Sitagliptin Versus Glipizide in Participants With Type 2 Diabetes Mellitus and End-Stage Renal Disease (MK-0431-073 AM1)

Inclusion Criteria: * Participant has T2DM. * Participant is on dialysis on day of signing informed consent. * Participant is unlikely to conceive or uses acceptable methods of birth control: hormonal contraceptive, intrauterine device (IUD), diaphragm with spermicide, contraceptive sponge, condom, or vasectomy. * Participant has hemoglobin A1c ≥7% and ≤9% measured at or within 2 weeks prior to Visit 4/Week -2. * Participant is ≥85% compliant with study medication during the single-blind placebo run-in (as determined by tablet/capsule count) and compliant with diet, exercise and other run-in treatments during the run-in period. Exclusion Criteria: * Participant has a history of type 1 diabetes mellitus or a history of ketoacidosis. * Participant is losing weight in a weight loss program and is not in the maintenance phase (defined as \<2 kg weight loss in 2 months), or intends to be involved in weight loss intervention outside that prescribed by the study. * Participant has a clinically significant hematological disorder (e.g., aplastic anemia, myeloproliferative or myelodysplastic syndromes, thrombocytopenia). * Participant has cirrhosis or active liver disease. * Participant has been on dialysis for \< 6 months. * Participant has been diagnosed with a significant cardiovascular disorder and has new or worsening signs or symptoms of congestive heart failure within 3 months of signing informed consent. * Participant has severe active peripheral vascular disease. * Participant has a history of malignancy ≤ 5 years prior to signing informed consent, or \> 5 years without documentation of remission/cure. * Participant is under treatment for hyperthyroidism. * Participant has a hypersensitivity or contraindication to glipizide.