LEvetiracetam to Prevent Seizures in Symptomatic Alzheimer's Disease in Adults With Down Syndrome

This study is a clinical trial that will examine the efficacy and safety of a medication called levetiracetam in people with Down syndrome and Alzheimer's disease. Adults with Down syndrome have a high risk of developing Alzheimer's disease. Epilepsy frequently coexists in these patients, and is associated with a worse clinical outcome. The early dysfunction of inhibitory interneuronal circuits, found in epilepsy, contributes to cognitive decline in Alzheimer's disease patients. Modifying this abnormal activity with levetiracetam could have potential benefits in the treatment of Alzheimer's disease, beyond its benefits on epileptic seizures' control and interictal epileptic activity recorded on EEG. Levetiracetam is a widely used drug with a proven safety profile, with more than 20 years of commercialization. This trial will evaluate the preventive benefit on the development of epileptic seizures in Alzheimer's disease associated with Down syndrome and, secondarily, its effect on cognitive decline and Alzheimer's disease markers. If the described benefits of levetiracetam use are independent of its antiepileptic effect, it could be a drug with a potential disease-modifying effect in Alzheimer's disease. Primary objective: To evaluate the efficacy of levetiracetam as a preventive measure for bilateral tonic-clonic seizures at 96 weeks in adults with Alzheimer's disease associated with Down syndrome. Secondary objectives: 1. To quantify the time to the first bilateral tonic-clonic seizure between groups (levetiracetam vs. placebo). 2. To evaluate the incidence of mortality between groups (levetiracetam vs. placebo). 3. To study changes in biomarkers related to Alzheimer's disease: 1. Functional changes (CAMDEX-DS) 2. Cognitive changes (CAMCOG, mCRT) 3. Plasma biomarkers (217-pTau, NfL) 4. Brain structure (cortical thickness, hippocampal volume, gray matter volume) 5. Epileptiform activity (EEG) 4. Safety: Incidence of adverse events and serious adverse events in the LEV vs. placebo groups. A total of 120 participants will be included (60 per group). The dose of levetiracetam to be used in this clinical trial is 1000 mg/day (two doses of 500mg each 12 hours) orally. During the first 4 weeks of the treatment period, LEV, treatment will be administered 500mg/d (250mg/12h) to facilitate the compliance. During the last 4 weeks of the treatment period, LEV will be administered 500mg/d (250mg/12h) to enable a gradual withdrawal. Participants in placebo arm will receive placebo 1 capsule/12h during the 96 weeks of the treatment period. The patients will have a total of 12 medical visits during their participation in the study. In those visits the following medical procedures will be carried out: * Neuropsychological evaluation * Blood analysis * Magnetic resonance imaging (MRI) * Electroencephalogram (EEG) This study not only aims to improve the health and quality of life of people with Down syndrome but also to advance our general understanding of Alzheimer's disease, which could benefit more patients in the future.