The purpose of the research is to evaluate a new schedule of alternating cycles of induction chemoimmunotherapy (chemotherapy plus pembrolizumab) and immunotherapy (pembrolizumab) alone for the initial treatment of patients with advanced lung or head and neck cancers.

This study is looking at the effect of alternating combination chemotherapy plus immunotherapy with immunotherapy alone during the induction phase (resulting in less frequent use of chemotherapy, once every six weeks instead of the usual every three weeks during induction) on the ability to fight your tumor. We expect that less frequent exposure to chemotherapy in this setting will control your cancer effectively while preserving your quality of life. The primary endpoint of this three-arm, parallel phase II study is the percentage of patients receiving one, two, three and four (up to six for patients with head and neck cancer) combination chemoimmunotherapy cycles. Along with, overall response rates at six weeks and the best response rate. Additionally, to record the safety and tolerability of therapy.