Additional Study Information: The purpose of this study is to compare the effects, good or bad, of drugs alectinib and crizotnib on patients with lung disease to find out which is better for patients with a special type of non-small cell lung cancer (NSCLC) that is called anaplastic lymphoma kinase (ALK)-positive NSCLC. In this study, participants will receive either alectinib or crizotnib. Study procedures also include, MRI scans, cancer tissue collections, blood and urine samples as well as other psychical examinations.