Combination Upper-Airway Electrical and Pharmacological Stimulation for Obstructive Sleep Apnea

Inclusion Criteria for Enrolment: * Ages 18 - 79 years * Diagnosed OSA * Implantation of a hypoglossal nerve stimulation device (HGNS, Inspire Medical) or scheduled for implantation (implantation required for randomization) * Willingness to withhold HGNS while testing therapies (up to 6 weeks with HGNS off \[with/without pharmacotherapy\] to assess benefits of HGNS therapy). Exclusion Criteria: * Any uncontrolled medical condition * Current use of the medications under investigation. * Issues relating to short-term withdrawal of HGNS therapy * Excluded: Occupational driving (truck drivers, fork-lift operation, taxi/uber drivers) * Excluded: History of traffic accidents attributable to sleepiness or fatigue (\<2 years). * Use of SNRIs/SSRIs or anticholinergic medications during the study. * Conditions likely to affect obstructive sleep apnea physiology: neuromuscular disease or other major neurological disorder, heart failure (also below), or any other unstable major medical condition. * Respiratory disorders other than sleep disordered breathing: chronic hypoventilation/hypoxemia (awake SaO2 \< 92% by oximetry) due to chronic obstructive pulmonary disease or other respiratory conditions. * Other sleep disorders: narcolepsy, parasomnias. Insomnia * Contraindications for atomoxetine and oxybutynin, including: * hypersensitivity to atomoxetine or oxybutynin (angioedema or urticaria) * pheochromocytoma * use of monoamine oxidase inhibitors * diagnosed benign prostatic hypertrophy, urinary retention * suspected benign prostatic hypertrophy / urinary retention based on a positive answer to either of the following questions: 1. "During the last month, when urinating, have you had the sensation of not emptying your bladder completely more often than 1 out of 5 times?" 2. "During the last month, have you had a weak urinary stream more often than 1 out of 5 times? * known untreated narrow angle glaucoma * known bipolar disorder, mania, psychosis * known history of major depressive disorder (age\<24). * known history of attempted suicide or suicidal ideation within one year prior to screening * known clinically significant constipation, gastric retention * known pre-existing seizure disorders * known clinically-significant kidney disorders (eGFR\<60 ml/min/1.73m2) * known clinically-significant liver disorders * known clinically-significant cardiovascular conditions * moderate-to-severe hypertension (SBP\>160 mmHg or DBP\>100 mmHg measured at baseline; average of evening and morning measures) * known cardiomyopathy (LVEF\<50%) or heart failure * known advanced atherosclerosis * recent cerebrovascular events (within 2 years) * recent history of cardiac arrhythmias e.g., atrial fibrillation, QT prolongation (within 2 years) * other serious cardiac conditions that would raise the consequences of an increase in blood pressure or heart rate * myasthenia gravis * pregnancy/breast-feeding