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Background Obstructive sleep apnea is underdiagnosed in surgical patients. The cost-effectiveness of obstructive sleep apnea screening is unknown. This study’s objective was to evaluate the cost-effectiveness of preoperative obstructive sleep apnea screening (1) perioperatively and (2) including patients’ remaining lifespans. Methods An individual-level Markov model was constructed to simulate the perioperative period and lifespan of patients undergoing inpatient elective surgery. Costs (2016 Canadian dollars) were calculated from the hospital perspective in a single-payer health system. Remaining model parameters were derived from a structured literature search. Candidate strategies included: (1) no screening; (2) STOP-Bang questionnaire alone; (3) STOP-Bang followed by polysomnography (STOP-Bang + polysomnography); and (4) STOP-Bang followed by portable monitor (STOP-Bang + portable monitor). Screen-positive patients (based on STOP-Bang cutoff of at least 3) received postoperative treatment modifications and expedited definitive testing. Effectiveness was expressed as quality-adjusted life month in the perioperative analyses and quality-adjusted life years in the lifetime analyses. The primary outcome was the incremental cost-effectiveness ratio. Results In perioperative and lifetime analyses, no screening was least costly and least effective. STOP-Bang + polysomnography was the most effective strategy and was more cost-effective than both STOP-Bang + portable monitor and STOP-Bang alone in both analyses. In perioperative analyses, STOP-Bang + polysomnography was not cost-effective compared to no screening at the $4,167/quality-adjusted life month threshold (incremental cost-effectiveness ratio $52,888/quality-adjusted life month). No screening was favored in more than 90% of iterations in probabilistic sensitivity analyses. In contrast, in lifetime analyses, STOP-Bang + polysomnography was favored compared to no screening at the $50,000/quality-adjusted life year threshold (incremental cost-effectiveness ratio $2,044/quality-adjusted life year). STOP-Bang + polysomnography was favored in most iterations at thresholds above $2,000/quality-adjusted life year in probabilistic sensitivity analyses. Conclusions The cost-effectiveness of preoperative obstructive sleep apnea screening differs depending on time horizon. Preoperative screening with STOP-Bang followed by immediate confirmatory testing with polysomnography is cost-effective on the lifetime horizon but not the perioperative horizon. The integration of preoperative screening based on STOP-Bang and polysomnography is a cost-effective means of mitigating the long-term disease burden of obstructive sleep apnea. Editor’s Perspective What We Already Know about This Topic What This Article Tells Us That Is New