Volume 5, Issue 1 -

Estimating the effects of interventions in networks is complicated due to interference, such that the outcomes for one experimental unit may depend on the treatment assignments of other units. Familiar statistical formalism, experimental designs, and analysis methods assume the absence of this interference, and result in biased estimates of causal effects when it exists. While some assumptions can lead to unbiased estimates, these assumptions are generally unrealistic in the context of a network and often amount to assuming away the interference. In this work, we evaluate methods for designing and analyzing randomized experiments under minimal, realistic assumptions compatible with broad interference, where the aim is to reduce bias and possibly overall error in estimates of average effects of a global treatment. 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; these conditions also give lower bounds on treatment effects. 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 reductions and, despite a bias–variance tradeoff, 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.

Standard causal mediation analysis decomposes the total effect into a direct effect and an indirect effect in settings with only one single mediator. Under the settings with multiple mediators, all mediators are often treated as one single block of mediators. The effect mediated by a certain combination of mediators, i. e. path-specific effect (PSE), is not always identifiable without making strong assumptions. In this paper, the authors propose a method, defining a randomly interventional analogue of PSE (rPSE), as an alternative approach for mechanism investigation. This method is valid under assumptions of no unmeasured confounding and allows settings with mediators dependent on each other, interaction, and mediator-outcome confounders which are affected by exposure. In addition, under linearity and no-interaction, our method has the same form of traditional path analysis for PSE. Furthermore, under single mediator without a mediator-outcome confounder affected by exposure, it also has the same form of the results of causal mediation analysis. We also provide SAS code for settings of linear regression with exposure-mediator interaction and perform analysis in the Framingham Heart Study dataset, investigating the mechanism of smoking on systolic blood pressure as mediated by both cholesterol and body weight. Allowing decomposition of total effect into several rPSEs, our method contributes to investigation of complicated causal mechanisms in settings with multiple mediators.

Covariate balance is a conventional key diagnostic for methods estimating causal effects from observational studies. Recently, there is an emerging interest in directly incorporating covariate balance in the estimation. We study a recently proposed entropy maximization method called Entropy Balancing (EB), which exactly matches the covariate moments for the different experimental groups in its optimization problem. We show EB is doubly robust with respect to linear outcome regression and logistic propensity score regression, and it reaches the asymptotic semiparametric variance bound when both regressions are correctly specified. This is surprising to us because there is no attempt to model the outcome or the treatment assignment in the original proposal of EB. Our theoretical results and simulations suggest that EB is a very appealing alternative to the conventional weighting estimators that estimate the propensity score by maximum likelihood.

We study the framework for semi-parametric estimation and statistical inference for the sample average treatment-specific mean effects in observational settings where data are collected on a single network of possibly dependent units (e.g., in the presence of interference or spillover). Despite recent advances, many of the current statistical methods rely on estimation techniques that assume a particular parametric model for the outcome, even though some of the important statistical assumptions required by these methods are often violated in observational network settings. In this work we rely on recent methodological advances in the field of targeted maximum likelihood estimation (TMLE) and describe an estimation approach that permits for more realistic classes of data-generative models while providing valid inference in the context of observational network-dependent data. We start by assuming that the true data-generating distribution belongs to a large class of semi-parametric statistical models. We then impose some restrictions on the possible set of such distributions. For example, we assume that the dependence among the observed outcomes can be fully described by an observed network. We then show that under our modeling assumptions, our estimand can be described as a functional of the mixture of the observed data-generating distribution. With this key insight in mind, we describe the TMLE for possibly-dependent units as an iid data algorithm and we demonstrate the validity of our approach with a simulation study. Finally, we extend prior work towards estimation of novel causal parameters such as the unit-specific indirect and direct treatment effects under interference and the effects of interventions that modify the structure of the network.

The management of chronic conditions is characterized by frequent re-assessment of therapy decisions in response to the patient’s changing condition over the course of the illness. Evidence most suitable to inform care thus often concerns the contrast of adaptive treatment strategies that repeatedly personalize treatment decisions over time using the latest accumulated data available from the patient’s previous clinic visits such as laboratory exams (e.g., hemoglobin A1c measurements in diabetes care). The frequency at which such information is monitored implicitly defines the causal estimand that is typically evaluated in an observational or randomized study of such adaptive treatment strategies. Analytic control of monitoring with standard estimation approaches for time-varying interventions can therefore not only improve study generalizibility but also inform the optimal timing of clinical surveillance. Valid inference with these estimators requires the upholding of a positivity assumption that can hinder their applicability. To potentially weaken this requirement for monitoring control, we introduce identifiability results that will facilitate the derivation of alternate estimators of effects defined by general joint treatment and monitoring interventions in the context of time-to-event outcomes. These results are developed based on the nonparametric structural equation modeling framework using a no direct effect assumption originally introduced in a prior paper that inspired this work. The relevance and scope of the results presented here are illustrated with examples in diabetes comparative effectiveness research.

This note illustrates, using simple examples, how causal questions of non-trivial character can be represented, analyzed and solved using linear analysis and path diagrams. By producing closed form solutions, linear analysis allows for swift assessment of how various features of the model impact the questions under investigation. We discuss conditions for identifying total and direct effects, representation and identification of counterfactual expressions, robustness to model misspecification, and generalization across populations.