Glioblastoma, also known as glioblastoma multiforme (GBM), is an extremely fast-growing and lethal form of brain cancer. Tumor recurrence in GBM is often attributed to acquired resistance to the standard chemotherapeutic agent temozolomide (TMZ). Promoter methylation of the DNA repair gene MGMT has been associated with sensitivity to TMZ, while increased expression of MGMT has been associated with TMZ resistance. Clinical studies have observed a downward shift in MGMT methylation percentage from primary to recurrent stage tumors. However, the evolutionary processes driving this shift are still poorly understood. In this talk we develop a branching process model, parameterized using clinical and experimental data, to investigate the role of MGMT methylation in TMZ resistance during the standard treatment regimen for GBM. We explore possible explanations for the observed methylation shift during treatment, and we study the optimal number of TMZ doses per adjuvant cycle for GBM patients with high and low levels of MGMT methylation at diagnosis.