A Study of Brigatinib Compared to Alectinib in Adults With Non-Small-Cell Lung Cancer

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.