A study of 102,000 children found that children with asthma have a higher rate of ADHD, depression, and learning disabilities than children without asthma. The more severe the asthma, the more severe the symptoms of ADHD, depression, and LD.
The researchers point out this may be partly due to the fact that children with asthma are more likely to be bullied, and children with asthma are more likely to abuse drugs. (Whether they are more likely to abuse drugs due to the fact that they are ADHD or depressed was not addressed).
Blackman, J. & Gurka, M. (2007). Developmental and behavioral comorbidities of asthma in children. Journal of Developmental and Behavioral Pediatrics28(2), 92-99.