Semi-Parametric Estimation and Inference for the Mean Outcome of the Single Time-Point Intervention in a Causally Connected Population

Abstract 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.