Phase I/II Trial of Alectinib and Bevacizumab in Patients With Advanced, Anaplastic Lymphoma Kinase (ALK)-Positive, Non-Small Cell Lung Cancer

Inclusion Criteria: * Histologically or cytologically confirmed advanced, non-squamous, non-small cell lung cancer. * Molecular confirmation of an ALK rearrangement. * Age ≥ 18 years old. * Life expectancy \> 12 weeks. * Performance status 0-2. * Adequate hematologic function: * Adequate renal function: * An estimated Glomerular Filtration Rate (eGFR) of at least 45 mL/min/1.73 m2 * International normalized ration (INR)≤ 1.5 * Partial thromboplastin time (PTT) ≤1.5 x upper limit of normal (ULN) * For all females of childbearing potential, a negative pregnancy test must be obtained within 3 days before starting study treatment. * Able and willing to provide written informed consent * Phase II Only: * Presence of at least one measurable central nervous system (CNS) target lesion (At least 5 mm in size) * Lesions must be untreated or progressive according to Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 after previous local therapy. * Participants who are receiving corticosteroids must be on a stable or decreasing dose * At least one measurable extra-CNS lesion based upon RECIST version 1.1. Exclusion Criteria: * Squamous cell histology or mixed, predominantly squamous adenosquamous carcinoma * Previous history of haemoptysis * Tumour infiltrating into large vessels or infiltrating into the proximal tracheobronchial network * Unstable, symptomatic brain metastases. * History of hemorrhagic CNS metastases * History of intracranial hemorrhage (either by clinical history or neuroimaging) * History of or genetic predisposition to a bleeding diathesis or coagulopathy * Therapeutic anticoagulation * Current or recent (within 10 days of first dose of bevacizumab) use of aspirin (\> 325 mg/day) * Clinically significant heart disease (i.e., active), stroke or myocardial infarction within 6 months prior to enrolment, unstable angina pectoris, congestive heart failure of grade \> II according to the New York Heart Association (NYHA), or cardiac arrhythmia requiring specific treatment * Arterial or venous thromboembolic events within 6 months of study enrollment. * Poorly controlled arterial hypertension (systolic \> 150 mm Hg and/or diastolic \> 100 mm Hg) * Invasive surgical intervention within 28 days prior to the start of treatment * Minor surgical intervention, including placement of a permanent catheter within 24 hours prior to the first infusion of bevacizumab. * Non-healing wound, active peptic ulcer or bone fracture. * Previous history of abdominal fistula, tracheoesophageal fistula or other fistula with grade 4 severity, gastrointestinal perforation or intra-abdominal abscess within 6 months prior to enrolment. * Proteinuria at baseline. * Previous anti-angiogenic treatment * Patients previously treated with alectinib (Phase II only). * Radical radiotherapy to the thorax with curative intent within 28 days * Cytotoxic chemotherapy within 21 days prior to enrolment. * Treatment with crizotinib within 7 days prior to enrolment. For all other ALK Tyrosine kinase inhibitors (TKIs), the washout period should be ≥5 half-lives prior to enrolment. * Any GI disorder that may affect absorption of oral medications * Alanine transaminase (ALT) or aspartate transaminase (AST) \> 3 × ULN (≥5 × ULN for patients with concurrent liver metastasis) * Impaired excretory function (e.g., hyperbilirubinemia) or synthetic function or other conditions of decompensated liver disease such as coagulopathy, hepatic encephalopathy, hypoalbuminemia, ascites, and bleeding from esophageal varices * Acute viral or active autoimmune, alcoholic, or other types of hepatitis * National Cancer Institute Common Terminology Criteria for Adverse Events (NCI CTCAE) (version 4.0) Grade 3 or higher toxicities due to any prior therapy (e.g. radiotherapy) (excluding alopecia), * History of organ transplant. * Co-administration of anti-cancer therapies other than those administered in this study. * QTc \> 470 ms or patients with symptomatic bradycardia. * Administration of strong/potent cytochrome P450 (CYP)3A inhibitors or inducers within 14 days * Administration of agents with potential QT interval prolonging effects within 14 days prior to the first administration of study drug and while on treatment. * History of hypersensitivity to any of the additives in the alectinib drug formulation * Documented allergy or hypersensitivity to monoclonal antibodies (bevacizumab) * History of drug-induced pneumonitis or hypersensitivity pneumonitis from prior ALK TKI therapy. * Pregnant or lactating women. * Known HIV positivity or AIDS-related illness. * Any condition or illness that could compromise patient safety or interfere with the evaluation of the study drugs.