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The assumption that no subject's exposure affects another subject's outcome,known as the no-interference assumption, has long held a foundational positionin the study of causal inference. However, this assumption may be violated inmany settings, and in recent years has been relaxed considerably. Often thishas been achieved with either the aid of a known underlying network, or theassumption that the population can be partitioned into separate groups, betweenwhich there is no interference, and within which each subject's outcome may beaffected by all the other subjects in the group via the proportion exposed (thestratified interference assumption). In this paper, we instead consider acomplete interference setting, in which each subject affects every othersubject's outcome. In particular, we make the stratified interferenceassumption for a single group consisting of the entire sample. This can occurwhen the exposure is a shared resource whose efficacy is modified by the numberof subjects among whom it is shared. We show that a targeted maximum likelihoodestimator for the i.i.d.~setting can be used to estimate a class of causalparameters that includes direct effects and overall effects under certaininterventions. 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 applicationwhere we study the effect of a nurse-based triage system on the outcomes ofpatients receiving HIV care in Kenyan health clinics.

Causal Inference When Counterfactuals Depend on the Proportion of All Subjects Exposed