A Study of Romiplostim to Prevent Low Platelet Counts in Children and Young Adults Receiving Chemotherapy for Solid Tumors

Inclusion Criteria: * Documented diagnosis of a primary solid tumor. Patients must have histological verification of malignancy at MSKCC. * Male and female patients aged 1-21 years with a primary solid tumor undergoing treatment with the pre-defined chemotherapy regimens of EFT, MAP, D9803. Prior to enrollment patient could have been undergoing induction therapy with a similarly myelosuppressive regimen as long as they will be continuing with EFT, MAP, D9803 at the time of study enrollment. * Patients undergoing treatment with MAP chemotherapy w ho have had ≥ 1 platelet transfusion during induction stage of treatment. * Total Bilirubin (sum of conjugated + unconjugated) ≤ 3 times institutional upper limit of normal (ULN) for age and ALT/AST ≤ 3 times institutional ULN for age. * Normal cardiac function: * Shortening fraction greater than or equal to 28% by echocardiogram OR Left ventricular ejection fraction (LVEF) greater than or equal to 50% on technetium- 99m pertechnetate radionuclide cineangiography (MUGA) or echocardiogram. * Screening ECG with corrected QT (QTc) interval of \< 470 msec. * Timing of cardiac assessment: We will utilize the most recent EKG/ECHO when assessing cardiac function. See section 9.0 for additional details. * Adequate renal function, defined as an estimated Creatinine Clearance or GFR \>40ml/min or an normal creatine for age (see below) Serum Creatinine by age: Age (years) \<6: Maximum Serum Creatinine (mg/dL), Male 0.8, Female 0.8 Age (years) 6 to \<10: Maximum Serum Creatinine (mg/dL), Male 1, Female 1 Age (years) 10 to \<13: Maximum Serum Creatinine (mg/dL), Male 1.2, Female 1.2 Age (years) 13 to \<16: Maximum Serum Creatinine (mg/dL), Male 1.5, Female 1.4 Age (years) \>16: Maximum Serum Creatinine (mg/dL), Male 1.7, Female 1.4 These threshold creatine values were derived from the Scwartz formula estimating GFR, utilizing child length and statured published by the CDC. Exclusion Criteria: * Patients with history of hematologic malignancies or allogenic/autogenic stem cell transplant. * Patients with a currently known predisposition to a myeloid stem cell disorder, myeloid leukemia, and/or bone marrow failure syndrome including, but not limited to: * Aplastic anemia * Ataxia telangiectasia * Bloom syndrome * Congenital amegakaryocytic thrombocytopenia * Cyclic neutropenia * Diamond Blackfan anemia * Dyskeratosis congenita * Familial AML/MDS syndromes (including ANKRD26, CEBPA, DDX41, ETV6, GATA2, RUNX1, SRP72) * Fanconi anemia * Kostmann disease * Li-Fraumeni syndrome * Neurofibromatosis * Nijmegen breakage syndrome * Noonan syndrome * Paroxysmal nocturnal hemoglobinuria * Pearson syndrome * Poland syndrome * Rothmund-Thomson syndrome * Severe congenital neutropenia * Thrombocytopenia absent radii syndrome * Trisomy 8 * Trisomy 21 * WHIM syndrome * Wiskott Aldrich syndrome * Xeroderma pigmentosa * Secondary malignancy in the past 5 years. * Patients who have previously undergone up-front chemotherapy and have relapsed or progressed through therapy. * Patients who have received 4 or more cycles of induction chemotherapy for their current malignancy prior to time of enrollment. * Previous use of romiplostim, eltrombopag, recombinant human TPO, or any other TPO receptor agonist, or any investigational platelet producing agent. * Patients receiving other investigational agents are not eligible for study entry. History of uncontrolled arrhythmias, clinically significant electrocardiogram (ECG) abnormalities, active heart failure or pericardial disease. * Patients with current or prior venous thrombotic event or arterial thrombotic event at time of enrollment will be ineligible for this study. * Pregnant women/lactating mothers. * Patients unwilling to use effective contraception method, which includes abstinence. * Patients with an inability to return for follow-up visits or obtain follow-up studies required to assess toxicity to therapy.