Effect of CAFfeine on Cognition in Alzheimer's Disease

Inclusion Criteria: * Age ≥ 50 at screening * Probable Alzheimer dementia according to the criteria of the National Institute on Aging-Alzheimer's Association; diagnosis must be supported by brain imaging (CT or MRI) and blood test (including ionogram, kidney and liver function, calcemia, CRP, TSH, B12 vitamins and folates) performed in routine care * MMSE score ≥16 * Presence of an informant and caregiver, living with the patient * IAChE and/or Memantine treatment non-compulsory ; If implemented it must be effective and stable for 2 months before the selection visit and must remain stable for the duration of the study Exclusion Criteria: * Patients who refuse to adopt a low caffeine diet (eviction of tea, caffeinated sodas, chocolate in large quantities) * Current major depressive episode according to DSM-5 criteria * Another chronic pathology of the central nervous system * Major anxiety according to the clinician (consistent with the corresponding nPI-R items that must indicate a severity \>2 and an impact \>3) * Sleep disorders defined by severity and an impact on NPI-R; a patient fitted for OSA may be included if the device has been in use for 3 months and well tolerated (stable) * Decompensated heart disease or severe rhythm disorder (excluding slow, treated and stable chronic atrial fibrillation) * Active smoking * For childbearing women : pregnancy in progress or planned (A pregnancy test will be performed) * Patients who take forbidden treatment : * Psychotropi…