A Phase 3, Randomized, Double-blind, Parallel-group, Comparative Study and a Phase 3, Multicenter, Open-label, Long-term Study of SYR-472 (25 mg) in Patients With Type 2 Diabetes Mellitus Complicated by Severe Renal Impairment or End-stage Renal Disease

Inclusion Criteria: 1. The participant has a diagnosis of type 2 diabetes mellitus. 2. The participant has a fasting C-peptide value of 0.6 ng/mL or higher at the start of the screening period (Week -6) and Week -2 of the screening period. 3. The participant has a hemoglobin value of 10.0 g/dL or higher at the start of the screening period (Week -6) and Week -2 of the screening period. 4. The participant has a Haemoglobin A1c (HbA1c) value of 7.0% or higher but less than 10.0% at Week -2 of the screening period. For participants undergoing hemodialysis (with End-stage Renal Disease \[ESRD\]), those with a glycoalbumin value of 20% or higher could be enrolled even if their HbA1c value is below 7.0% at Week -2 of the screening period. 5. \<HbA1c value of 7.0% or higher but less than 10.0% at Week -2 of the screening period\> The participant has an HbA1c value difference between the start of the screening period (Week -6) and Week -2 of the screening period within 10.0%\* of the HbA1c value at the start of the screening period (Week -6). \<For participants undergoing hemodialysis (with ESRD), glycoalbumin value of 20% or higher and HbA1c value of below 7.0% at Week -2 of the screening period\> The participant has a glycoalbumin difference between the start of the screening period (Week -6) and Week -2 of the screening period within 10.0%\* of the glycoalbumin value at the start of the screening period (Week -6). \*: rounded to one decimal place 6. The participant has been on a fixed diet and/or exercise therapy (if any) for at least 6 weeks prior to the start of the screening period (Week -6). 7. The participant meets any of the following: * The participant has not received any antidiabetic medications (including insulin preparations) from at least 6 weeks prior to the start of the screening period (Week -6). * The participant is being treated with one oral hypoglycemic drug\* starting from at least 6 weeks prior to the start of the screening period (Week -6) at a fixed dose and regimen. \*: any one of the following medications: mitiglinide calcium hydrate, repaglinide, acarbose, miglitol, or voglibose * The participant is being treated with one insulin preparation\*\* starting from at least 6 weeks prior to the start of the screening period (Week -6) at a fixed dose and regimen (≤40 units/day) of the insulin preparation. * Any one of the following insulin monotherapies: mixed (short-acting or rapid-acting insulin containing no more than 30% volume), intermediate-acting, or long-acting soluble insulin preparations 8. The participant is not undergoing hemodialysis or peritoneal dialysis and has severe renal impairment \[creatinine clearance (Ccr) \<30 mL/min at the start of the screening period (Week -6)\], or the participant is undergoing hemodialysis and has end-stage renal failure. 9. In the opinion of the investigator or sub-investigator, the initiation of hemodialysis or peritoneal dialysis at least within 12 weeks after starting the investigational product is not expected. \[in cases where the participant is not undergoing hemodialysis or peritoneal dialysis (patients with severe renal impairment)\] 10. The participant has been undergoing hemodialysis starting from at least 6 months prior to informed consent and, in the opinion of the investigator or sub-investigator, the participant is clinically stable. \[in cases where the participant is undergoing hemodialysis (patient with end-stage renal failure)\] 11. The participant is male or female and is aged 20 years or older at the time of informed consent. 12. A female participant of childbearing potential who is sexually active with a nonsterilized male partner agrees to use routinely adequate contraception from signing of informed consent until one month after the end of the study. 13. In the opinion of the investigator or sub-investigator, the participant is capable of understanding and complying with protocol requirements. 14. The participant signs and dates a written, informed consent form prior to the initiation of any study procedures. Exclusion Criteria: 1. The participant has clinically evident hepatic impairment \[e.g., aspartate aminotransferase (AST) or alanine aminotransferase (ALT) ≥2.5 times the upper limit of normal or total bilirubin of ≥2.0 mg/dL at the start of the screening period (Week -6) or at Week -2 of the screening period\]. 2. The participant has any serious cardiac diseases, cerebrovascular disorders, or serious pancreatic or hematological diseases (e.g., participants who require inpatient treatment or are hospitalized for treatment within 24 weeks prior to the start of the screening period). 3. The participant has severe ketosis, diabetic coma or precoma, type 1 diabetes, severe infection, before or after surgery, or severe external trauma. 4. The participant has hemoglobinopathy (sickle cell disease, thalassemia, etc.). 5. The participant experienced hypoglycemia (participants with a blood glucose value of ≤70 mg/dL or hypoglycemic symptoms) within 6 weeks prior to the start of the screening period or during the screening period (at least twice per week). 6. The participant has inadequately controlled hypertension. 7. For participants who are being treated with one antidiabetic agent, the participant was using at least two antidiabetic therapies on the day before 6 weeks prior to the start of the screening period (Week -6) (43 days prior to the start of the screening period). 8. The participant has malignancies. 9. The participant has a history of hypersensitivity or allergies to dipeptidyl peptidase 4 (DPP-4) inhibitors. 10. The participant has a history of gastrectomy or small intestinal resection. 11. The participant is a habitual drinker and consumes a daily average of more than 100 mL of alcohol. 12. The participant has a history of drug abuse (defined as the use of an illegal drug) or alcohol dependence. 13. The participant is required to take excluded medications during the study period. 14. The participant has previously received trelagliptin. 15. The participant received any other investigational products (including study drugs in a post-marketing clinical study) within 12 weeks prior to the start of the screening period. 16. The participant is participating in other clinical studies at the time of informed consent. 17. If female, the participant is pregnant or lactating or intending to become pregnant from the time of informed consent to within 1 month after the end of the study; or intending to donate ova during such time period. 18. The participant is an immediate family member of a study site employee, or is in a dependent relationship with a study site employee who is involved in the conduct of this study (e.g., spouse, parent, child, sibling) or may consent under duress. 19. The participant is hospitalized during the screening period or is deemed as requiring hospitalization during the study period by the investigator or sub-investigator, unless the hospitalization is for short-term evaluations including complete health checkups or shunt (including shunt maintenance). 20. The participant is deemed ineligible for the study for any other reason by the investigator or sub-investigator.