Targeted Maximum Likelihood Estimation of Community-based Causal Effect of Community-Level Stochastic Interventions

Unlike the commonly used parametric regression models such as mixed models, that can easily violate the required statistical assumptions and result in invalid statistical inference, target maximum likelihood estimation allows more realistic data-generative models and provides double-robust, semi-parametric and efficient estimators. Target maximum likelihood estimators (TMLEs) for the causal effect of a community-level static exposure were previously proposed by Balzer et al. In this manuscript, we build on this work and present identifiability results and develop two semi-parametric efficient TMLEs for the estimation of the causal effect of the single time-point community-level stochastic intervention whose assignment mechanism can depend on measured and unmeasured environmental factors and its individual-level covariates. The first community-level TMLE is developed under a general hierarchical non-parametric structural equation model, which can incorporate pooled individual-level regressions for estimating the outcome mechanism. The second individual-level TMLE is developed under a restricted hierarchical model in which the additional assumption of no covariate interference within communities holds. The proposed TMLEs have several crucial advantages. First, both TMLEs can make use of individual level data in the hierarchical setting, and potentially reduce finite sample bias and improve estimator efficiency. Second, the stochastic intervention framework provides a natural way for defining and estimating casual effects where the exposure variables are continuous or discrete with multiple levels, or even cannot be directly intervened on. Also, the positivity assumption needed for our proposed causal parameters can be weaker than the version of positivity required for other casual parameters.

tmleCommunity: A R Package Implementing Target Maximum Likelihood Estimation for Community-level Data

Over the past years, many applications aim to assess the causal effect of treatments assigned at the community level, while data are still collected at the individual level among individuals of the community. In many cases, one wants to evaluate the effect of a stochastic intervention on the community, where all communities in the target population receive probabilistically assigned treatments based on a known specified mechanism (e.g., implementing a community-level intervention policy that target stochastic changes in the behavior of a target population of communities). The tmleCommunity package is recently developed to implement targeted minimum loss-based estimation (TMLE) of the effect of community-level intervention(s) at a single time point on an individual-based outcome of interest, including the average causal effect. Implementations of the inverse-probability-of-treatment-weighting (IPTW) and the G-computation formula (GCOMP) are also available. The package supports multivariate arbitrary (i.e., static, dynamic or stochastic) interventions with a binary or continuous outcome. Besides, it allows user-specified data-adaptive machine learning algorithms through SuperLearner, sl3 and h2oEnsemble packages. The usage of the tmleCommunity package, along with a few examples, will be described in this paper.