A Phase 2 and Pharmacodynamic Study of Sitagliptin in Patients With Progressive Grade 4 Gliomas

Inclusion Criteria: 1. Participants must have histologically or cytologically confirmed WHO grade 4 glioma (including tumors with molecularly defined grade 4 astrocytoma) for whom a clinically-indicated tumor resection is planned. 2. Participants must not have received sitagliptin or other gliptins. 3. Participants must, in the opinion of the investigator be able to tolerate a pre-operative dexamethasone dose of 4 mg/d or the equivalent dose of an alternate glucocorticoid. 4. Age \>18 years 5. Karnofsky performance status ≥ 60% 6. Participants must have adequate organ function and laboratory parameters within 21 days of study entry as defined below: * Hemoglobin ≥ 9 g/dl * Absolute neutrophil count ≥ 1,500/mcL * Platelet count ≥ 100,000/mcL * Total bilirubin \< 1.5x institutional upper limit of normal (ULN) * AST (SGOT) ≤ 3x institutional ULN * ALT (SGPT) ≤ 3x institutional ULN * Calculated creatinine clearance \> 50 mL/min or creatinine \< 1.5x institutional upper limit of normal (ULN) * Prothrombin time/international normalized ratio (PT/INR) \< 1.4 for participants not on warfarin. 7. Participants on full-dose anticoagulants (e.g., warfarin or LMW heparin) must meet both of the following criteria: * No active bleeding or pathological condition that carries a high risk of bleeding (e.g., tumor involving major vessels or known varices) * In-range INR (between 2 and 3) on a stable dose of oral anticoagulant or on a stable dose of low molecular weight heparin. 8. Women of childbearing potential must have a negative pregnancy test within 21 days of study entry. Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and through 30 days after the last dose of study drug. Should a woman become pregnant or suspect she is pregnant while taking part in this study, she should inform her treating physician immediately. Men of reproductive potential treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and through 30 days after the last dose of study drug. 9. Participants must be able to swallow whole tablets. 10. Participants must have the following minimum intervals from prior treatments: * surgery - 4 weeks * nitrosoureas - 6 weeks * cytotoxic chemotherapy - standard intervals depending on the most recent regimen. E.g., for temozolomide 23 days after most recent dose. * For drugs not listed, the research nurse, treating investigator, and principal investigator will decide on the appropriate interval. * Investigational therapy or non-cytotoxic therapy - 2 weeks. * For bevacizumab - 4 weeks from expected date of protocol surgery 11. Participants positive for human immunodeficiency virus (HIV) are allowed on study (note: HIV testing is not required), but HIV-positive participants must have: * An undetectable viral load within 6 months of registration. * A stable regimen of highly active anti-retroviral therapy (HAART) * No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections 12. For participants with a history of hepatitis C virus (HCV) infection must have been treated and cured. For participants with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load Note: Known positive test for HCV ribonucleic acid (HCV RNA) indicating acute or chronic infection would make the patient ineligible unless the viral load becomes undetectable on suppressive therapy. 13. For participants with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. Note: A known positive test for HBV surface antigen (HBV sAg) indicating acute or chronic infection would make the patient ineligible unless the viral load becomes undetectable on suppressive therapy. Participants who are immune to hepatitis B (anti-Hepatitis B surface antibody positive) are eligible (e.g., participants immunized against hepatitis B) 14. Patient must be deemed by investigator to be a candidate for post-operative chemotherapy. 15. Participants must have the ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: 16. Prior treatment toxicities not resolved to ≤ Grade 1 according to NCI CTCAE Version 5.0 except alopecia and neuropathy. 17. Participants receiving any other investigational agents. 18. History of allergic reactions attributed to compounds of similar chemical or biologic composition to sitagliptin. 19. Participants with uncontrolled diabetes mellitus 20. Participants who require insulin therapy or a sulfonylurea 21. Participants with documented history of hypoglycemia requiring medical intervention or who in the opinion of the investigator are not suitable to receive sitagliptin. 22. Participants with 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. 23. Other prior or concurrent malignancy whose natural history or treatment has the potential to interfere with the safety or efficacy assessment of the investigational regimen are excluded. Otherwise, participants with prior or concurrent malignancy are eligible. 24. Significant chronic gastrointestinal disorder with diarrhea as a major symptom (e.g., Crohn's disease, malabsorption, or Grade ≥2 diarrhea of any etiology at screening) (National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events Version 5.0 \[CTCAE v.5.0\]). 25. Pregnant or breastfeeding. 26. Unable or unwilling to swallow tablets. 27. Evidence of significant medical illness, abnormal laboratory finding, or psychiatric illness/social situations that would, in the investigator's judgment, make the patient inappropriate for this study.