  When there is interference, a subject's outcome depends on the treatment of
others and treatment effects may take on several different forms. This
situation arises often, particularly in vaccine evaluation. In settings where
interference is likely, two-stage cluster randomized trials have been suggested
as a means of estimating some of the causal contrast of interest. Working in
the finite population setting to investigate rare and unplanned subgroup
analyses using some of the estimators that have been suggested in the
literature, include Horvitz-Thompson, Hajek, and what might be called the
natural extension of the marginal estimators suggested in Hudgens and Halloran
2008. I define the estimands of interest conditional on individual, group and
both individual and group baseline variables, giving unbiased Horvitz-Thompson
style estimates for each. I also provide variance estimators for several
estimators. I show that the Horvitz-Thompson (HT) type estimators are always
unbiased provided at least one subject within the group or population, whatever
the level of interest for the estimator, is in the subgroup of interest. This
is not true of the "natural" or the Hajek style estimators, which will often be
undefined for rare subgroups.
