Quite a few people are allergic to eggs, but I believe this is because they are cooked. When you heat the egg, the protein changes its chemical shape, and this type of distortion can easily lead to allergies. When consumed in their raw state, the incidence of egg allergy virtually disappears.
This distortion may be further magnified depending on the manner in which it's cooked. Microwaves heat food by causing water molecules in it to resonate at very high frequencies and eventually turn to steam, which heats your food. But it also changes your food's chemical structure in ways that regular cooking does not.
It is my belief that eating eggs raw helps preserve many of the highly perishable nutrients, and the results in the featured study confirms this as raw egg yolk lost about half of its antioxidant potential when boiled, fried, or worse, microwaved.
Remember that most of the nutrition in an egg is in the yolk, not the white which is merely protein and many have a texture problem when eating them raw. The yolk on the other hand is loaded with nutrients, like bioflavonoids, brain fats like phosphatidyl choline, powerful antioxidants and sulfur. I have four raw egg yolks almost every day and throw away the whites as I don't need the extra protein, but one can soft boil or poach them I personally put my raw egg yolks over a bed of dehydrated kale and cucumber pulp left over from juicing, along with a whole avocado and some chopped red onions.
If you choose not to eat your eggs raw, poached or soft-boiled is your next best option. Aside from microwaving, scrambling your eggs is one of the worst ways to cook them as it oxidizes the cholesterol in the egg yolk, which may in fact harm your health.