The goal of this clinical trial is to learn if the treatment by systemic Brigatinib (ALUNBRIG®) associated to local ablative therapy (LAT) treatment is improved if administered when the brigatinib works best in participants presenting an advanced non-small cells lung cancer with an ALK gene anomaly (this anomaly produces a defective protein that is responsible for the multiplication of cancer cells). This clinical trial is expected to involve 45 participants in several sites in France. Advanced non-small cell lung cancer (NSCLC) participants with ALK rearrangements treated with brigatinib in first line of non-curable setting will be screened. If the disease assessment done between 3 to 9 months after initiation of brigatinib shows: * a tumor response or stabilization (according to RECIST 1.1) * a disease which meets the definition of an oligometastatic disease (five metastatic lesions or less and a maximum of two lesions per organ) * all tumor targets are accessible to a local ablative therapy (confirmed by an expert panel of clinicians before inclusion): surgery, stereotactic radiosurgery (SRS). For liver, adrenal, or other metastases, percutaneous thermal ablation will be accepted. Participants will be asked to visit the clinic: * for eligibility criteria assessment prior to LAT * for LAT * every 8 weeks for checkups and tests the first year after LAT * and then every 12 weeks, for a maximum period of 3 years. Eligible patients will benefit from local ablative therapy with continuation of brigatinib.
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Progression free survival (PFS) centrally assessed
Timeframe: From the start date of treatment up to the disease progression as per central reading or for a maximum of 3 years.