Pharmacokinetics, Pharmacodynamics, and Safety of Alogliptin in Children, Adolescents and Adults With Type 2 Diabetes Mellitus

Inclusion criteria for children and adolescent participants only (Groups 1 and 2, respectively): 1. Participant was male or female between 10 and 17 years of age. 2. Participant or parent or legal guardian was capable of understanding and complying with the protocol requirements. 3. Participant was capable of understanding an informed consent form (ICF) or assenting to participate. The parent or legal guardian of the participant must have been able to understand and sign an ICF prior to the initiation of any study procedures. 4. Participant weighed at least 36 kg (79 pounds) and had a Screening body mass index (BMI) of at least 18 kg/m\^2. 5. Participants had a diagnosis of type 2 diabetes mellitus (T2DM) (non-insulin dependent) based on diagnostic criteria of the American Diabetes Association (ADA). Criteria included: 1. Fasting plasma glucose level of ≥ 126 mg/dL where fasting is defined as no caloric intake for at least 8 hours, or 2. 2-hour plasma glucose level of ≥ 200 mg/dL during an oral glucose tolerance test, or 3. random plasma glucose level of ≥ 200 mg/dL, or 4. glycated hemoglobin (HbA1c) ≥ 6.5%. 6. Diagnosis could have been historical (documented), or participants could have been diagnosed for this study. 7. Participants had a fasting serum C-peptide concentration ≥ 0.8 ng/mL (≥ 0.26 nmol/L) at the Screening Visit only. 8. Participants may have been taking concomitant metformin if the dose was stable for at least 30 days prior to Day 1 (day of first dosing). Inclusion criteria for adult participants only (Group 3): 9. Participant was male or female, and between 18 and 65 years of age, inclusive for gender and race matched adult participants with T2DM only. 10. Participant was capable of understanding and complying with protocol requirements and was willing to sign the ICF prior to the initiation of any study procedures for gender and race matched adult participants with T2DM only. 11. Participant weighed at least 50 kg (110 pounds) and had a Screening BMI between 23 kg/m\^2 and 45 kg/m\^2 (except for Asian or Asian-descendant participants for whom the range was between 20 kg/m\^2 and 35 kg/m\^2), inclusive for gender and race matched T2DM adult participants only. 12. Participants had a diagnosis of T2DM (non-insulin dependent) based on diagnostic criteria of the ADA. Criteria included: 1. Fasting plasma glucose level of ≥ 126 mg/dL where fasting is defined as no caloric intake for at least 8 hours, or 2. 2-hour plasma glucose level of ≥ 200 mg/dL during an oral glucose tolerance test, or 3. random plasma glucose level of ≥ 200 mg/dL, or 4. HbA1c ≥ 6.5%. 13. Diagnosis could have been historical (documented) or participants could have been diagnosed for this study. 14. Participants may have been taking concomitant metformin if the dose was stable for at least 30 days prior to Day 1. 15. Participants may have been taking statin or antihypertensive drugs if the dose was stable for at least 30 days prior to Day 1. Inclusion criteria for all participants (Groups 1, 2, and 3): 16. Female participants of childbearing potential and male participants who were sexually active agreed to routinely use adequate contraception from Screening until 30 days after receiving the dose of study drug. NOTE: Women not of childbearing potential were defined as those who were surgically sterilized (hysterectomy, bilateral oophorectomy, tubal ligation) or who were postmenopausal (defined as at least 45 years of age and 1 year since last regular menses). 17. Participant had a negative urine test result for selected substances of abuse (including alcohol and cotinine) at Screening and Check-in (Day -1). 18. Participant had clinical chemistry, hematology, and complete urinalysis (fasted for at least 8 hours) results within the reference range for the testing laboratory (except results associated with T2DM) unless the out-of-range results were deemed not clinically meaningful by the investigator or sponsor. 19. Participant had a negative test result for hepatitis B surface antigen (HBsAg) and hepatitis C virus antibody (anti-HCV), and no known history of human immunodeficiency virus. Exclusion Criteria: 1. Participant was currently participating in another investigational study or took an investigational drug within 30 days prior to Day 1. 2. Participant received alogliptin previously. 3. Participant was a study site employee, or was an immediate family member (ie, spouse, parent, child, or sibling) of a study site employee involved in conduct of this study. 4. Participant received or donated blood or blood products within 30 days prior to Screening or planned to donate blood during the study. 5. Participant had a known hypersensitivity to alogliptin or related compounds. 6. Participant had a history of drug abuse (defined as any illicit drug use) or a history of alcohol abuse (defined as consumption of more than 4 alcoholic drinks per day) within 1 year prior to study Day 1. 7. Participant had an acute, clinically significant illness (excluding T2DM) within 30 days prior to study Day 1. 8. Participant had any other condition or prior therapy that, in the opinion of the investigator, would have made the participant unsuitable for the study. 9. Participant had a history or clinical manifestations of significant metabolic (excluding T2DM), hematologic, pulmonary, cardiovascular, gastrointestinal, neurologic, hepatic, renal, urologic, immunologic, musculoskeletal, or psychiatric disorder. 10. Participant had a hemoglobin value \< 12 g/dL. 11. Participant had a systolic blood pressure \> 140 mm Hg or had a diastolic blood pressure \> 90 mmHg at Screening or Check-in (Day -1). 12. Adult participant had an alanine aminotransferase (ALT) or aspartate aminotransferase (AST) level greater than 2 times the upper limit of normal (ULN), active liver disease, or jaundice at the Screening Visit or on Check-in (Day -1). 13. Pediatric participant had an ALT or AST level greater than 1.5 times the ULN at the Screening Visit or on Check-in (Day -1). 14. Participant had a serum creatinine level \> 1.5 mg/dL. 15. Participant had a creatinine clearance (CrCl) \< 50 mL/min (normalized to body surface area of 1.73 m\^2). 16. Participant had a history of abdominal surgery (except laparoscopic cholecystectomy or uncomplicated appendectomy) or thoracic or nonperipheral vascular surgery within 6 months prior to Day 1. 17. Participant had a history or presence of a clinically significant abnormal 12-lead electrocardiogram (ECG) result as determined by the investigator or Takeda at Screening or Check-in (Day -1). 18. Participant had a history of cancer, other than basal cell carcinoma or Stage I squamous cell carcinoma of the skin that had not been in remission for at least 5 years prior to the first dose of study drug. 19. If female, participant was pregnant or lactating or intending to become pregnant before, during, or within 30 days after receiving study drug. 20. If male, participant intended to impregnate others during the study or for 30 days after receiving study drug. 21. Participant consumed or was unable to abstain from consumption of products containing alcohol, caffeine, or xanthine, and food or beverages containing grapefruit juice or Seville-type oranges within 72 hours prior to study Day 1 and for the duration of the study. 22. Participant used any tobacco (ie, nicotine) products (including but not limited to cigarettes, pipe, cigar, chewing tobacco, nicotine patch, or nicotine gum) within 6 weeks prior to study Day 1, and was unwilling to abstain from these products for the duration of the study. 23. Participant used any nutraceutical preparations within 28 days prior to study Day 1. 24. Participant was currently taking ketoconazole, fluconazole, gemfibrozil, rifampin, or carbamazepine or taken within 28 days prior to Check-in (Day -1). 25. Participant had poor peripheral venous access. 26. Participant had a medical history of clinical or laboratory evidence to indicate a diagnosis of type 1 diabetes or secondary forms of diabetes, including maturity-onset diabetes of the young (MODY).