The purpose of this study is to better understand how to use celecoxib, a popular drug widely used for arthritis, for head and neck cancer patients. Some doctors believe that celecoxib may have helpful effects when used for head and neck cancer. Celecoxib has been shown to prevent some cancers in animals. It has also been used to make standard chemotherapy and radiation work better in both animals and humans. However, all of the previous studies focused on tumors outside the head and neck region. To better understand how to use celecoxib for head and neck cancer patients, doctors at MSKCC are studying the effects of the drug on certain chemicals in the body that are thought to be important for cancer treatment.