Importance: Obstructive sleep apnea has been associated with postoperative delirium, which predisposes patients to major adverse outcomes. Positive airway pressure may be an effective intervention to reduce delirium in this population. Objectives: To determine if preoperative obstructive sleep apnea is associated with postoperative incident delirium in the intensive care unit and if preoperative positive airway pressure adherence modifies the association. Design, Setting, and Participants: A retrospective single-center cohort study was conducted at a US tertiary hospital from November 1, 2012, to August 31, 2016, among 7792 patients admitted to an intensive care unit who underwent routine Confusion Assessment Method for the intensive care unit after major surgery. Patients were adults who had undergone a complete preoperative anesthesia assessment, received general anesthesia, underwent at least 1 delirium assessment, were not delirious preoperatively, and had a preoperative intensive care unit stay of less than 6 days. Statistical analysis was conducted from August 20, 2019, to January 11, 2020. Exposures: Self-reported obstructive sleep apnea, billing diagnosis of obstructive sleep apnea, or STOP-BANG (Snoring, Tiredness, Observed Apnea, Blood Pressure, Body Mass Index, Age, Neck Circumference and Gender) questionnaire score greater than 4, as well as self-reported use of preoperative positive airway pressure. Main Outcomes and Measures: Delirium within 7 days of surgery. Results: A total of 7792 patients (4562 men; mean [SD] age, 59.2 [15.3] years) met inclusion criteria. Diagnosed or likely obstructive sleep apnea occurred in 2044 patients (26%), and delirium occurred in 3637 patients (47%). The proportion of patients with incident delirium was lower among those with obstructive sleep apnea than those without (897 of 2044 [44%] vs 2740 of 5748 [48%]; unadjusted risk difference, -0.04; 99% credible interval [CrI], -0.07 to -0.00). Positive airway pressure adherence had minimal association with delirium (risk difference, -0.00; 99% CrI, -0.09 to 0.09). Doubly robust confounder adjustment eliminated the association between obstructive sleep apnea and delirium (risk difference, -0.01; 99% CrI, -0.04 to 0.03) and did not change that of preoperative positive airway pressure adherence (risk difference, -0.00, 99% CrI, -0.07 to 0.07). The results were consistent across multiple sensitivity analyses. Conclusions and Relevance: After risk adjustment, this study found no association between obstructive sleep apnea and postoperative delirium in the context of usual care in the intensive care unit, with 99% CrIs excluding clinically meaningful associations. With limited precision, no association was found between positive airway pressure adherence and delirium. Selection bias and measurement error limit the validity and generalizability of these observational associations; however, they suggest that interventions targeting sleep apnea and positive airway pressure are unlikely to have a meaningful association with postoperative intensive care unit delirium.