Excrement and debris from decomposing cockroach bodies are of just the right size to be lifted into the air, breathed onto the bronchial tubes, and recognized by the immune system — in certain people — as a signal to make an allergic reaction. As you know, the allergic reaction in the bronchial tubes is asthma.
Recently, a major, federally-funded research project looked for allergy producing substances in the homes of several hundred children with asthma living in several major cities across the United States. Specifically, they measured the amount of cat, dust mite, and cockroach allergen in the bedrooms of these children aged 4 to 9 years. The results were quite striking.