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The excess incidence of wheezing in smoking households appears to be largely non-atopic "wheezy bronchitis" with a relatively benign prognosis, but among children with established asthma, parental smoking is associated with more severe disease. This apparent paradox may be reconciled if environmental tobacco smoke is considered a co-factor provoking wheezing attacks, rather than a cause of the underlying asthmatic tendency.
Strachan et al. (Sun,) studied this question.