A Study of Gefapixant (MK-7264) in Adult Participants With Chronic Cough (MK-7264-027)

The main objectives of this study will be to evaluate the efficacy of gefapixant in reducing cough frequency as measured over a 24-hour period at Week 12, and to evaluate the safety and tolerability of gefapixant. The primary hypothesis is that at least one gefapixant dose is superior to placebo in reducing coughs per hour (over 24 hours) at Week 12.

The study will include a screening period to determine participant inclusion, and the Baseline visit will include 24 hours of objective measurement of cough. The study will consist of two treatment periods, a main 12-week treatment period and a 40-week extension period (52 weeks total treatment), followed by a 14-day telephone follow-up period.

Participants at selected sites and countries who complete the main and extension study periods may consent to participate in an observational, 3-month, Off-treatment Durability Study Period, which extends the Estimated Study Completion Date. The Off-treatment Durability Study Period will explore the impact of withdrawing gefapixant in refractory or unexplained chronic cough participants who have been treated for 1 year.

Eligibility Criteria:
Inclusion Criteria:

* Chest radiograph or computed tomography scan of the thorax (within 5 years of Screening/Visit 1 and after the onset of chronic cough) not demonstrating any abnormality considered to be significantly contributing to the chronic cough or any other clinically significant lung disease in the opinion of the principal investigator or the sub-investigator
* Has had chronic cough for at least 1 year with a diagnosis of refractory chronic cough or unexplained chronic cough
* Female participants are eligible if not pregnant, not breastfeeding, and either not of childbearing potential, or agree to follow contraceptive guidance
* Provides written informed consent and is willing and able to comply with the study protocol (including use of the digital cough recording device and completion of study questionnaires)

Exclusion Criteria:

* Is a current smoker or has given up smoking within 12 months of Screening
* Has forced expiratory volume in 1 second (FEV1)/ forced vital capacity (FVC) ratio \<60%
* Has a history of respiratory tract infection or recent clinically significant change in pulmonary status
* Has a history of chronic bronchitis
* Is currently taking an angiotensin converting enzyme inhibitor (ACEI), or has used an ACEI within 3 months of Screening
* Has an estimated glomerular filtration rate (eGFR) \<30mL/min/1.73 m\^2 at Screening OR eGFR ≥30 mL/min/1.73 m\^2 and \<50 mL/min/1.73 m\^2 at Screening with unstable renal function
* Has a history of malignancy \<=5 years
* Is a user of recreational or illicit drugs or has had a recent history of drug or alcohol abuse or dependence
* Has a history of anaphylaxis or cutaneous adverse drug reaction (with or without systemic symptoms) to sulfonamide antibiotics or other sulfonamide-containing drugs
* Has systolic blood pressure \>160 mm Hg or diastolic blood pressure \>90 mm Hg at Screening
* Has a known allergy/sensitivity or contraindication to gefapixant
* Has donated or lost \>=1 unit of blood within 8 weeks prior to the first dose of gefapixant
* Has previously received gefapixant or is currently participating in or has participated in an interventional clinical study
* Had significantly abnormal laboratory tests at Screening