  The assumption that no subject's exposure affects another subject's outcome,
known as the no-interference assumption, has long held a foundational position
in the study of causal inference. However, this assumption may be violated in
many settings, and in recent years has been relaxed considerably. Often this
has been achieved with either the aid of a known underlying network, or the
assumption that the population can be partitioned into separate groups, between
which there is no interference, and within which each subject's outcome may be
affected by all the other subjects in the group via the proportion exposed (the
stratified interference assumption). In this paper, we instead consider a
complete interference setting, in which each subject affects every other
subject's outcome. In particular, we make the stratified interference
assumption for a single group consisting of the entire sample. This can occur
when the exposure is a shared resource whose efficacy is modified by the number
of subjects among whom it is shared. We show that a targeted maximum likelihood
estimator for the i.i.d.~setting can be used to estimate a class of causal
parameters that includes direct effects and overall effects under certain
interventions. This estimator remains doubly-robust, semiparametric efficient,
and continues to allow for incorporation of machine learning under our model.
We conduct a simulation study, and present results from a data application
where we study the effect of a nurse-based triage system on the outcomes of
patients receiving HIV care in Kenyan health clinics.
