Randomized experiments on social networks pose statistical challenges, due to the possibility of interference between units. We propose new methods for estimating attributable treatment effects in such settings. The methods do not require partial interference, but instead require an identifying assumption that is similar to requiring nonnegative treatment effects. Network or spatial information can be used to customize the test statistic; in principle, this can increase power without making assumptions on the data generating process.
During the past 20 years, social scientists using observational studies have generated a large and inconclusive literature on neighborhood effects. Recent workers have argued that estimates of neighborhood effects based on randomized studies of housing mobility, such as the “Moving to Opportunity” (MTO) demonstration, are more credible. These estimates are based on the implicit assumption of no interference between units; that is, a subject's value on the response depends only on the treatment to which that subject is assigned, not on the treatment assignments of other subjects. For the MTO studies, this assumption is not reasonable. Although little work has been done on the definition and estimation of treatment effects when interference is present, interference is common in studies of neighborhood effects and in many other social settings (e.g., schools and networks), and when data from such studies are analyzed under the “no-interference assumption,” very misleading inferences can result. Furthermore, ... Recently, there has been increasing interest in making causal inference when interference is possible. In the presence of interference, treatment may have several types of effects. In this article, we consider inference about such effects when the population consists of groups of individuals where interference is possible within groups but not between groups. A two-stage randomization design is assumed where in the first stage groups are randomized to different treatment allocation strategies and in the second stage individuals are randomized to treatment or control conditional on the strategy assigned to their group in the first stage. For this design, the asymptotic distributions of estimators of the causal effects are derived when either the number of individuals per group or the number of groups grows large. Under certain homogeneity assumptions, the asymptotic distributions provide justification for Wald-type confidence intervals (CIs) and tests. Empirical results demonstrate that the Wald CIs have good coverage in finite samples and are narrower than CIs based on either the Chebyshev or Hoeffding inequalities provided the number of groups is not too small. The methods are illustrated by two examples which consider the effects of cholera vaccination and an intervention to encourage voting.  A fundamental assumption usually made in causal inference is that of no interference between individuals (or units); that is, the potential outcomes of one individual are assumed to be unaffected by the treatment assignment of other individuals. However, in many settings, this assumption obviously does not hold. For example, in the dependent happenings of infectious diseases, whether one person becomes infected depends on who else in the population is vaccinated. In this article, we consider a population of groups of individuals where interference is possible between individuals within the same group. We propose estimands for direct, indirect, total, and overall causal effects of treatment strategies in this setting. Relations among the estimands are established; for example, the total causal effect is shown to equal the sum of direct and indirect causal effects. Using an experimental design with a two-stage randomization procedure (first at the group level, then at the individual level within groups), un...   Estimating the effects of interventions in networks is complicated when the units are interacting, such that the outcomes for one unit may depend on the treatment assignment and behavior of many or all other units (i.e., there is interference). When most or all units are in a single connected component, it is impossible to directly experimentally compare outcomes under two or more global treatment assignments since the network can only be observed under a single assignment. Familiar formalism, experimental designs, and analysis methods assume the absence of these interactions, and result in biased estimators of causal effects of interest. While some assumptions can lead to unbiased estimators, these assumptions are generally unrealistic, and we focus this work on realistic assumptions. Thus, in this work, we evaluate methods for designing and analyzing randomized experiments that aim to reduce this bias and thereby reduce overall error. In design, we consider the ability to perform random assignment to treatments that is correlated in the network, such as through graph cluster randomization. In analysis, we consider incorporating information about the treatment assignment of network neighbors. We prove sufficient conditions for bias reduction through both design and analysis in the presence of potentially global interference. Through simulations of the entire process of experimentation in networks, we measure the performance of these methods under varied network structure and varied social behaviors, finding substantial bias and error reductions. These improvements are largest for networks with more clustering and data generating processes with both stronger direct effects of the treatment and stronger interactions between units.  Interference is said to be present when the exposure or treatment received by one individual may affect the outcomes of other individuals. Such interference can arise in settings in which the outcomes of the various individuals come about through social interactions. When interference is present, causal inference is rendered considerably more complex, and the literature on causal inference in the presence of interference has just recently begun to develop. In this article we summarise some of the concepts and results from the existing literature and extend that literature in considering new results for finite sample inference, new inverse probability weighting estimators in the presence of interference and new causal estimands of interest. 