The goal of this clinical research study is to learn if eltrombopag can help to improve platelet counts in patients with low platelets after they have had a stem cell transplant. The safety of this drug will also be studied.

The Study Drug:

Platelets are cells that help the blood clot. Platelet counts are often lower after receiving a stem cell transplant. When the number of platelets in your body gets too low, it can cause bleeding. Eltrombopag is designed to imitate a protein in your body that helps make platelets. This may help your platelet counts stay normal.

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 study groups:

• If you are in Group 1, you will receive eltrombopag.
• If you are in Group 2, you will receive a placebo. A placebo is a substance that looks like the study drug but has no active ingredients.

If you are 1 of the first 20 participants enrolled in this study, you will have an equal chance of being assigned to either group. If you join the study after 20 participants have been enrolled, you will have a better chance of being assigned to Group 1 if eltrombopag has been shown to be more effective.

Neither you nor the study staff will know if you are receiving the study drug or the placebo. However, if needed for your safety, the study staff will be able to find out what you are receiving.

Study Drug Administration:

You will take the study drug/placebo pills by mouth 1 time each day while you are on study. The study drug/placebo should be taken on an empty stomach (1 hour before or 2 hours after food/drink). You may drink water, coffee, and/or tea with the study drug/placebo. You should drink any coffee or tea without milk or cream.

The dose of study drug/placebo may be adjusted (raised or lowered) throughout the study based on your reaction to the study drug/placebo.

Study Visits:

Every 2 weeks, the following tests and procedures will be performed:

• You will have a physical exam, including measurement of your weight and vital signs.
• You will be asked about any side effects you may have had.
• Blood (about 2 tablespoons) will be drawn for routine tests.
• Blood (about 1 teaspoon) will be drawn for PK testing.
• Blood (about 1 tablespoon) will be drawn to check your immune system.

If your blood tests show that you may have fiber deposits (build-up) in the bone marrow, you will have a bone marrow biopsy to check the status of the disease

If you have symptoms of cataracts (clouding of the lens of the eye) anytime during the study, you will have an eye exam.

Length of Study:

You will take the study drug for up to 8 weeks. You will have study visits for 12 weeks. You will be taken off study if you have intolerable side effects.

End-of-Treatment Visit:

After completion of study drug, you will have the following tests and procedures performed:

• You will have a physical exam, including measurement of your weight and vital signs.
• You will be asked about any side effects you may have had.
• Blood (about 3 tablespoons) will be drawn for routine tests.
• Blood (about 1 tablespoon) will be drawn to check your blood's clotting ability.
• Blood (about 1 tablespoon) will be drawn to check your immune system.

Weeks 10 and 12 (+/- 3 days), you will have the following tests and procedures performed:

• You will have a telephone interview.
• You will be asked about any side effects you may have had.
• Blood (about 3 tablespoons) will be drawn for routine tests.
• Blood (about 1 tablespoon) will be drawn to check your blood's clotting ability.
• You will either have blood drawn locally or where you live regionally.

Within the 3 months after your last dose of study drug, you will have a bone marrow biopsy to check the status of the disease and an eye exam. The eye exam may be performed sooner if you develop symptoms of a cataract, such as blurry vision.

This is an investigational study. Eltrombopag is FDA approved and commercially available for the treatment of low platelet counts in patients with idiopathic thrombocytopenic purpura (ITP -- a severe bleeding disease). Its use in patients with low platelet counts after a stem cell transplant is investigational.

Up to 64 patients will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Patients >/= 35 days post HCT with Platelet count </= 20 x 10^9/l sustained for 7 days or patients are platelet transfusion dependent, and
2. Neutrophil count >/= 1.5 x 10^9/l anytime within the last seven days before enrollment. Patients can be on myeloid or erythroid growth factors for example filgrastim), and
3. Age >/= 18

Exclusion Criteria:

1. Recurrence or progression of primary malignancy after HCT
2. ALT >/= 2.5 times the ULN
3. Serum bilirubin >2mg/dl (unless due to Gilbert's syndrome)
4. Documented deep vein thrombosis within 1 year before enrollment on the study, except if upper arm thrombosis related to central venous catheters, within 3 months before enrollment on the study.
5. ECOG Performance status >2
6. Pregnancy: Women of child-bearing potential and men must agree to use contraception prior to study entry and for the duration of study participation. A woman of child-bearing potential is defined as a woman who has not been naturally post-menopausal for at least 12 consecutive months or with no previous surgical sterilization. A negative pregnancy test result will be required before any study drug is given.

Through study completion, average of 12 weeks