Hospital-acquired infections, most of which are caused by Gram-negative bacteria, are common in intensive care units and have a major impact on patient prognosis. Patient survival in severe sepsis and septic shock depends on the early administration of appropriate antibiotic therapy, with mortality increasing by 7.6% for each hour of delay, justifying the probabilistic use of broad-spectrum antibiotics such as ceftazidime, an essential betalactamine, particularly used for its activity against Pseudomonas aeruginosa, a frequent pathogen in nosocomial infections.

It is currently recommended that ceftazidime should initially be administered as a 2g loading dose, followed by maintenance treatment by continuous infusion, at a dose adapted to renal function.

The recommended dosage regimen, with its 2g loading dose, was developed using the median value of parameters from a pharmacokinetic model. This explains the findings of many critical care studies, which have found that 40-60% of patients initially have concentrations below target with the recommended dosing regimen.

In the context of critical care, maintaining concentrations within the target therapeutic range is difficult due to variations in the elimination clearance of ceftazidime. Ceftazidime is mainly eliminated by the kidneys. Critical patients may have increased glomerular filtration rate, or, conversely, impaired renal function, with rapid variations in the event of severe infection. This leads to high intra- and inter-individual variability, and increases the risk of antibiotic under- or overdose when the maintenance dose is administered at a fixed dose (6g/d continuously). This high variability can also be observed in the volume of distribution (capillary leakage, oedema, perfusion volumes, effusions ...).

In order to propose an individualised dosing regimen, we therefore propose an iterative randomised study to :

• Step 1: FORTOPTIM_1 Evaluation of an optimised dosage regimen based on literature data compared with the standard psological regimen.
• Step 2: FORTOPTIM_2 Build a pharmacokinetic model from the prospective data obtained in step 1. Based on this model, an individualised dosage regimen (loading dose and maintenance dose) will be obtained for step 3.
• Step 3: FORTOPTIM_3 Prospectively evaluate in a randomised trial the individualised dosing regimen previously defined (Step 2) by comparing it to the best dosing regimen determined in Step 1 or to the standard dosing regimen if there is no significant difference in Step 1.

Inclusionn criteria:

• Patient hospitalized in intensive care unit for an expected duration of at least 72 hours, with an infection for which initiation of ceftazidime therapy is being considered.
• Patient with an arterial catheter for blood sampling.
• Patients affiliated to or entitled under a social security scheme.

Exclusion Criteria:

• Pregnant woman, parturient, nursing mother;
• Person deprived of liberty, hospitalized without consent,
• Adults under legal protection (guardianship-curatorship)
• Patients undergoing extra-renal purification or whose CKD-EPI at the start of treatment is less than 15 ml/min.