Phase 2 Study of Brigatinib in Japanese Participants With Anaplastic Lymphoma Kinase (ALK)-Positive Non-Small Cell Lung Cancer (NSCLC)

1. Male or female Japanese participants aged \>=20 years on the day of consent.

2. Voluntary written consent must be given before performance of any study-related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the participant at any time without prejudice to future medical care.

3. Have histologically or cytologically confirmed stage IIIB, stage IIIC (locally advanced or recurrent and not a candidate for definitive multimodality therapy), or stage IV NSCLC.

4. Have documentation of ALK rearrangement that meets following criteria.

For the Safety Evaluation Lead-in Part and the Refractory Expansion Part, participants must meet 1 of the following 2 criteria:

1. Have documentation of ALK rearrangement by a positive result from the Vysis ALK Break Apart fluorescence in situ hybridization (FISH) Probe Kit, the Nichirei Histofine ALK iAEP Kit, or the Ventana ALK (D5F3) Companion Diagnostics (CDx) Assay at any time during prior disease course. The sponsor may require an adequate tissue available for central laboratory testing by the Vysis ALK Break Apart FISH test if a documented ALK rearrangement is confirmed by a positive result from the Nichirei Histofine ALK iAEP Kit "ONLY".

2. Had a documented ALK rearrangement by a different test at any time during prior disease course, and adequate tissue available for central laboratory testing by the Vysis ALK Break Apart FISH test. Central confirmation of ALK rearrangement is not required before enrollment.

For TKI-naïve Expansion Cohort, participants must meet the following criteria Have documentation of ALK rearrangement by a positive result from Ministry of Health, Labour and Welfare (MHLW) Approved tests (e.g Vysis ALK Break Apart FISH Probe Kit, the Nichirei Histofine ALK iAEP Kit, or the Ventana ALK \[D5F3\] CDx Assay) prior to enrollment, and required to submit sufficient tumor tissue for central laboratory testing upon request of sponsor. Central confirmation of ALK rearrangement is not required before enrollment

5. The Refractory Expansion Part only: had documented progressive disease (PD) during treatment or within 30 days after discontinuation of treatment with ALK inhibitor.

* Note 1: The Refractory Expansion Part consists of the Main Cohort and a Sub-cohort based on prior ALK inhibitor treatment. The Main Cohort includes participants who had previously received alectinib (as their only ALK inhibitor) or both crizotinib and alectinib (regardless the sequence of those 2 ALK inhibitors), and a total of 47 participants will be enrolled. Participants with all other sequences of up to 2 prior ALK inhibitor(s) may be included in the Sub-cohort, and the number of participants will be limited to 20.

* Note 2: Participants who will be included in the Main Cohort of the refractory should have documented PD during treatment or within 30 days after discontinuation of treatment with alectinib.

6. Have at least 1 measurable (ie, target) lesion per RECIST version 1.1. Note: Previously irradiated lesions may not be used for target lesions, unless there is unambiguous radiological progression after radiotherapy. Brain lesions may not be used as target lesions if they were 1) previously treated with whole brain radiation therapy (WBRT) within 3 months, or 2) previously treated by stereotactic radiosurgery (SRS) or surgical resection.

7. Recovered from toxicities related to prior anticancer therapy to National Cancer Institute Common Terminology Criteria for Adverse Events (NCI CTCAE) version 4.03 Grade =\<1. Note: Treatment-related alopecia is allowed.

8. Have a life expectancy of \>=3 months.

9. Have adequate organ and hematologic function, as determined by:

1. Both alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\<2.5 times the upper limit of the normal range (ULN) (=\<5×ULN is acceptable if liver metastases are present).

2. Total serum bilirubin =\<1.5×ULN (\<3.0×ULN for participants with Gilbert syndrome).

4. Serum lipase =\<1.5×ULN and serum amylase =\<1.5×ULN.

5. Absolute neutrophil count (ANC) \>=1.5×10\^9/Liter (L).

6. Platelet count \>=75×10\^9/L.

7. Hemoglobin \>=9 gram (g)/ deciliter (dL).

8. Percutaneous oxygen saturation (SpO2) \>=94% without oxygen support. Participants who need oxygen support are excluded.

10. Have an Eastern Cooperative Oncology Group (ECOG) performance status of =\<2.

11. Must meet the following criteria:

1. Female participants who:

* Are postmenopausal for at least 1 year before the screening visit, OR

* Are surgically sterile, OR

* If they are of childbearing potential, agree to practice 1 highly effective non-hormonal method of contraception and 1 additional effective (barrier) method at the same time, from the time of signing the informed consent through 4 months after the last dose of study drug, OR

* Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the participant, from the time of signing the informed consent through 4 months after that last dose of study drug. (Periodic abstinence \[eg, calendar, ovulation, symptothermal, postovulation methods\], withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception. Female and male condoms should not be used together.)

2. Male participants, even if surgically sterilized (ie, status postvasectomy), who:

* Agree to practice effective barrier contraception during the entire study treatment period and through 4 months after the last dose of study drug, OR

* Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the participant, during the entire study treatment period and through 4 months after that last dose of study drug. (Periodic abstinence \[eg, calendar, ovulation, symptothermal, postovulation methods\], withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception. Female and male condoms should not be used together.)

12. Have the willingness and ability to comply with scheduled visit and study procedures.

What this study is about