Inclusion Criteria:
* Diagnosis of one of the following:
* Previously untreated Ph-positive ALL \[either t(9;22) and/or bcr-abl positive\] (includes patients initiated on first course of hyper-CVAD before cytogenetics known) or with lymphoid accelerated or blast phase chronic myelogenous leukemia (CML)
* Previously treated Ph-positive ALL or CML (in accelerated phase or blast phase), after 1-2 courses of chemotherapy with or without other tyrosine kinase inhibitors (TKIs)
* If they achieved complete response (CR), they are assessable only for event-free and overall survival, or
* If they failed to achieve CR, they are assessable for CR, event-free, and overall survival
* Performance status ≤ 2 (Eastern Cooperative Oncology Group \[ECOG\] scale, Appendix E)
* Adequate liver function as defined by the following criteria:
* Total serum bilirubin ≤ 1.5 x upper limit of normal (ULN), unless due to Gilbert's syndrome
* Alanine aminotransferase (ALT) ≤ 2 x ULN
* Aspartate aminotransferase (AST) ≤ 2.5 x ULN
* Adequate pancreatic function as defined by the following criteria:
* Serum lipase and amylase ≤ 1.5 x ULN
* For females of childbearing potential, a negative pregnancy test must be documented prior to randomization
* Female and male patients who are fertile must agree to use an effective form of contraception with their sexual partners from randomization through 4 months after the end of treatment
* Adequate cardiac function as assessed clinically by history and physical examination
* Signed informed consent
Exclusion Criteria:
* Active serious infection not controlled by oral or intravenous antibiotics
* History of acute pancreatitis within 1 year of study or history of chronic pancreatitis
* History of alcohol abuse
* Uncontrolled hypertriglyceridemia (triglycerides \> 450 mg/dL)
* Active secondary malignancy other than skin cancer (e.g., basal cell carcinoma or squamous cell carcinoma) that in the investigator's opinion will shorten survival to less than 1 year
* Active grade III-V cardiac failure as defined by the New York Heart Association criteria
* Clinically significant, uncontrolled, or active cardiovascular disease, specifically including, but not restricted to:
* Any history of myocardial infarction (MI), stroke, or revascularization
* Unstable angina or transient ischemic attack prior to enrollment
* Congestive heart failure prior to enrollment, or left ventricular ejection fraction (LVEF) less than lower limit of normal per local institutional standards prior to enrollment
* Diagnosed or suspected congenital long QT syndrome
* Any history of clinically significant atrial or ventricular arrhythmias (such as atrial fibrillation, ventricular tachycardia, ventricular fibrillation, or torsades de pointes) as determined by the treating physician
* Prolonged corrected QT (QTc) interval on pre-entry electrocardiogram (\> 470 msec) unless corrected after electrolyte replacement
* Any history of venous thromboembolism including deep venous thrombosis or pulmonary embolism
* Uncontrolled hypertension (diastolic blood pressure \> 90 mmHg; systolic \> 140 mmHg); patients with hypertension should be under treatment on study entry to effect blood pressure control
* Patients currently taking drugs that are generally accepted to have a risk of causing torsades de pointes (unless these can be changed to acceptable alternatives)
* Taking any medications or herbal supplements that are known to be strong inhibitors of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) within at least 14 days before the first dose of ponatinib
* Prior history of treatment with ponatinibfor \> 1 month; patient who has been treated with ponatinib for 1 month prior starting the treatment is eligible
* Treatment with any investigational antileukemic agents or chemotherapy agents in the last 7 days before study entry, unless full recovery from side effects has occurred or patient has rapidly progressive disease judged to be life-threatening by the investigator; patient who has been treated with ponatinib for 1 month prior starting the treatment is eligible
* Pregnant and lactating women will not be eligible; women of childbearing potential should have a negative pregnancy test prior to entering on the study and be willing to practice methods of contraception; women do not have childbearing potential if they have had a hysterectomy or are postmenopausal without menses for 12 months; in addition, men enrolled on this study should understand the risks to any sexual partner of childbearing potential and should practice an effective method of birth control
* History of significant bleeding disorder unrelated to cancer, including:
* Diagnosed congenital bleeding disorders (e.g., von Willebrand's disease)
* Diagnosed acquired bleeding disorder within one year (e.g., acquired anti-factor VIII antibodies)
* Patients with documented significant pleural or pericardial effusions unless they are thought to be secondary to their leukemia
