There is a well-established link between fat intake and heart disease and stroke risk. Diets rich in saturated fat and trans fat (both "bad" fats) raise blood cholesterol concentrations, contributing to clogged arteries that block the flow of oxygen-rich blood to the heart and brain.
The worst type of dietary fat is the kind known as trans fat. It is a byproduct of a process called hydrogenation that is used to turn healthy oils into solids and to prevent them from becoming rancid. Trans fats have no known health benefits and that there is no safe level of consumption.