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.
The most common identifying assumption is that the units form groups (such as households or villages) that do not interfere with each other; this is termed partial interference @cite_18 . The paper @cite_1 derives unbiased point estimates under partial interference, and variance bounds on the estimation error under a stronger condition termed stratified interference. Asymptotically normal estimates are given in @cite_8 , again assuming stratified interference, and finite sample error bounds are derived in @cite_12 . For settings where partial interference does not apply, more general exposure models have been investigated by @cite_13 @cite_21 @cite_23 @cite_11 @cite_6 , with rigorous results if one assumes knowledge of the network dynamics, such as who influences whom. As a result, they may not be suitable when the underlying social mechanisms are not well understood. The recent paper @cite_15 also studies biased estimation of treatment effects under weaker assumptions than partial or fully modeled interference, which is similar in spirit to this present work.
@cite_18 @cite_8 @cite_21 @cite_1 @cite_6 @cite_23 @cite_15 @cite_13 @cite_12 @cite_11
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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. 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. Despite being ubiquitous in practice, the performance of maximal-ratio combining (MRC) in the presence of interference is not well understood. Because the interference received at each antenna originates from the same set of interferers but partially decorrelates over the fading channel, it possesses a complex correlation structure. This paper develops a realistic analytic model that accurately accounts for the interference correlation using stochastic geometry. Modeling interference by a Poisson shot noise process with independent Nakagami fading, we derive the link success probability for dual-branch interference-aware MRC. Using this result, we show that the common assumption that all receive antennas experience equal interference power underestimates the true performance, although this gap rapidly decays with increasing the Nakagami parameter @math of the interfering links. In contrast, ignoring interference correlation leads to a highly optimistic performance estimate for MRC, especially for large @math . In the low outage probability regime, our success probability expression can be considerably simplified. Observations based from the analysis include the following: 1) For small path loss exponents, MRC and minimum mean square error combining exhibit similar performance, and 2) the gains of MRC over selection combining are smaller in the interference-limited case than in the well-studied noise-limited case.