Robust and Flexible Estimation of Stochastic Mediation Effects: A Proposed Method and Example in a Randomized Trial Setting

Causal mediation analysis can improve understanding of the mechanisms underlying epidemiologic associations. However, the utility of natural direct and indirect effect estimation has been limited by the assumption of no confounder of the mediator-outcome relationship that is affected by prior exposure---an assumption frequently violated in practice. We build on recent work that identified alternative estimands that do not require this assumption and propose a flexible and double robust semiparametric targeted minimum loss-based estimator for data-dependent stochastic direct and indirect effects. The proposed method treats the intermediate confounder affected by prior exposure as a time-varying confounder and intervenes stochastically on the mediator using a distribution which conditions on baseline covariates and marginalizes over the intermediate confounder. In addition, we assume the stochastic intervention is given, conditional on observed data, which results in a simpler estimator and weaker identification assumptions. We demonstrate the estimator's finite sample and robustness properties in a simple simulation study. We apply the method to an example from the Moving to Opportunity experiment. In this application, randomization to receive a housing voucher is the treatment/instrument that influenced moving to a low-poverty neighborhood, which is the intermediate confounder. We estimate the data-dependent stochastic direct effect of randomization to the voucher group on adolescent marijuana use not mediated by change in school district and the stochastic indirect effect mediated by change in school district. We find no evidence of mediation. Our estimator is easy to implement in standard statistical software, and we provide annotated R code to further lower implementation barriers.Comment: 24 pages, 2 tables, 2 figure

Evolving Optical Networks for Latency-Sensitive Smart-Grid Communications via Optical Time Slice Switching (OTSS) Technologies

In this paper, we proposed a novel OTSS-assisted optical network architecture for smart-grid communication networks, which has unique requirements for low-latency connections. Illustrative results show that, OTSS can provide extremely better performance in latency and blocking probability than conventional flexi-grid optical networks.Comment: IEEE Photonics Society 1st Place Best Poster Award, on CLEO-PR/OECC/PGC 201

A new approach to hierarchical data analysis: Targeted maximum likelihood estimation for the causal effect of a cluster-level exposure

We often seek to estimate the impact of an exposure naturally occurring or randomly assigned at the cluster-level. For example, the literature on neighborhood determinants of health continues to grow. Likewise, community randomized trials are applied to learn about real-world implementation, sustainability, and population effects of interventions with proven individual-level efficacy. In these settings, individual-level outcomes are correlated due to shared cluster-level factors, including the exposure, as well as social or biological interactions between individuals. To flexibly and efficiently estimate the effect of a cluster-level exposure, we present two targeted maximum likelihood estimators (TMLEs). The first TMLE is developed under a non-parametric causal model, which allows for arbitrary interactions between individuals within a cluster. These interactions include direct transmission of the outcome (i.e. contagion) and influence of one individual's covariates on another's outcome (i.e. covariate interference). The second TMLE is developed under a causal sub-model assuming the cluster-level and individual-specific covariates are sufficient to control for confounding. Simulations compare the alternative estimators and illustrate the potential gains from pairing individual-level risk factors and outcomes during estimation, while avoiding unwarranted assumptions. Our results suggest that estimation under the sub-model can result in bias and misleading inference in an observational setting. Incorporating working assumptions during estimation is more robust than assuming they hold in the underlying causal model. We illustrate our approach with an application to HIV prevention and treatment

Asymptotic Theory for Cross-validated Targeted Maximum Likelihood Estimation

We consider a targeted maximum likelihood estimator of a path-wise differentiable parameter of the data generating distribution in a semi-parametric model based on observing n independent and identically distributed observations. The targeted maximum likelihood estimator (TMLE) uses V-fold sample splitting for the initial estimator in order to make the TMLE maximally robust in its bias reduction step. We prove a general theorem that states asymptotic efficiency (and thereby regularity) of the targeted maximum likelihood estimator when the initial estimator is consistent and a second order term converges to zero in probability at a rate faster than the square root of the sample size, but no other meaningful conditions are needed. In particular, the conditions of this theorem allow the full utilization of loss based super learning to obtain the initial estimator. In particular, the theorem proves that first order efficient and unbiased estimation is enhanced in an important way by using adaptive estimators such as an super learner, thereby formally dealing with the concern that adaptive estimation might make it harder to construct valid confidence intervals. On the contrary, the theorem teaches us that to achieve first order efficiency and regularity, it is crucial to estimate the relevant parts of the true data generating distribution as good as possible. The theorem is applied to prove asymptotic efficiency of the targeted maximum likelihood estimator of the additive causal effect of a binary treatment on an outcome in a randomized controlled trial and in an observational study. Excellent finite sample performance of this estimator has been demonstrated in past articles (e.g.van der Laan et al. (September, 2009), Gruber and van der Laan (2010), Stitelman and van der Laan (2010), Petersen et al. (2010)

Causal Mediation in a Survival Setting with Time-Dependent Mediators

The effect of an expsore on an outcome of interest is often mediated by intermediate variables. The goal of causal mediation analysis is to evaluate the role of these intermediate variables (mediators) in the causal effect of the exposure on the outcome. In this paper, we consider causal mediation of a baseline exposure on a survival (or time-to-event) outcome, when the mediator is time-dependent. The challenge in this setting lies in that the event process takes places jointly with the mediator process; in particular, the length of the mediator history depends on the survival time. As a result, we argue that the definition of natural effects in this setting should be based on only blocking those paths from treatment to mediators that are not through the survival history. We propose to use a stochastic interventions (SI) perspective, introduced by Didelez, Dawid, and Geneletti (2006), to formulate the causal mediation analysis problem in this setting. Under this formulation, the mediators are regarded as intervention variables, onto which a given counterfactual distribution is enforced. The natural direct and indirect effects can be defined analogously to the ideas in Pearl (2001). In particular, they also allow for a total effect decomposition and an interpretation of the natural direct effect as a weighted average of controlled direct effects. The statistical parameters that should arise are defined nonparametrically; therefore, they have meaningful interpretations, independent of the causal formulations and assumptions. We present a general semiparametric inference framework for these parameters. Using their efficient influence functions, we develop semiparametric efficient and robust targeted substitution-based (TMLE) and estimating-equation-based (A-IPTW) estimators. An IPTW estimator and g-computation estimator will also be presented

Targeted Maximum Likelihood Estimation of Natural Direct Effect

In many causal inference problems, one is interested in the direct causal effect of an exposure on an outcome of interest that is not mediated by certain intermediate variables. Robins and Greenland (1992) and Pearl (2000) formalized the definition of two types of direct effects (natural and controlled) under the counterfactual framework. Since then, identifiability conditions for these effects have been studied extensively. By contrast, considerably fewer efforts have been invested in the estimation problem of the natural direct effect. In this article, we propose a semiparametric efficient, multiply robust estimator for the natural direct effect of a binary treatment using the targeted maximum likelihood framework of van der Laan and Rubin (2006) and van der Laan and Rose (2011). The proposed estimator is asymptotically unbiased if either one of the following holds: i) the conditional outcome expectation given exposure, mediator, and confounders, and the mediated mean outcome difference are consistently estimated; (ii) the exposure mechanism given confounders, and the conditional outcome expectation are consistently estimated; or (iii) the exposure mechanism given confounders, and a ratio of conditional mediator densities are consistently estimated. Moreover, case (iii) implies in particular that estimation of the conditional mediator density may be replaced by consistent estimation of the exposure mechanism and the conditional distribution of exposure given confounders and mediator. If all three conditions hold, then the effect estimate is asymptotically efficient

Documented Evidence of Agricultural Injury in China

Objective: To describe the documented evidence concerning agricultural injury in China and to identify topics for future research.Method: Literature search and review were conducted to collect publications that were relevant to agricultural injury in China. The process included defining agricultural injury for the purpose of this study, selecting articles according to inclusion criteria and extracting data from each paper. Descriptive methods were used to analyze the contents, research approaches, distribution of authors, and cooperation percentage of agricultural injury studies.Results: After applying the inclusion criteria, 89 articles were included in this study. The author collaboration percentage (number of articles with more than one author divided by number of total articles) and the institutional collaboration percentage (number of articles with more than one organization divided by number of total articles) among the 89 articles were 85.4% and 42.7%, respectively. Most of the authors are affiliated with a Center for Disease Control and Prevention (CDC) or an academic institution located in 10 of the 31 provinces in mainland China. Among the 89 articles, only 6 were on injuries related to agricultural work, the rest (83) dealt with injuries among rural residents with or without clarifying occupations or ongoing activities. Conclusions: Research on agricultural injuries in China is currently in its early stage. More research is needed to obtain evidence that can be used in policy making for agricultural injury control. Our study is the first to describe the documented evidence on agricultural injuries in China and identify topics for future research

Marginal Structural Models with Counterfactual Effect Modifiers

In health and social sciences, research questions often involve systematic assessment of the modification of treatment causal effect by patient characteristics, in longitudinal settings with time-varying or post-intervention effect modifiers of interest. In this work, we investigate the robust and efficient estimation of the so-called Counterfactual-History-Adjusted Marginal Structural Model (van der Laan and Petersen (2007)), which models the conditional intervention-specific mean outcome given modifier history in an ideal experiment where, possible contrary to fact, the subject was assigned the intervention of interest, including the treatment sequence in the conditioning history. We establish the semiparametric efficiency theory for these models, and present a substitution-based, semiparametric efficient and doubly robust estimator using the targeted maximum likelihood estimation methodology (TMLE, e.g. van der Laan and Rubin (2006), van der Laan and Rose (2011)). To facilitate implementation in applications where the effect modifier is high dimensional, our third contribution is a projected influence curve (and the corresponding TMLE estimator), which retains most of the robustness of its efficient peer and can be easily implemented in applications where the use of the efficient influence curve becomes taxing. In addition to these two robust estimators, we also present an Inverse-Probability-Weighted (IPW) estimator (e.g. Robins (1997a), Hernan, Brumback, and Robins (2000)), and a non-targeted G-computation estimator (Robins (1986)). The comparative performance of these estimators are assessed in a simulation study. The use of the TMLE estimator (based on the projected influence curve) is illustrated in a secondary data analysis for the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) trial