Recent failures of clinical trials in Alzheimer's Disease underline the critical importance of identifying optimal intervention time to maximize cognitive benefit. While several models of disease progression have been proposed, we still lack quantitative approaches simulating the effect of treatment strategies on the clinical evolution. In this work, we present a data-driven method to model dynamical relationships between imaging and clinical biomarkers. Our approach allows simulating intervention at any stage of the pathology by modulating the progression speed of the biomarkers, and by subsequently assessing the impact on disease evolution. When applied to multi-modal imaging and clinical data from the Alzheimer's Disease Neu-roimaging Initiative our method enables to generate hypothetical scenarios of amyloid lowering interventions. Our results show that in a study with 1000 individuals per arm, accumulation should be completely arrested at least 5 years before Alzheimer's dementia diagnosis to lead to statistically powered improvement of clinical endpoints.