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Rationale Obstructive sleep apnoea (OSA) is a prevalent disorder with major health consequences for which there is no approved pharmacological therapy targeting upper airway muscle pathophysiology. A combination of a noradrenergic (atomoxetine) and antimuscarinic (oxybutynin) (AtoOxy) may meaningfully reduce apnoea-hypopnoea index (AHI), but further repeated-dose intervention data are needed.Methods 58 participants with moderate-to-severe OSA were randomised to receive AtoOxy (80/5 mg) and placebo in a 1-month cross-over study. Primary analysis quantified the effect of AtoOxy versus placebo on AHI (percent change from baseline). Individual pathophysiology was characterised at baseline in a stand-alone gold-standard physiology study to determine whether OSA traits (collapsibility per ‘Pcrit’; arousal threshold and muscle effectiveness per intraoesophageal catheter; loop gain) modified AtoOxy effectiveness.Results AHI was lowered by −23.8 (−35.2, −10.6)% baseline (estimate (95% CI)) with AtoOxy versus by −11.7 (−24.3, 2.9)%baseline with placebo; the treatment difference of −12.1 (−22.4, −0.5)%baseline was significant (p=0.041). Only arousal threshold was a significant modifier of response: AtoOxy treatment effect was greater in high versus low arousal threshold (−25 vs +3 %baseline treatment difference from placebo). Point-estimate treatment differences were observed within low but not high muscle effectiveness (−20 vs −4 %baseline) and mild but not severe collapsibility (−17 vs −7 %baseline). Sensitivity analysis suggested a twofold greater treatment difference using AHI4 (4% hypopnoea criteria).Conclusions AtoOxy reduced AHI over 1 month; although the average response was not clinically meaningful, greater improvements were observed in participants with a higher arousal threshold, lower muscle effectiveness and milder collapsibility, which could enable targeted pharmacological intervention.