On inverse probability-weighted estimators in the presence of interference

Revisiting the effects of maternal education on adolescents' academic performance: Doubly robust estimation in a network-based observational study

In many contexts, particularly when study subjects are adolescents, peer effects can invalidate typical statistical requirements in the data. For instance, it is plausible that a student's academic performance is influenced both by their own mother's educational level as well as that of their peers. Since the underlying social network is measured, the Add Health study provides a unique opportunity to examine the impact of maternal college education on adolescent school performance, both direct and indirect. However, causal inference on populations embedded in social networks poses technical challenges, since the typical no interference assumption no longer holds. While inverse probability-of-treatment weighted (IPW) estimators have been developed for this setting, they are often highly unstable. Motivated by the question of maternal education, we propose doubly robust (DR) estimators combining models for treatment and outcome that are consistent and asymptotically normal if either model is correctly specified. We present empirical results that illustrate the DR property and the efficiency gain of DR over IPW estimators even when the treatment model is misspecified. Contrary to previous studies, our robust analysis does not provide evidence of an indirect effect of maternal education on academic performance within adolescents' social circles in Add Health.

Physical activity across midlife and health-related quality of life in Australian women: A target trial emulation using a longitudinal cohort

BACKGROUND

There is little long-term causal evidence on the effect of physical activity on health-related quality of life. This study aimed to examine the associations between longitudinal patterns of physical activity over 15 years and health-related quality of life in both the physical and mental health domains, in a cohort of middle-aged Australian women.

METHODS AND FINDINGS

We used data collected at 3-year intervals (1998 to 2019) from 11,336 participants in the Australian Longitudinal Study on Women's Health (ALSWH) (1946 to 1951 birth cohort). Primary outcomes were the physical (PCS) and mental health component summary (MCS) scores (range from 0 to 100; higher scores indicate higher perceived physical/mental health) from the SF-36 in 2019 (when women aged 68 to 73 years). Using target trial emulation to imitate a randomized controlled trial (RCT), we tested 2 interventions: (1) meeting the World Health Organization (WHO) physical activity guidelines consistently throughout the 15-year "exposure period" (2001 to 2016; when women aged 50-55 to 65-70 years; physical activity assessed every 3 years); and (2) not meeting the guidelines at the beginning of the exposure period but starting to first meet the guidelines at age 55, 60, or 65; against the control of not meeting the guidelines throughout the exposure period. Analysis controlled for confounding using marginal structural models which were adjusted for sociodemographic and health variables and conditions. Consistent adherence to guidelines during the exposure period (PCS: 46.93 [99.5% confidence interval [CI]: 46.32, 47.54]) and first starting to meet the guidelines at age 55 (PCS: 46.96 [99.5% CI: 45.53, 48.40]) were associated with three-point higher PCS (mean score difference: 3.0 [99.5% CI: 1.8, 4.1] and 3.0 [99.5% CI:1.2, 4.8]) than consistent non-adherence (PCS: 43.90 [99.5% CI: 42.79, 45.01]). We found a similar pattern for most SF-36 subscales but no significant effects of the interventions on MCS. The main limitations of the study were that it may not account for all underlying health conditions and/or other unmeasured or insufficiently measured confounders, the use of self-reported physical activity and that findings may not be generalizable to all mid-age women.

CONCLUSIONS

Results from the emulated RCT suggest women should be active throughout mid-age, ideally increasing activity levels to meet the guidelines by age 55, to gain the most benefits for physical health in later life.

Livestock, pathogens, vectors, and their environment: A causal inference-based approach to estimating the pathway-specific effect of livestock on human African trypanosomiasis risk

Livestock are important reservoirs for many zoonotic diseases, however the effects of livestock on human and environmental health extend well beyond direct disease transmission. In this retrospective ecological cohort study we use pre-existing data and the parametric g-formula, which imputes potential outcomes to quantify mediation, to estimate three hypothesized mechanisms by which livestock can influence human African trypanosomiasis (HAT) risk: the reservoir effect, where infected cattle and pigs are a source of infection to humans; the zooprophylactic effect, where preference for livestock hosts exhibited by the tsetse fly vector of HAT means that their presence protects humans from infection; and the environmental change effect, where livestock keeping activities modify the environment in such a way that habitat suitability for tsetse flies, and in turn human infection risk, is reduced. We conducted this study in four high burden countries: at the point level in Uganda, Malawi, and Democratic Republic of Congo (DRC), and at the county level in South Sudan. Our results indicate cattle and pigs play a reservoir role for the rhodesiense form (rHAT) in Uganda (rate ratio (RR) 1.68, 95% CI 0.84, 2.82 for cattle; RR 2.16, 95% CI 1.18, 3.05 for pigs), however zooprophylaxis outweighs this effect for rHAT in Malawi (RR 0.85, 95% CI 0.68, 1.00 for cattle, RR 0.38, 95% CI 0.21, 0.69 for pigs). For the gambiense form (gHAT) we found evidence that pigs may be a competent reservoir (RR 1.15, 95% CI 0.92, 1.72 in Uganda; RR 1.25, 95% CI 1.11, 1.42 in DRC). Statistical significance was reached for rHAT in Malawi (pigs and cattle) and Uganda (pigs only) and for gHAT in DRC (pigs and cattle). We did not find compelling evidence of an environmental change effect (all effect sizes close to 1).

Estimating Causal Effects of HIV Prevention Interventions with Interference in Network-based Studies among People Who Inject Drugs

Evaluating causal effects in the presence of interference is challenging in network-based studies of hard-to-reach populations. Like many such populations, people who inject drugs (PWID) are embedded in social networks and often exert influence on others in their network. In our setting, the study design is observational with a non-randomized network-based HIV prevention intervention. Information is available on each participant and their connections that confer possible HIV risk through injection and sexual behaviors. We considered two inverse probability weighted (IPW) estimators to quantify the population-level spillover effects of non-randomized interventions on subsequent health outcomes. We demonstrated that these two IPW estimators are consistent, asymptotically normal, and derived a closed-form estimator for the asymptotic variance, while allowing for overlapping interference sets (groups of individuals in which the interference is assumed possible). A simulation study was conducted to evaluate the finite-sample performance of the estimators. We analyzed data from the Transmission Reduction Intervention Project, which ascertained a network of PWID and their contacts in Athens, Greece, from 2013 to 2015. We evaluated the effects of community alerts on subsequent HIV risk behavior in this observed network, where the connections or links between participants were defined by using substances or having unprotected sex together. In the study, community alerts were distributed to inform people of recent HIV infections among individuals in close proximity in the observed network. The estimates of the risk differences for spillover using either IPW estimator demonstrated a protective effect. The results suggest that HIV risk behavior could be mitigated by exposure to a community alert when an increased risk of HIV is detected in the network.

Assessing intervention effects in a randomized trial within a social network

Studies of social networks provide unique opportunities to assess the causal effects of interventions that may impact more of the population than just those intervened on directly. Such effects are sometimes called peer or spillover effects, and may exist in the presence of interference, that is, when one individual's treatment affects another individual's outcome. Randomization-based inference (RI) methods provide a theoretical basis for causal inference in randomized studies, even in the presence of interference. In this article, we consider RI of the intervention effect in the eX-FLU trial, a randomized study designed to assess the effect of a social distancing intervention on influenza-like-illness transmission in a connected network of college students. The approach considered enables inference about the effect of the social distancing intervention on the per-contact probability of influenza-like-illness transmission in the observed network. The methods allow for interference between connected individuals and for heterogeneous treatment effects. The proposed methods are evaluated empirically via simulation studies, and then applied to data from the eX-FLU trial.

Methods for Assessing Spillover in Network-Based Studies of HIV/AIDS Prevention among People Who Use Drugs

Human Immunodeficiency Virus (HIV) interventions among people who use drugs (PWUD) often have spillover, also known as interference or dissemination, which occurs when one participant's exposure affects another participant's outcome. PWUD are often members of networks defined by social, sexual, and drug-use partnerships and their receipt of interventions can affect other members in their network. For example, HIV interventions with possible spillover include educational training about HIV risk reduction, pre-exposure prophylaxis, or treatment as prevention. In turn, intervention effects frequently depend on the network structure, and intervention coverage levels and spillover can occur even if not measured in a study, possibly resulting in an underestimation of intervention effects. Recent methodological approaches were developed to assess spillover in the context of network-based studies. This tutorial provides an overview of different study designs for network-based studies and related methodological approaches for assessing spillover in each design. We also provide an overview of other important methodological issues in network studies, including causal influence in networks and missing data. Finally, we highlight applications of different designs and methods from studies of PWUD and conclude with an illustrative example from the Transmission Reduction Intervention Project (TRIP) in Athens, Greece.

Propensity Score in the Face of Interference: Discussion of

Rosenbaum and Rubin's (1983) propensity score revolutionized the field of causal inference and has emerged as a standard tool when researchers reason about cause-and-effect relationship across many disciplines. This discussion centers around the key "no interference" assumption in Rosenbaum and Rubin's original development of the propensity score and reviews some recent advances in extending the propensity score to studies involving dependent happenings.

Toward evaluation of disseminated effects of medications for opioid use disorder within provider-based clusters using routinely-collected health data

Routinely-collected health data can be employed to emulate a target trial when randomized trial data are not available. Patients within provider-based clusters likely exert and share influence on each other's treatment preferences and subsequent health outcomes and this is known as dissemination or spillover. Extending a framework to replicate an idealized two-stage randomized trial using routinely-collected health data, an evaluation of disseminated effects within provider-based clusters is possible. In this article, we propose a novel application of causal inference methods for dissemination to retrospective cohort studies in administrative claims data and evaluate the impact of the normality of the random effects distribution for the cluster-level propensity score on estimation of the causal parameters. An extensive simulation study was conducted to study the robustness of the methods under different distributions of the random effects. We applied these methods to evaluate baseline prescription for medications for opioid use disorder among a cohort of patients diagnosed with opioid use disorder and adjust for baseline confounders using information obtained from an administrative claims database. We discuss future research directions in this setting to better address unmeasured confounding in the presence of disseminated effects.

The effect of livestock density on Trypanosoma brucei gambiense and T. b. rhodesiense: A causal inference-based approach

Domestic and wild animals are important reservoirs of the rhodesiense form of human African trypanosomiasis (rHAT), however quantification of this effect offers utility for deploying non-medical control activities, and anticipating their success when wildlife are excluded. Further, the uncertain role of animal reservoirs-particularly pigs-threatens elimination of transmission (EOT) targets set for the gambiense form (gHAT). Using a new time series of high-resolution cattle and pig density maps, HAT surveillance data collated by the WHO Atlas of HAT, and methods drawn from causal inference and spatial epidemiology, we conducted a retrospective ecological cohort study in Uganda, Malawi, Democratic Republic of the Congo (DRC) and South Sudan to estimate the effect of cattle and pig density on HAT risk. For rHAT, we found a positive effect for cattle (RR 1.61, 95% CI 0.90, 2.99) and pigs (RR 2.07, 95% CI 1.15, 2.75) in Uganda, and a negative effect for cattle (RR 0.88, 95% CI 0.71, 1.10) and pigs (RR 0.42, 95% CI 0.23, 0.67) in Malawi. For gHAT we found a negative effect for cattle in Uganda (RR 0.88, 95% CI 0.50, 1.77) and South Sudan (RR 0.63, 95% CI 0.54, 0.77) but a positive effect in DRC (1.17, 95% CI 1.04, 1.32). For pigs, we found a positive gHAT effect in both Uganda (RR 2.02, 95% CI 0.87, 3.94) and DRC (RR 1.23, 95% CI 1.10, 1.37), and a negative association in South Sudan (RR 0.66, 95% CI 0.50, 0.98). These effects did not reach significance for the cattle-rHAT effect in Uganda or Malawi, or the cattle-gHAT and pig-gHAT effects in Uganda. While ecological bias may drive the findings in South Sudan, estimated E-values and simulation studies suggest unmeasured confounding and underreporting are unlikely to explain our findings in Malawi, Uganda, and DRC. Our results suggest cattle and pigs may be important reservoirs of rHAT in Uganda but not Malawi, and that pigs-and possibly cattle-may be gHAT reservoirs.

Regression-based negative control of homophily in dyadic peer effect analysis

A prominent threat to causal inference about peer effects in social science studies is the presence of homophily bias , that is, social influence between friends and families is entangled with common characteristics or underlying similarities that form close connections. Analysis of social study data has suggested that certain health conditions such as obesity and psychological states including happiness and loneliness can spread between friends and relatives. However, such analyses of peer effects or contagion effects have come under criticism because homophily bias may compromise the causal statement. We develop a regression-based approach which leverages a negative control exposure for identification and estimation of contagion effects on additive or multiplicative scales, in the presence of homophily bias. We apply our methods to evaluate the peer effect of obesity in Framingham Offspring Study.

A Review of Spatial Causal Inference Methods for Environmental and Epidemiological Applications

The scientific rigor and computational methods of causal inference have had great impacts on many disciplines but have only recently begun to take hold in spatial applications. Spatial causal inference poses analytic challenges due to complex correlation structures and interference between the treatment at one location and the outcomes at others. In this paper, we review the current literature on spatial causal inference and identify areas of future work. We first discuss methods that exploit spatial structure to account for unmeasured confounding variables. We then discuss causal analysis in the presence of spatial interference including several common assumptions used to reduce the complexity of the interference patterns under consideration. These methods are extended to the spatiotemporal case where we compare and contrast the potential outcomes framework with Granger causality and to geostatistical analyses involving spatial random fields of treatments and responses. The methods are introduced in the context of observational environmental and epidemiological studies and are compared using both a simulation study and analysis of the effect of ambient air pollution on COVID-19 mortality rate. Code to implement many of the methods using the popular Bayesian software OpenBUGS is provided.

Bipartite Causal Inference with Interference

Statistical methods to evaluate the effectiveness of interventions are increasingly challenged by the inherent interconnectedness of units. Specifically, a recent flurry of methods research has addressed the problem of interference between observations, which arises when one observational unit's outcome depends not only on its treatment but also the treatment assigned to other units. We introduce the setting of bipartite causal inference with interference, which arises when 1) treatments are defined on observational units that are distinct from those at which outcomes are measured and 2) there is interference between units in the sense that outcomes for some units depend on the treatments assigned to many other units. The focus of this work is to formulate definitions and several possible causal estimands for this setting, highlighting similarities and differences with more commonly considered settings of causal inference with interference. Towards an empirical illustration, an inverse probability of treatment weighted estimator is adapted from existing literature to estimate a subset of simplified, but interesting, estimands. The estimators are deployed to evaluate how interventions to reduce air pollution from 473 power plants in the U.S. causally affect cardiovascular hospitalization among Medicare beneficiaries residing at 18,807 zip code locations.

AVERAGE TREATMENT EFFECTS IN THE PRESENCE OF UNKNOWN INTERFERENCE

We investigate large-sample properties of treatment effect estimators under unknown interference in randomized experiments. The inferential target is a generalization of the average treatment effect estimand that marginalizes over potential spillover effects. We show that estimators commonly used to estimate treatment effects under no interference are consistent for the generalized estimand for several common experimental designs under limited but otherwise arbitrary and unknown interference. The rates of convergence depend on the rate at which the amount of interference grows and the degree to which it aligns with dependencies in treatment assignment. Importantly for practitioners, the results imply that if one erroneously assumes that units do not interfere in a setting with limited, or even moderate, interference, standard estimators are nevertheless likely to be close to an average treatment effect if the sample is sufficiently large. Conventional confidence statements may, however, not be accurate.

Inverse probability weighted estimators of vaccine effects accommodating partial interference and censoring

Estimating population-level effects of a vaccine is challenging because there may be interference, that is, the outcome of one individual may depend on the vaccination status of another individual. Partial interference occurs when individuals can be partitioned into groups such that interference occurs only within groups. In the absence of interference, inverse probability weighted (IPW) estimators are commonly used to draw inference about causal effects of an exposure or treatment. Tchetgen Tchetgen and VanderWeele proposed a modified IPW estimator for causal effects in the presence of partial interference. Motivated by a cholera vaccine study in Bangladesh, this paper considers an extension of the Tchetgen Tchetgen and VanderWeele IPW estimator to the setting where the outcome is subject to right censoring using inverse probability of censoring weights (IPCW). Censoring weights are estimated using proportional hazards frailty models. The large sample properties of the IPCW estimators are derived, and simulation studies are presented demonstrating the estimators' performance in finite samples. The methods are then used to analyze data from the cholera vaccine study.

Causal inference, social networks and chain graphs

Traditionally, statistical inference and causal inference on human subjects rely on the assumption that individuals are independently affected by treatments or exposures. However, recently there has been increasing interest in settings, such as social networks, where individuals may interact with one another such that treatments may spill over from the treated individual to their social contacts and outcomes may be contagious. Existing models proposed for causal inference using observational data from networks of interacting individuals have two major shortcomings. First, they often require a level of granularity in the data that is infeasible in practice to collect in most settings and, second, the models are high dimensional and often too big to fit to the available data. We illustrate and justify a parsimonious parameterization for network data with interference and contagion. Our parameterization corresponds to a particular family of graphical models known as chain graphs. We argue that, in some settings, chain graph models approximate the marginal distribution of a snapshot of a longitudinal data-generating process on interacting units. We illustrate the use of chain graphs for causal inference about collective decision making in social networks by using data from US Supreme Court decisions between 1994 and 2004 and in simulations.

Auto-G-Computation of Causal Effects on a Network

Methods for inferring average causal effects have traditionally relied on two key assumptions: (i) the intervention received by one unit cannot causally influence the outcome of another; and (ii) units can be organized into nonoverlapping groups such that outcomes of units in separate groups are independent. In this article, we develop new statistical methods for causal inference based on a single realization of a network of connected units for which neither assumption (i) nor (ii) holds. The proposed approach allows both for arbitrary forms of interference, whereby the outcome of a unit may depend on interventions received by other units with whom a network path through connected units exists; and long range dependence, whereby outcomes for any two units likewise connected by a path in the network may be dependent. Under network versions of consistency and no unobserved confounding, inference is made tractable by an assumption that the networks outcome, treatment and covariate vectors are a single realization of a certain chain graph model. This assumption allows inferences about various network causal effects via the auto-g-computation algorithm, a network generalization of Robins' well-known g-computation algorithm previously described for causal inference under assumptions (i) and (ii). Supplementary materials for this article are available online.

Estimands and inference in cluster-randomized vaccine trials

Cluster-randomized trials are often conducted to assess vaccine effects. Defining estimands of interest before conducting a trial is integral to the alignment between a study's objectives and the data to be collected and analyzed. This paper considers estimands and estimators for overall, indirect, and total vaccine effects in trials, where clusters of individuals are randomized to vaccine or control. The scenario is considered where individuals self-select whether to participate in the trial, and the outcome of interest is measured on all individuals in each cluster. Unlike the overall, indirect, and total effects, the direct effect of vaccination is shown in general not to be estimable without further assumptions, such as no unmeasured confounding. An illustrative example motivated by a cluster-randomized typhoid vaccine trial is provided.

Causal models adjusting for time-varying confounding-a systematic review of the literature

BACKGROUND

Obtaining unbiased causal estimates from longitudinal observational data can be difficult due to exposure-affected time-varying confounding. The past decade has seen considerable development in methods for analysing such complex longitudinal data. However, the extent to which those methods have been implemented is unclear. This study describes and characterizes the state of the field in methods adjusting for exposure-affected time-varying confounding, and examines their use in the literature.

METHODS

We systematically reviewed the literature from 2000 to 2016 for studies adjusting for time-dependent confounding, including use of specific methods like inverse probability of treatment weighting (IPTW). Articles were coded based on the methods used and, for applied articles, the topic areas covered.

RESULTS

We screened 4239 abstracts, and subsequently reviewed 1100 articles, leaving 542 relevant articles in the analyses. The number of published articles increased from two in 2000, to 112 in 2016. This increase was primarily in applied articles using IPTW, which increased from one study in 2000, to 90 in 2016. Of the 432 studies with applications to observed data, 60.9% were on at least one of: HIV (30.6%), cardiopulmonary health (13.2%), kidney disease (11.8%) or mental health (10.0%).

CONCLUSIONS

There has been marked growth in reports addressing exposure-affected time-varying confounding. This was driven by work in a small number of topic areas, with other areas showing relatively little uptake. In addition, despite developments in more advanced methods such doubly robust techniques and estimation via machine learning, implementation has been largely concentrated on the simpler, yet potentially less robust, IPTW.

Coordinated Care Organizations and mortality among low-income infants in Oregon

OBJECTIVE

To examine the impact of Oregon's Coordinated Care Organizations (CCOs), an accountable care model for Oregon Medicaid enrollees implemented in 2012, on neonatal and infant mortality.

DATA SOURCES

Oregon birth certificates linked with death certificates, and Medicaid/CCO enrollment files for years 2008-2016.

STUDY DESIGN

The sample consisted of the pre-CCO birth cohort of 135 753 infants (August 2008-July 2011) and the post-CCO birth cohort of 148 650 infants (August 2012-December 2015). We used a difference-in-differences probit model to estimate the difference in mortality between infants enrolled in Medicaid and infants who were not enrolled. We examined heterogeneous effects of CCOs for preterm and full-term infants and the impact of CCOs over the implementation timeline. All models were adjusted for maternal and infant characteristics and secular time trends.

PRINCIPAL FINDINGS

The CCO model was associated with a 56 percent reduction in infant mortality compared to the pre-CCO level (-0.20 percentage points [95% CI: -0.35; -0.05]), and also with a greater reduction in infant mortality among preterm infants compared to full-term infants. The impact on mortality grew in magnitude over the postimplementation timeline.

CONCLUSIONS

The CCO model contributed to a reduction in mortality within the first year of birth among infants enrolled in Medicaid.

Causal inference with interfering units for cluster and population level treatment allocation programs

Interference arises when an individual's potential outcome depends on the individual treatment level, but also on the treatment level of others. A common assumption in the causal inference literature in the presence of interference is partial interference, implying that the population can be partitioned in clusters of individuals whose potential outcomes only depend on the treatment of units within the same cluster. Previous literature has defined average potential outcomes under counterfactual scenarios where treatments are randomly allocated to units within a cluster. However, within clusters there may be units that are more or less likely to receive treatment based on covariates or neighbors' treatment. We define new estimands that describe average potential outcomes for realistic counterfactual treatment allocation programs, extending existing estimands to take into consideration the units' covariates and dependence between units' treatment assignment. We further propose entirely new estimands for population-level interventions over the collection of clusters, which correspond in the motivating setting to regulations at the federal (vs. cluster or regional) level. We discuss these estimands, propose unbiased estimators and derive asymptotic results as the number of clusters grows. For a small number of observed clusters, a bootstrap approach for confidence intervals is proposed. Finally, we estimate effects in a comparative effectiveness study of power plant emission reduction technologies on ambient ozone pollution.

Modelling and estimation for optimal treatment decision with interference

In many network-based intervention studies, treatment applied on an individual or his or her own characteristics may also affect the outcome of other connected people. We call this interference along network. Approaches for deriving the optimal individualized treatment regimen remain unknown after introducing the effect of interference. In this paper, we propose a novel network-based regression model that is able to account for interaction between outcomes and treatments in a network. Both Q-learning and A-learning methods are derived. We show that the optimal treatment regimen under our model is independent from interference, which makes its application in practice more feasible and appealing. The asymptotic properties of the proposed estimators are established. The performance of the proposed model and methods is illustrated by extensive simulation studies and an application to a mobile game network data.

Spillover effects in epidemiology: parameters, study designs and methodological considerations

Many public health interventions provide benefits that extend beyond their direct recipients and impact people in close physical or social proximity who did not directly receive the intervention themselves. A classic example of this phenomenon is the herd protection provided by many vaccines. If these 'spillover effects' (i.e. 'herd effects') are present in the same direction as the effects on the intended recipients, studies that only estimate direct effects on recipients will likely underestimate the full public health benefits of the intervention. Causal inference assumptions for spillover parameters have been articulated in the vaccine literature, but many studies measuring spillovers of other types of public health interventions have not drawn upon that literature. In conjunction with a systematic review we conducted of spillovers of public health interventions delivered in low- and middle-income countries, we classified the most widely used spillover parameters reported in the empirical literature into a standard notation. General classes of spillover parameters include: cluster-level spillovers; spillovers conditional on treatment or outcome density, distance or the number of treated social network links; and vaccine efficacy parameters related to spillovers. We draw on high quality empirical examples to illustrate each of these parameters. We describe study designs to estimate spillovers and assumptions required to make causal inferences about spillovers. We aim to advance and encourage methods for spillover estimation and reporting by standardizing spillover parameter nomenclature and articulating the causal inference assumptions required to estimate spillovers.

Doubly Robust Estimation in Observational Studies with Partial Interference

Interference occurs when the treatment (or exposure) of one individual affects the outcomes of others. In some settings it may be reasonable to assume individuals can be partitioned into clusters such that there is no interference between individuals in different clusters, i.e., there is partial interference. In observational studies with partial interference, inverse probability weighted (IPW) estimators have been proposed of different possible treatment effects. However, the validity of IPW estimators depends on the propensity score being known or correctly modeled. Alternatively, one can estimate the treatment effect using an outcome regression model. In this paper, we propose doubly robust (DR) estimators which utilize both models and are consistent and asymptotically normal if either model, but not necessarily both, is correctly specified. Empirical results are presented to demonstrate the DR property of the proposed estimators, as well as the efficiency gain of DR over IPW estimators when both models are correctly specified. The different estimators are illustrated using data from a study examining the effects of cholera vaccination in Bangladesh.

Dependent Happenings: A Recent Methodological Review

One hundred years ago Sir Ronald Ross published his treatise on a general Theory of Happenings. Dependent happenings are those in which the frequency depends on the number already affected. When there is dependency of events, interventions can have different types of effects. Interventions such as vaccination can have direct protective effects for the person receiving the treatment, as well as indirect/spillover effects for others in the population. Causal inference is a framework for carefully defining the causal effect of a treatment, exposure, or policy, and then determining conditions under which such effects can be estimated from the observed data. We consider here scenarios in which the potential outcomes of an individual can depend on the treatment of other individuals in the population, known as causal inference with interference. Much of the research so far has assumed the population is divided into groups or clusters, and individuals can interfere with others within their clusters but not across clusters. Recent developments have assumed more general forms of interference. We review some of the different types of effects that have been defined for dependent happenings, particularly using the methods of causal inference with interference. Many of the methods are applicable across disciplines, such as infectious diseases, social sciences, and economics.