Study of Sitagliptin for the Treatment of Type 2 Diabetes Mellitus With Inadequate Glycemic Control on Insulin (MK-0431-260)

Inclusion Criteria: * has type 2 diabetes mellitus * has one of the following criteria: * diagnosed with diabetes after age 40 years and insulin therapy was initiated at least 3 years following diagnosis * if diagnosed with diabetes under age 40 years or insulin started earlier than 3 years after diagnosis, has a fasting C-peptide greater than 0.7 ng/mL * must be at least 18 years of age and less than or equal to 80 years of age (for participants in India: must be at least 18 years of age and less than or equal to 65 years of age) * on a stable regimen of insulin for at least 10 weeks with or without metformin (at least 1500 mg/day) and/or sulfonylurea for at least 10 weeks * is highly unlikely to become pregnant (not of reproductive potential or agrees to remain abstinent or use (or have their partner use) an acceptable method of birth control during the study and for 14 days after the last dose of study medication Exclusion Criteria: * has been treated with a dipeptidyl peptidase IV (DPP-4) inhibitor, a thiazolidinedione (TZD), or a glucagon-like peptide-1 (GLP-1) mimetic or analogue, within the past 12 weeks * currently on treatment with daily use (one or more injections per day) of a pre-prandial short-acting or rapid-acting insulin alone or as part of a basal/bolus insulin regimen * has symptomatic hyperglycemia that requires immediate initiation, adjustment, or addition of antihyperglycemic therapy * has a history of 2 or more episodes of hypoglycemia resulting in seizure, coma, or loss of consciousness, - or - has had recurrent (≥3 times per week) episodes of hypoglycemia over the past 8 weeks * has a history of ketoacidosis * is not appropriate for or does not agree to target a fasting glucose of 72-100 mg/dL \[4.0-5.6 mmol/L\] * is on or likely to require treatment with corticosteroids * has undergone a surgical procedure within 4 weeks or has planned major surgery during the study * is currently being treated for hyperthyroidism or is on thyroid hormone therapy and has not been on a stable dose for at least 6 weeks * has a history of active liver disease (other than non-alcoholic hepatic steatosis) * has had new or worsening signs or symptoms of coronary heart disease or congestive heart failure within the past 3 months, or has any of the following disorders within the past 3 months: * acute coronary syndrome * coronary artery intervention * stroke or transient ischemic neurological disorder * has a systolic blood pressure greater than 160 mm Hg or a diastolic blood pressure greater than 90 mm Hg * has human immunodeficiency virus (HIV) * has severe peripheral vascular disease * has a clinically important hematological disorder * has a history of malignancy that is less than 5 years from study start, except for adequately treated basal cell or squamous cell skin cancer or in situ cervical cancer * has a positive urine pregnancy test * is pregnant or breast-feeding, or is expecting to conceive or donate eggs during the study * a user of recreational or illicit drugs or has had a recent history of drug abuse