Effects of Suvorexant in Participants With Obstructive Sleep Apnea (MK-4305-036)

Inclusion Criteria: * Female participants of reproductive potential must demonstrate a serum β-human chorionic gonadotrophin (hCG) level consistent with the nongravid state at the pre-study (screening) visit and agree to use (and/or have their partner use) two (2) acceptable methods of birth control beginning at the pre-study visit throughout the study. * Women who are postmenopausal without menses for at least 1 year and a follicle stimulating hormone (FSH) value in the postmenopausal range upon pre-study (screening) evaluation, and/or are status post hysterectomy, oophorectomy or tubal ligation may participate. * Participants with a Body Mass Index (BMI) ≤40 kg/m2 at the pre-study (screening) visit. * Participants have to be in good health based on medical history, physical examination, vital sign measurements, and laboratory safety tests. * Participants without clinically significant abnormality on electrocardiogram (ECG) performed at the pre-study (screening) visit and/or prior to administration of the initial dose of study drug. * Participants have an International Classification of Sleep Disorders diagnosis of OSA. * Participants have confirmed mild or moderate OSA (defined as mild OSA with AHI ≥5 and \<15, and moderate OSA with AHI ≥15 and \<30) based on the screening nighttime polysomnography (NPSG). * Participants have a usual bedtime between 20:00 (8:00 post meridiem \[PM\]) and 00:30 (12:30 ante meridiem \[AM)\] and is not subject to any other unusual changes in sleeping routine and sleeps for 4 hours or more per night. * Participants must complete a sleep history diary for at least 5 consecutive days and up to 21 days prior to the screening PSG visit. * Participant has been a nonsmoker and/or has not used nicotine or nicotine-containing products for at least approximately 6 months; participants who have discontinued smoking or the use of nicotine/nicotine containing products for at least approximately 3 months may be enrolled in the study at the discretion of the investigator. Exclusion Criteria: * Participants have used continuous positive airway pressure devise (CPAP) or a dental appliance within the preceding 7 days prior to screening NPSG Visit, or is required to use CPAP or a dental appliance during course of the study (7 days prior to the screening NPSG, throughout the study \[including washout intervals between treatment periods\], and until the poststudy visit). * Participants have other than OSA and evidence of another clinically significant, active pulmonary disorder such as bronchiectasis, emphysema, or asthma documented by history, physical examination, or chest x-ray. * Participant have either a history within the past 6 months prior to the prestudy visit or current evidence of an unstable or clinically significant cardiovascular disorder, including but not limited to acute coronary syndrome, unstable angina, congestive heart failure, cardiogenic syncope, cardiomyopathy, any symptomatic arrhythmia, orthostatic hypotension, or uncontrolled hypertension. * Participants have abnormal pre-randomization laboratory values other clinically significant, unexplained laboratory abnormality in the opinion of the investigator with alanine transaminase (ALT) \>1.5 x the upper limit of normal (x ULN), aspartate transaminase (AST) \>1.5 x ULN, total bilirubin \>1.5 x ULN, or serum creatinine of \>2 mg/dL. * Participants have a history or diagnosis of narcolepsy, cataplexy (familial or idiopathic), circadian rhythm sleep disorder, parasomnia including nightmare disorder, sleep terror disorder, sleepwalking disorder, and REM behavior disorder, periodic limb movement (PLM) disorder, restless legs syndrome, or primary hypersomnia. * Participants have a screening PSG recording with oxygen (O2) saturation \<80% for ≥5% of the total sleep time, and \>10 PLM per hour associated with an arousal (periodic limb movement arousal index \[PLMAI\]). * Participant is mentally or legally incapacitated, has significant emotional problems at the time of prestudy (screening) visit or expected during the conduct of the study or has a history of a clinically significant psychiatric disorder over the last 5 to 10 years. Participant who have had situational depression may be enrolled in the study at the discretion of the investigator. * Participant has lifetime history of bipolar disorder, a psychotic disorder, or posttraumatic stress disorder; or, a psychiatric condition requiring treatment with a prohibited medication; or, other psychiatric condition that, in the investigator's opinion, would interfere with the participant's ability to participate in the study. * Participant, in the opinion of the investigator, has a history or current evidence of any condition, therapy, lab or ECG abnormality or other circumstances that might confound the results of the study, or interfere with the participant's participation for the full duration of the study. * Participant has any history of a neurological disorder, including but not limited to seizure disorder (other than single episodes of childhood febrile seizures), stroke, transient ischemic attack, multiple sclerosis, cognitive impairment, or significant head trauma with sustained loss of consciousness within the last 10 years. * Participant has a history of clinically significant endocrine, gastrointestinal, cardiovascular, hematological, hepatic, immunological, renal, respiratory, or genitourinary abnormalities or diseases. Participants with a history of uncomplicated kidney stones may be enrolled in the study at the discretion of the investigator. * Participant has a history of neoplastic disease except: 1. adequately treated non-melanomatous skin carcinoma or carcinoma in situ of the cervix may participate in the study; 2. participants with other malignancies which have been successfully treated ≥10 years prior to the prestudy (screening) visit where, in the judgment of both the Investigator and treating physician, appropriate follow-up has revealed no evidence of recurrence from the time of treatment through the time of the prestudy (screening) visit, or 3. participants, who, in the opinion of the Investigator, are highly unlikely to sustain a recurrence for the duration of the study. * Participant is a nursing mother. * Participant has a positive screening urine alcohol test or drug test. * Participant has a need for more than 3 toilet visits during the night. * Participant is taking, or plans to take, one or more of prohibited concomitant medication. * Participant consumes excessive amounts of alcohol (greater than 3 glasses of alcoholic beverages), excessive amounts of coffee, tea, cola, or other caffeinated beverages per day. * Participant has had major surgery, donated or lost 1 unit of blood (approximately 500 mL) or participated in another investigational study within 4 weeks prior to the prestudy (screening) visit. * Participant has a history of significant multiple and/or severe allergies (including latex allergy), or has had an anaphylactic reaction or significant intolerability to prescription or non-prescription drugs or food. * Participant is currently a regular user (including "recreational use") of any illicit drugs or has a history of drug (including alcohol) abuse within approximately 2 years. * Participant works a night shift and is not able to avoid night shift work within 2 weeks before each treatment visit (or before the study start and during the study). * Participant has traveled across 3 or more time zones (transmeridian travel) in the last 1 week prior to study start. * Participant is at imminent risk of self-harm or harm to others * Any concern by the investigator regarding the safe participation of the participant in the study or for any other reason; the investigator considers the participant inappropriate for participation in the study.