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Thank you for your suggestion. We agree with you that parental autistic disorders might increase the risk of ASD in children. In our study, we set all parental psychiatric disorders (ICD-10 codes F00-F99) including autism disorders (ICD-10 codes F84.0 F84.1, F84.5, F84.8 and F84.9) as potential confounding factors, and we adjusted for mother psychiatric disorders (including ASD) in model 1, and father psychiatric disorders (including ASD) in model 2. Besides, we also conducted sibling-matched analyses to control for shared family-related confounding factors like genetic liability for neuropsychiatric conditions.
It does not appear that you have considered the possibility of the parents, especially the fathers, being autistic themselves, in this study. We know that around 70% of autistics suffer mental health problems so it would follow that a there is a high likelihood of an autistic parent (who may or may not have a diagnosis themselves) might be on SSRI or other depression medication prior to conception. I would see this as a highly significant potential confounding factor to this study.