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Elliott, Michael R., M.M. Joffe, and Z. Chen. 2006. "A potential outcomes approach to developmental toxicity analyses." Biometrics, 62(2), 352-360.
Estimating the effects of a toxin on fetal development in animal models such as mice can be problematic, because the number of pups that develop and survive until birth may simultaneously affect developmental outcomes such as birth weight and be affected by the introduction of a toxin into the fetal environment. Also, comparing pups that survived until birth at a high dose of the toxin with pups that survived at low doses may underestimate the effect of the toxin, because the lower dose means include the less healthy pups that would not survive if exposed to a higher level of toxin. We consider this problem in a potential outcomes framework that defines the effect of the dose on the outcome as the difference between what the outcome would have been for a pup had the dam in which the pup develops been exposed to dose level Z = z* rather than dose level Z = z. To disentangle the direct effect of dose from the effect of litter size, we focus on effects defined within principal strata that are a function of the survival status of the pups at each of the possible dose levels. A unique contribution to the potential outcomes literature is that we allow the outcome for a subject to be dependent on the principal stratum to which other subjects within a cluster belong.