Sorafenib in Treating Patients With Relapsed or Refractory Acute Myeloid Leukemia, Acute Lymphoblastic Leukemia, or Chronic Myelogenous Leukemia

Inclusion Criteria: Patients must have pathological confirmation (histologically or cytologically) of relapsed or refractory acute myeloid leukemia (other than acute promyelocytic leukemia), acute lymphocytic leukemia, or chronic myeloid leukemia in blast crisis The morphologic diagnosis of AML (non-APL), ALL, and CML in blast crisis will be made independently by members of the hematologic pathology division; routine staining and standard criteria as outlined by the Report of the NCI-Sponsored Workshop will be followed All patients must have been refractory to or relapsed from their most recent therapy AND are considered ineligible for potential curative approaches including allogeneic stem cell transplant; in addition, patients must be at least: 3 weeks from last cytotoxic chemotherapy (excluding hydroxyurea) Hydroxyurea may be used for blast count control but must be discontinued within 48 hours of the initiation of BAY 43-9006 2 weeks from last radiation therapy 3 week from last biologic therapy (including myeloid growth factors) ECOG performance status =< 2 (Karnofsky >= 60%) Life expectancy of greater than 2 months Multilineage bone marrow failure due to the subject's underlying leukemia Total blast count in the peripheral blood < 30,000 Total bilirubin =< 2 mg/dl AST(SGOT)/ALT(SGPT) =< 5 X institutional upper limit of normal Serum creatinine within normal institutional limits OR creatinine clearance >= 60 mL/min/1.73 m^2 for patients with creatinine levels above institutional normal All women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; the effects of BAY 43-9006 on the developing human fetus at the recommended therapeutic dose are unknown; however, kinase inhibitors are known to be teratogenic; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: Patients with APL are not eligible for this clinical trial Patients who have not recovered from adverse events due to agents administered more than 3 weeks earlier Patients with rapidly increasing peripheral blood blast counts (increase in the absolute peripheral blast count > 50% within one week) or uncontrolled (absolute blast count > 30,000) while on hydroxyurea will be excluded Patients with uncontrolled hypertension (i.e., persistent grade 3 while undergoing treatment) Patients may not be actively receiving any other investigational agents Patients active and / or untreated CNS leukemia will not be eligible History of allergic reactions attributed to compounds of similar chemical or biologic composition to BAY 43-9006 Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with BAY 43-9006 Patients with immune deficiency are at increased risk of lethal infections when treated with marrow suppressive therapy; therefore, HIV-positive patients receiving combination anti-retroviral therapy are excluded from the study because of possible pharmacokinetic interactions with BAY 43-9006; appropriate studies will be undertaken in patients receiving combination anti-retroviral therapy when indicated Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements Patients must not have any evidence of bleeding diathesis Patients must not be on therapeutic anticoagulation; prophylactic anticoagulation (i.e. low dose warfarin) of venous or arterial access devices is allowed provided that the requirements for PT, INR or PTT are met Patients must not be taking the cytochrome P450 enzyme-inducing antiepileptic drugs (phenytoin, carbamazepine, or phenobarbital), rifampin or St. John's wort