The goal of this clinical research study is to learn if the combination of azacitidine and vorinostat can help to control AML or MDS better than azacitidine alone. The safety of this drug combination will also be studied.

The Study Drugs:

Azacitidine is designed to block certain genes in cancer cells whose job is to stop the function of the tumor-fighting genes. By blocking the "bad" genes, the tumor-fighting genes may be able to work better.

Vorinostat is designed to cause chemical changes in different groups of proteins that are attached to DNA (the genetic material of cells), which may slow the growth of cancer cells or cause the cancer cells to die.

Study Groups:

If you are found to be eligible to take part in this study, you will be randomly assigned (as in the flip of a coin) to 1 of 2 groups.

• If you are in Group 1, you will receive azacitidine and vorinostat.
• If you are in Group 2, you will receive azacitidine alone.

For the first 40 patients, you will have an equal chance of being in either group. After the first 40 patients, you will have a higher chance of being assigned to a group based on the results from previous participants.

Study Drug Administration:

On Days 1-5 of every cycle, you will receive azacitidine by vein over 15-30 minutes.

If you are in Group 1, you will also take vorinostat by mouth 3 times a day with food on Days 1-5 of every cycle.

If you cannot take vorinostat by mouth during a cycle, you will receive only azacitidine during that cycle. You will begin taking vorinostat by mouth again when you are able.

Your dose of study drugs may be lowered if you experience side effects.

You may receive a drug such as ondansetron before each dose of azacitidine to prevent nausea and vomiting.

If you have diarrhea, you will take a drug such as Imodium (loperamide) to prevent diarrhea.

Study Visits:

Once a week of Cycle 1, the following tests and procedures will be performed:

• Your complete medical history will be recorded.
• You will have a physical exam.
• You will be asked if you have experienced any intolerable side effects.
• Blood (about 1-2 tablespoons) will be drawn for routine tests.

On Day 28 of Cycle 1 (+/- 3 days), you will have bone marrow aspiration to check the status of the disease. To collect a bone marrow aspirate, an area of the hip is numbed with anesthetic, and a small amount of bone marrow is withdrawn through a large needle.

If the doctor thinks it is needed, you will have extra bone marrow aspirations during the later cycles to check the status of the disease.

One (1) time each cycle of Cycles 2 and beyond, the following tests and procedures will be performed:

• Your complete medical history will be recorded.
• You will have a physical exam.
• You will be asked if you have experienced any intolerable side effects.
• If the doctor thinks it is needed, blood (about 2 tablespoons) will be drawn for routine tests.

Length of Study:

You will be on active study for up to 12 cycles (about 12-18 months). You will be taken off study if the disease gets worse or you experience intolerable side effects.

This is an investigational study. Vorinostat is FDA approved and commercially available for the treatment of cutaneous T-cell lymphoma. Azacitidine is FDA approved commercially available for the treatment of MDS. The combination of these drugs for use in patients with intermediate-1 or higher risk MDS and AML is investigational.

Up to 80 participants will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Patients with newly diagnosed AML or MDS (Intermediate 1 or higher risk)
2. Patient must have at least one of the following: a. Creatinine >/= 2 mg/dL; b. total Bilirubin >/= 2 mg/dL; c.ECOG Performance Status equal to 3 or 4; and d. is ineligible for participation on a protocol of higher priority
3. Patients must provide written informed consent.
4. Patients must be age > 18 years due to lack of safety information with these agents in children.
5. Patient agrees to: 1) Use 2 adequate methods of contraception to prevent pregnancy (either 2 barrier methods or a barrier method plus a hormonal contraceptive method) or 2) abstain from heterosexual activity throughout the study starting with Visit 1.
6. Female patients of childbearing potential should have a negative pregnancy test (serum) within 72 hrs. of study enrollment.

Exclusion Criteria:

1. Patients must not have the favorable cytogenetic abnormalities of inv (16), t (16;16), t (8;21), or t (15;17).
2. Patients receiving any anti-leukemic therapy with the exception of Hydroxyurea prior to study enrollment. Prior growth factor therapy is acceptable. Hydroxyurea could be used at the discretion of the treating physician. A single or a two day dose of cytarabine (up to 3 g/m^2) for emergency use is allowed as prior therapy.
3. Patient has a prior history of treatment with HDAC inhibitors. Patients who have received valproic acid (VPA) for the treatment of seizures may be enrolled on this study, but must not have received VPA within 30 days of study enrollment.
4. Patient is unable to take and/or tolerate oral medications on a continuous basis, examples include patients on a ventilator, or have altered mental status that precludes safe oral route of administration.
5. Patient has active hepatitis A, B, or C infection.
6. Patient is pregnant or breast-feeding.
7. Patient has a known allergy or hypersensitivity to any component of vorinostat or azacitidine.
8. History of any psychiatric condition that might impair the patient's ability to understand or to comply with the requirements of the study or to provide informed consent.

Adverse event collected when occur within 30 days of discontinuation of dosing or completion of participation in study if the last scheduled visit occurs at a later time. Overall study period: January 2009 to April 2015.

Of the 31 participants enrolled in the phase I portion of this study, 1 participant did not receive treatment; hence only 30 participants were evaluable for serious and other adverse events.