Peroxides also can react with molecules in the cell to form free radicals. Rats fed a high fat diet got less cancer if they were also given antioxidants. Cooking of fats turns them into peroxides. You can see this by the food getting brown. You can sometimes taste the peroxides as a bitter taste.
Unsaturated fats are more likely than saturated fats to be converted to peroxides during cooking.
Some data with rats indicates that saturated fats in the diet aren't as bad of a cancer risk as unsaturated fats. But either kind is worse than having low fat. Also, unsaturated fats are better for preventing heart disease. Note that cooked fats may be worse than uncooked. Some studies have suggested that fats from uncooked dairy products are not bad and for instance do not contribute to risk of breast cancer.