Antibiotic Duration and Outcomes in High-Risk Febrile Neutropenia Patients

The goal of this clinical trial is to learn if a personalized duration of antibiotic therapy, based on clinical stability, is as effective as a standard duration of at least 10 days in hospitalized patients with hematologic malignancies (such as leukemia or lymphoma) who develop febrile neutropenia and Gram-negative bacteraemia. The main questions it aims to answer are: * Can a personalized antibiotic duration increase the number of days free from anti-Gram-negative therapy within 28 days without compromising patient safety? * How does the duration of antibiotic therapy (short vs. prolonged) affect the rate and modality of gut microbiota reconstitution? Researchers will compare: * Group A (Personalized Duration): Antibiotics are stopped after the patient maintains clinical stability (no fever and stable vital signs) for 72 consecutive hours. * Group B (Standard of Care): Antibiotics are continued for a standard duration, typically at least 10 days, based on current clinical surveys and physician decision. Participants will: * Be randomized to receive either the personalized or the standard duration of antibiotic therapy once a Gram-negative infection is confirmed in the blood. * Be monitored for 28 days to assess for new fever episodes, recurrence of infection, and overall survival. * If participating in the microbiological sub-study, provide biological samples (blood, feces, and rectal swabs) at specific time points (at the onset of fever, at the end of treatment, and at day 28). * Undergo specialized laboratory testing (Whole Metagenomic Sequencing) on the collected samples to evaluate the evolution of their intestinal and blood microbiota and the presence of antibiotic-resistant genes.