-bone disease (by Response Evaluation Criteria In Solid Tumors [RECIST]); c) positive bone scan with 2 or more new lesions (Prostate Cancer Working Group [PCWG2])
• For purposes of stratification, patients will be categorized as "responders" or "non-responders" based on their response to prior docetaxel-based therapy; a) responders will have demonstrated objective responses to first-line docetaxel as determined by any of the following: 1. decrease in PSA level >= 50% from baseline, maintained for >= 6 weeks; 2. partial or complete response in lymph nodes and soft tissue metastases by RECIST; responders must have received >= 225 mg/m^2 (~ 3 cycles) of docetaxel; b) patients not meeting response criteria above will be considered as non-responders; we anticipate 2 general categories of non-responders based on the following disease phenotypes: 1. progressive disease on therapy without any objective evidence of response ("primary-resistant disease"); progressive disease on therapy with prior objective evidence of response, but response duration is = = 1,500/ml (unless due to bone marrow infiltration by tumor in which case ANC >= 500/ml are allowed) (within 14 days before registration)
• Platelets >= 100, 000/ml (unless due to bone marrow infiltration by tumor in which case >= 50,000/ml are allowed) (within 14 days before registration)
• Total bilirubin = = 30 ml/min using the Cockcroft-Gault equation (within 14 days before registration)
• Men whose partner is a woman of childbearing potential must be willing to consent to using effective contraception while on treatment and for at least 3 months thereafter
• Patient or his legally authorized representative must provide written informed consent
• Eastern Cooperative Oncolog