The purpose of this study is to assess the efficacy of omarigliptin 25 mg weekly (as monotherapy) compared with sitagliptin 50 mg daily and placebo, and the long term safety (up to 52 weeks) of omarigliptin 25 mg weekly. The primary hypotheses are that after 24 weeks: 1) Omarigliptin 25 mg weekly provides a greater reduction from baseline in glycosylated hemoglobin (HbA1c) compared with placebo, and 2) The mean change from baseline in HbA1c in participants treated with omarigliptin 25 mg weekly is non-inferior compared with that in participants treated with sitagliptin 50 mg daily.