A Study to Compare the Efficacy and Safety of Entrectinib and Crizotinib in Participants With Advanced or Metastatic ROS1 Non-small Cell Lung Cancer (NSCLC) With and Without Central Nervous System (CNS) Metastases

Inclusion Criteria: * Histologically or cytologically-confirmed diagnosis of advanced or recurrent (Stage IIIB/C not amenable for radical treatment) or metastatic (Stage IV) NSCLC that harbors a documented ROS1 gene rearrangement. * No prior treatment with a ROS1 tyrosine kinase inhibitor, chemotherapy or other systemic therapy for advanced or recurrent (Stage IIIB/C not amenable for radical treatment) or metastatic (Stage IV) NSCLC * Prior radiotherapy is allowed if more than 14 days have elapsed between the end of treatment and randomization * Measurable systemic disease according to RECIST v1.1 * Participants with measurable and non-measurable CNS lesions per RECIST v1.1, including leptomeningeal carcinomatosis * Life expectancy of at least 12 weeks * Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2 * Adequate hematologic, renal, liver functions * Participants must have recovered from effects of any major surgery or significant traumatic injury at least 28 days before the first dose of study treatment * Ability to swallow entrectinib and crizotinib intact without chewing, crushing, or opening the capsules * For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods with a failure rate of \<1% per year during the treatment period and for up to 5 weeks after the last dose of entrectinib or for at least 90 days after the last dose of crizotinib * For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, and agreement to refrain from donating sperm. Exclusion Criteria: * Prior treatment with a ROS1 tyrosine kinase inhibitor, chemotherapy or other systemic therapy for advanced or recurrent (Stage IIIB/C not amenable for radical treatment) or metastatic (Stage IV) NSCLC * NCI-CTCAE v5.0 Grade 3 or higher toxicities due to any prior therapy (excluding alopecia, fatigue, nausea and lack of appetite), which have not shown improvement and are strictly considered to interfere with current study drug * History of recent (within the past 3 months) symptomatic congestive heart failure or ejection fraction ≤ 50% observed during screening for the study * History of prolonged corrected QTc interval * Peripheral sensory neuropathy ≥ Grade 2 * Known interstitial lung disease, interstitial fibrosis, or history of tyrosine kinase inhibitor-induced pneumonitis * Previous malignancy within the past 3 years * Incomplete recovery from any surgery prior to the start of study treatment * Active GI disease (e.g., Crohn's disease, ulcerative colitis or short gut syndrome) or other malabsorption syndrome that would reasonably impact drug absorption * History of prior therapy-induced pneumonitis * Any condition (in the past 3 months) e.g., myocardial infarction, unstable angina, coronary/peripheral artery bypass graft, cerebrovascular accident or transient ischemic attack, stroke, symptomatic bradycardia, or uncontrolled arrhythmias requiring medication * Known active infections (bacterial, fungal or viral, including human immunodeficiency virus positive) * History of hypersensitivity to any of the additives in the entrectinib and/or crizotinib drug formulations * Pregnant or lactating women * Known human immunodeficiency virus (HIV) positivity or acquired immunodeficiency syndrome (AIDS)-related illness * Any clinically significant concomitant disease or condition that could interfere with, or for which the treatment might interfere with, the conduct of the study or the absorption of oral medications.