Osimertinib and Gefitinib in EGFR Inhibitor naïve Advanced EGFR Mutant Lung Cancer

This research study is a Phase I clinical trial, which tests the safety of investigational drugs and also tries to define the appropriate dose of the investigational drugs to use for further studies. "Investigational" means that the drugs are being studied. The FDA (the U.S. Food and Drug Administration) has approved gefitinib and osimertinib as separate treatment options for this disease. The FDA has not approved the combination of these study drugs as a treatment option for this disease.Recently, the FDA approved osimertinib as a first-line treatment for patients that have NSCLC with an EGFR mutation, that have not received prior treatment for their disease. In this research study, the investigators are evaluating the combination of gefitinib and osimertinib in patients who have just been diagnosed with non-small cell lung cancer containing a mutation in the epidermal growth factor receptor (EGFR) gene. Normally, cells in the body divide in an orderly way. However, in cancer cells, this normal process of cell division becomes abnormal and allows the cancer cells to grow in a rapid, unregulated way. In some patients with lung cancer, this abnormal and rapid growth in the cancer cells is drive by a specific change in a gene called the Epidermal Growth Factor Receptor (EGFR). This change in the EGFR gene in cancer cells is called a mutation. Patients with lung cancer harboring a mutation in EGFR can be treated with specific drugs called EGFR inhibitors. However, even though these drugs can be very effective, after a period of time, most EGFR tumors will develop resistance to this treatment, most often because of a second mutation in EGFR called T790M. Right now, patients with newly diagnosed lung cancer with an EGFR mutation would be treated with a single EGFR inhibitor. A drug like gefitinib is a standard first treatment for patients with this kind of lung cancer. Osimertinib is currently approved only to treat patients whose cancers develop resistance to gefitinib (or other similar EGFR inhibitors) because of the T790M mutation. However, ongoing clinical trials have shown that osimertinib is also effective when used as the first treatment in newly diagnosed patients with lung cancer containing an EGFR mutation. In addition, laboratory studies have shown that combining EGFR inhibitors may help prevent the development of drug resistance. The goal of this particular study is to evaluate two different methods of combining gefitinib and osimertinib in newly diagnosed patients with EGFR mutations: either with both drugs given together on the same day OR an alternating schedule where participants will alternate taking one drug at a time every 4 weeks. This study will help determine the optimal dosing strategy for combining these two drugs in lung cancer patients with EGFR mutations. The study will also follow the clinical response of participants treated with the drug combination to monitor how well and how long this strategy controls the disease.