Atherosclerosis is an inflammatory cardiovascular disease that leads to the formation of plaques inside arteries. The plaques result from the accumulation of lipidic substances over the years and could obstruct the blood flow to downstream vessels and organs. We aim to predict through Computational Fluid Dynamics (CFD) simulations the possible onset of carotid plaques and to analyze the influence of hemodynamic and geometric parameters on the early stages of the disease. The ultimate objective is to establish risk criteria, considering patient-specific geometric factors. We combine CFD simulations with a model for plaque growth including Low-Density Lipoprotein (LDL) accumulation (Gessaghi et al., 2011). In this model, ordinary differential equations describe the plaque growth depending on the wall shear stress and LDL concentration in the intima. The thickening of the intima normal to the wall towards the arterial lumen is considered through a morphing procedure. We found in our previous studies that this model accurately predicts the onset region of the disease and provides reasonable estimates of the plaque growth rate in the early stages of the pathology. In this study, we utilize a clinical dataset that includes 3D segmented geometries of the left and right carotids, as well as flow rate waveforms in the common, external, and internal carotid arteries. From patient-specific cases, we construct a parametric geometry to single out which of the various geometrical parameters describing the carotid bifurcation is responsible for arteriosclerotic plaque's potential onset and growth. Continuous response surfaces in the parameter space are obtained using stochastic collocation methods with sparse grids.