Therapeutic Control of Aspirin-Exacerbated Respiratory Disease (Aspirin)

Inclusion Criteria for Participants with AERD: * History of physician-diagnosed asthma * History of nasal polyposis * History of at least one clinical reaction to oral aspirin or other nonselective COX inhibitor with features of both lower (cough, chest tightness, wheezing, dyspnea) and upper (rhinorrhea, sneezing, nasal obstruction, conjunctival itching and discharge) airway involvement. * Stable asthma (post-bronchodilator FEV1 of 70% or better, no increase in baseline dose of oral glucocorticoids for at least 3 months, and no history of hospitalization or emergency room visits for asthma for at least the prior 6 months). * No current smoking, defined as no daily tobacco smoking for at least 6 months and not more than one instance of tobacco smoking in the last 3 months. * Non-pregnant * Only those individuals who would otherwise meet clinical qualifications for aspirin desensitization and treatment with high-dose aspirin will be considered for enrollment in the study. Inclusion Criteria for Participants who are Aspirin Tolerant Asthmatics: * History of physician-diagnosed asthma. * No current nasal polyposis confirmed by nasal examination. * No history of any adverse reaction to aspirin or a COX inhibitor. * Stable asthma (post-bronchodilator FEV1 of 70% or better, no increase in baseline dose of oral glucocorticoids for at least 3 months, and no history of hospitalization or emergency room visits for asthma for at least the prior 6 months). * No current smoking * Non-pregnant Inclusion Criteria for Non Asthmatics with Allergic Rhinitis: * No history of physician-diagnosed asthma. * No current nasal polyposis confirmed by nasal examination. * No history of any adverse reaction to aspirin or a COX inhibitor. * No current smoking * Non-pregnant * Clinical history of symptoms consistent with allergic rhinitis and previously documented allergy to at least one environmental,immunoglobulin E (IgE) testing). * Normal lung function (baseline FEV1 of 80% of predicted or better). * A score of 4 or below on the Asthma Screening Questionnaire (33) and negative responses to asthma history questions Exclusion Criteria for participants with AERD: * Current breastfeeding * History of bleeding diathesis or current use of anticoagulant or antiplatelet drugs * Hypersensitivity to montelukast or thienopyridines * History of peptic ulcer disease or gastrointestinal bleed * Current severe gastro-esophageal reflux disease (GERD), defined as patient currently requiring more than 2 total doses of medication per day to treat persistent symptoms: either more than 2 doses of any single medication type (antacid, proton pump inhibitor, or H2 receptor antagonist), or more than 2 types of medication per day to treat symptoms * History of systemic or life-threatening respiratory reaction to aspirin requiring intubation or administration of adrenalin * Current use of any oral beta blocker (due to the risk of bronchospasm associated with beta blockers). * History of transient ischemic attack or stroke, or diabetes. * Current presence of uncontrolled hypertension. * History of hepatic impairment or alcoholism, or evidence of abnormal liver function at Screening Visit. Aspartate transaminase (AST) and alanine transaminase (ALT) levels may not exceed 1.5x the upper limit of normal at Screening Visit (AST may not exceed 52 IU/L, ALT may not exceed 78 IU/L). Exclusion Criteria for Participants with Aspirin Tolerant Asthma and Non Asthmatics with Allergic Rhinitis: * Current breastfeeding * History of bleeding diathesis or current use of anticoagulant or antiplatelet drugs * Hypersensitivity to montelukast or thienopyridines * History of peptic ulcer disease or gastrointestinal bleed * Current severe GERD * Current use of any oral beta blocker.