This is a trial of continuing sitagliptin versus withdrawing sitagliptin in participants with Type 2 diabetes mellitus (T2DM) and inadequate glycemic control who initiate and titrate insulin glargine (LANTUS®) based on a treat-to-target algorithm to achieve fasting glucose levels of 72-100 mg/dL (4-5.6 mmol/L). A primary hypothesis of this trial is that after 30 weeks, continuing sitagliptin results in a greater reduction of hemoglobin A1C (A1C) relative to withdrawing sitagliptin.