In toxicology analyses, 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.
Thus 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, since the lower dose means include the less healthy pups
that would not survive if exposed to a higher level of toxin.
This analysis uses 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.