A Study of Omarigliptin (MK-3102) in Participants With Type 2 Diabetes Mellitus With Chronic Kidney Disease or Kidney Failure on Dialysis (MK-3102-019)

Inclusion Criteria: * Type 2 diabetes mellitus and be at least 30 years of age * Moderate or severe chronic renal insufficiency or end stage renal disease on dialysis * Meet one of the following criteria: 1. is currently not on an antihyperglycemic agent (AHA) and has A1C \>=7% and \<=10% at screening 2. is currently on a single oral AHA or low-dose dual oral combination AHA and has A1C \>=6.5% and \<=9% at screening 3. is currently on a stable insulin regimen (\>= 15 U/day) for \>= 10 weeks, with no oral AHA, and has A1C \>=7.5% and \<=10% and FPG \>130 mg/dL at screening * (1) Male; (2) female not of reproductive potential; or (3) female of reproductive potential who agrees to remain abstinent or use alone or in conjunction with their partner 2 methods of contraception to prevent pregnancy during the study and for 28 days after the last dose of study drug Exclusion Criteria: * History of type 1 diabetes mellitus or a history of ketoacidosis * Treated with any incretin mimetic or thiazolidinedione (TZD) within 12 weeks prior to screening or with omarigliptin at any time prior to study participation * History of hypersensitivity to a dipeptidyl peptidase IV (DPP-4) inhibitor * History of intolerance or hypersensitivity to glipizide or insulin glargine or any contraindication to glipizide or insulin glargine * On a weight loss program and is not in the maintenance phase, or has been on a weight loss medication in the past 6 months, or has undergone bariatric surgery within 12 months prior to study participation * Undergone a surgical procedure within 4 weeks prior to screening or has planned major surgery during the trial * On or likely to require treatment for \>=2 consecutive weeks or repeated courses of corticosteroids (note: inhaled, nasal or topical corticosteroids are permitted) * Currently being treated for hyperthyroidism or is on thyroid replacement therapy and has not been on a stable dose for at least 6 weeks * If on dialysis, does not regularly adhere to dialysis schedule * Diagnosis of congestive heart failure with New York Heart Association (NYHA) Class IV * Medical history of active liver disease (other than non-alcoholic hepatic steatosis), including chronic active hepatitis B or C, primary biliary cirrhosis, or symptomatic gallbladder disease * Human immunodeficiency virus (HIV) * New or worsening coronary heart disease, congestive heart failure, myocardial infarction, unstable angina, coronary artery intervention, stroke, or transient ischemic neurological disorder within the past 3 months * Poorly controlled hypertension * Severe active peripheral vascular disease * History of malignancy \<=5 years prior to study participation, except for adequately treated basal cell or squamous cell skin cancer, or in situ cervical cancer * Clinically important hematological disorder (such as aplastic anemia, myeloproliferative or myelodysplastic syndromes, thrombocytopenia) * Positive pregnancy test * Pregnant or breast-feeding, or is expecting to conceive or donate eggs during the trial, including 28 days following the last dose of study drug * User of recreational or illicit drugs or has had a recent history of drug abuse or routinely consumes \>2 alcoholic drinks per day or \>14 alcoholic drinks per week, or engages in binge drinking