Brigatinib is a medicine that binds to the surface of tumor cells in some cancers and delivers a dose of chemotherapy directly to the tumor. In this study, participants will be people with non-small-cell lung cancer (NSCLC for short). The main aim of the study is to learn if brigatinib stops the tumors from growing, or if the tumors have shrunk or disappeared, compared to a medicine called alectinib.

At the first visit, the study doctor will check who can take part. Participants who can take part will be picked for 1 of 2 treatments by chance:

• Brigatinib tablets
• Alectinib capsules

All participants will take brigatinib or alectinib at about the same time every day. They will continue with treatment throughout the study unless their cancer gets worse, they have side effects from the treatment, they leave the study for certain reasons, or the study is stopped.

After stopping treatment, participants will visit the study clinic for a check-up 30 days later.

The drug being tested in this study is called brigatinib. Brigatinib has been demonstrated to benefit people with anaplastic lymphoma kinase-positive (ALK+) NSCLC.

The comparator drug is called alectinib. Alectinib has been demonstrated to benefit people with ALK+ NSCLC. Both drugs belong to a class of drugs called anaplastic lymphoma kinase (ALK) inhibitors. Both drugs are taken by mouth. Both drugs are approved by the United States Food and Drug Administration (US FDA).

The study will enroll approximately 246 participants. Participants will be randomly assigned (by chance, like flipping a coin) in 1:1 ratio to one of the two treatment groups:

• Brigatinib
• Alectinib

All participants will be asked to take brigatinib or alectinib at the same time each day throughout the study. For each participant eligible to continue in the study and to facilitate the remaining participants from Brigatinib-2002 (NCT03535740) to have continued treatment access, the study extension phase may be initiated for participants to continue receiving their randomized study treatment (i.e., brigatinib or alectinib) until they meet at least one of the treatment discontinuation criteria.

This multi-center trial will be conducted in the United States, Argentina, Austria, Canada, Chile, China, Croatia, France, Germany, Greece, Hong Kong, Italy, Mexico, Romania, Russia, South Korea, Spain, Sweden, Taiwan, and Thailand. The overall time to participate in this study is 5 years. Participants will make multiple visits to the clinic, and 30 days after last dose of study drug for a follow-up assessment.

Inclusion Criteria:

1. Have Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2.

2. Have histologically or cytologically confirmed stage IIIB (locally advanced or recurrent) or stage IV NSCLC.

3. Must meet one of the following criteria:

   • Have documentation of ALK rearrangement by a positive result from the Vysis ALK Break-Apart fluorescence in situ hybridization (FISH) Probe Kit or the Ventana ALK (D5F3) CDx Assay or Foundation Medicine's FoundationOne CDx.
   • Have documented ALK rearrangement by a different test and be able to provide tumor sample to the central laboratory. (Note: central laboratory ALK rearrangement testing results are not required to be obtained before randomization).

4. Had PD while on crizotinib, as assessed by the investigator or treating physician except for participants previously participating in the Brigatinib-2002 study (Note: crizotinib does not need to be the last therapy a participant received. The participant may have received chemotherapy as his/her last therapy).

5. Treatment with crizotinib for at least 4 weeks before progression except for participants previously participating in the Brigatinib-2002 study.

6. Have had no other ALK inhibitor other than crizotinib except for participants previously participating in the Brigatinib-2002 study.

7. Have had no more than 2 prior regimens of systemic anticancer therapy (other than crizotinib) in the locally advanced or metastatic setting. Note: a systemic anticancer therapy regimen will be counted if it is administered for at least 1 complete cycle. A new anticancer agent used as maintenance therapy will be counted as a new regimen. Neoadjuvant or adjuvant systemic anticancer therapy will be counted as a prior regimen if disease progression/recurrence occurred within 12 months upon completion of this neoadjuvant or adjuvant therapy. (Systemic therapy followed by maintenance therapy will be considered as one regimen if the maintenance therapy consists of a drug or drugs that were used in the regimen that immediately preceded maintenance).

8. Have at least 1 measurable (that is, target) lesion per RECIST v1.1.

9. Have recovered from toxicities related to prior anticancer therapy to national cancer institute common terminology criteria for adverse events (NCI CTCAE) version 4.03 grade less than or equal to (<=)1. (Note: treatment-related alopecia or peripheral neuropathy that are grade greater than (>) 1 are allowed, if deemed irreversible).

10. Have adequate organ function, at the time of initial screening, except for participants previously participating in the Brigatinib-2002 study as determined by:

    • Total bilirubin <=1.5 times the upper limit of normal (ULN).
    • Estimated glomerular filtration rate greater than equal to (>=) 30 milliliter per minute (mL/min)/1.73 square meter [m^2], using the modification of diet in renal disease equation.
    • Alanine aminotransferase (ALT)/aspartate aminotransferase (AST) <=2.5*ULN; <=5*ULN is acceptable if liver metastases are present.
    • Serum lipase <=1.5*ULN.
    • Platelet count >=75*10^9 per liter [/L].
    • Hemoglobin >=9 gram per deciliter (g/dL).
    • Absolute neutrophil count >=1.5*10^9 / L.

11. Suitable venous access for study-required blood sampling (that is, including pharmacokinetic [PK] and laboratory safety tests).

Exclusion Criteria:

1. Had participated in the control (crizotinib) arm of Study AP26113-13-301 (ALTA 1L) [NCT02737501].

2. Had received crizotinib within 7 days before randomization.

3. Have a history or presence at baseline of pulmonary interstitial disease, drug related pneumonitis, or radiation pneumonitis.

4. Have uncontrolled hypertension. Participants with hypertension should be under treatment for control of blood pressure upon study entry.

5. Had received systemic treatment with strong cytochrome P-450 (CYP) 3A inhibitors, moderate CYP3A inhibitors, strong CYP3A inducers, or moderate CYP3A inducers within 14 days before randomization.

6. Treatment with any investigational systemic anticancer agents within 14 days or 5 half-lives, whichever is longer, before randomization.

7. Have been diagnosed with another primary malignancy other than NSCLC, except for adequately treated nonmelanoma skin cancer or cervical cancer in situ; definitively treated nonmetastatic prostate cancer; or participants with another primary malignancy who are definitively relapse-free with at least 3 years elapsed since the diagnosis of the other primary malignancy.

8. Had received chemotherapy or radiation therapy within 14 days before randomization except for stereotactic radiosurgery (SRS) or stereotactic body radiation therapy.

9. Had received antineoplastic monoclonal antibodies within 30 days of randomization.

10. Had major surgery within 30 days of randomization. Minor surgical procedures, such as catheter placement or minimally invasive biopsies, are allowed.

11. Have symptomatic CNS metastases (parenchymal or leptomeningeal) at screening (participants with asymptomatic brain metastases or participants who have stable symptoms and did not require an increased dose of corticosteroids to control symptoms within 7 days before randomization will be enrolled). Note: If a participant has worsening neurological symptoms or signs due to CNS metastasis, the participant needs to complete local therapy and be neurologically stable (with no requirement for an increasing dose of corticosteroids or use of anticonvulsants) for 7 days before randomization.

12. Have current spinal cord compression (symptomatic or asymptomatic and detected by radiographic imaging). Participants with leptomeningeal disease and without cord compression are allowed.

13. Have significant, uncontrolled, or active cardiovascular disease, specifically including, but not restricted to the following:

    • Myocardial infarction within 6 months before randomization.
    • Unstable angina within 6 months before randomization.
    • New York Heart Association Class III or IV heart failure within 6 months before randomization.
    • History of clinically significant atrial arrhythmia (including clinically significant bradyarrhythmia), as determined by the treating physician.
    • Any history of clinically significant ventricular arrhythmia.

14. Had cerebrovascular accident or transient ischemic attack within 6 months before first dose of study drug.

15. Have malabsorption syndrome or other gastrointestinal illness or condition that could affect oral absorption of the study drug.

16. Have an ongoing or active infection, including but not limited to, the requirement for intravenous antibiotics.

17. Have a known history of human immunodeficiency virus (HIV) infection. Testing is not required in the absence of history.

18. Known hepatitis B surface antigen-positive, or known or suspected active hepatitis C infection. Testing is not required in the absence of history.

19. Any serious medical condition or psychiatric illness that could, in the investigator's opinion, potentially compromise participant safety or interfere with the completion of treatment according to this protocol.

20. Have a known or suspected hypersensitivity to brigatinib or alectinib or their excipients.

21. Life-threatening illness unrelated to cancer.

22. Female participants who are lactating and breastfeeding.

23. Admission or evidence of illicit drug use, drug abuse, or alcohol abuse.

Takeda provides access to the de-identified individual participant data (IPD) for eligible studies to aid qualified researchers in addressing legitimate scientific objectives (Takeda's data sharing commitment is available on https://clinicaltrials.takeda.com/takedas-commitment?commitment=5). These IPDs will be provided in a secure research environment following approval of a data sharing request, and under the terms of a data sharing agreement.

IPD from eligible studies will be shared with qualified researchers according to the criteria and process described on https://vivli.org/ourmember/takeda/. For approved requests, the researchers will be provided access to anonymized data (to respect patient privacy in line with applicable laws and regulations) and with information necessary to address the research objectives under the terms of a data sharing agreement.