Conceptus viability, malformation, and suspect mutagens or teratogens in humans. The Yule–Simpson paradox and implications for inferences of causality in studies of mutagenicity or teratogenicity limited to human livebirths

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Abstract
If a genetic disorder or a congenital malformation is associated with embryonic or fetal death, then this may distort reported associations of environmental or biological factors with genetic and congenital disorders. We illustrate how such distortion may occur in humans as a manifestation of the Yule–Simpson (or Simpson) statistical paradox. We analyze the reported negative association of maternal smoking and Down syndrome in livebirths and demonstrate that under plausible conditions, valid negative associations both in livebirths and in embryonic or fetal deaths can occur, despite the fact that in all conceptuses there may be no association whatsoever. A similar analogous manifestation of the Yule–Simpson paradox may hold for positive associations. That is, positive relative risks may occur for an alleged mutagen or teratogen in separate studies both of livebirths, and of embryonic and fetal deaths, despite the absence of any effect in all conceptuses. These considerations illustrate the need for data on genetic disorders and malformations in embryonic and fetal deaths, and the need for a synthesis of such data with those from studies in livebirths before valid inferences may be made about mutagenic or teratogenic effects of environmental or biological factors.

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