The purpose of the study is to propose that roflumilast is associated with meaningful reductions in biomarkers of pulmonary inflammation and sputum neutrophilia, including confirmation of previously described results, and correlate these findings with improvement in pulmonary function, sputum scores, and quality of life in stable moderate to severe COPD. The investigators aim to demonstrate this regardless of concomitant medication use, including inhaled corticosteroids. Additionally, the investigators hope to provide a mechanistic pathway by which these effects occur.