Sorafenib With or Without Paclitaxel and Carboplatin in Treating Patients With Recurrent Ovarian Cancer, Primary Peritoneal Cancer, or Fallopian Tube Cancer

Inclusion Criteria:

Diagnosis of ovarian epithelial, primary peritoneal, or fallopian tube cancer
Recurrent disease
Must have received a prior platinum-based regimen
Platinum-sensitive (treatment-free interval > 6 months)
No more than 2 prior chemotherapy regimens
Measurable disease
At least 1 unidimensionally measurable lesion >= 20 mm by conventional techniques OR >= 10 mm by spiral CT scan
Not in a prior irradiation field
No known brain metastases

Performance status:

ECOG 0-2 OR
Karnofsky 80-100%

Life expectancy:

More than 12 weeks

Hematopoietic:

Absolute neutrophil count >= 1,500/mm3
Platelet count >= 100,000/mm3
Hemoglobin >= 9 g/dL
No bleeding diathesis

Hepatic:

Bilirubin < 1.5 times upper limit of normal (ULN)
AST or ALT =< 2 times ULN
No history of allergic reaction attributed to compounds of similar chemical or biological composition to sorafenib or other agents used in the study
Patients who have had a reaction to a taxane or a platinum and have not yet been rechallenged may undergo a desensitization regimen on study
No hypersensitivity to paclitaxel or drugs using the vehicle Cremophor El:
Prior hypersensitivity reaction to paclitaxel allowed provided rechallenged successfully

Renal:

Creatinine < 2 mg/dL

Cardiovascular:

Abnormal cardiac conduction (e.g., bundle branch block or heart block) allowed if stable for the past 6 months
No symptomatic congestive heart failure
No uncontrolled hypertension
No cardiac arrhythmia
No unstable angina pectoris;
No myocardial infarction within the past 6 months
Negative pregnancy test
Fertile patients must use effective contraception
Adequate intestinal function
No concurrent requirements for IV hydration or nutritional support
No active or ongoing infection
No psychiatric illness or social situation that would preclude study compliance
No other concurrent uncontrolled illness
No other invasive malignancy with the past 5 years except nonmelanoma skin cancer
More than 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin) and recovered
More than 3 weeks since prior hormonal therapy
More than 4 weeks since prior radiotherapy and recovered
No prior sorafenib
No prior anticancer therapy that contraindicates study therapy
No concurrent cytochrome P450 enzyme-inducing antiepileptic drugs (phenytoin, carbamazepine, or phenobarbital), rifampin, or Hypericum perforatum (St. John's wort)
No concurrent combination antiretroviral therapy for HIV-positive patients
No concurrent therapeutic anticoagulation therapy
Concurrent prophylactic low-dose warfarin allowed for maintenance of venous or arterial access devices
No other concurrent anticancer therapies
No other concurrent investigational agents
Not pregnant or nursing