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Title: Estimating and testing individual mediation effects in high-dimensional settings Authors:  Preetam Nandy - University of Pennsylvania (United States) [presenting]
Hongzhe Li - University of Pennsylvania (United States)
Abstract: The problem of identifying intermediate variables (or mediators) that regulate the effect of a treatment on an outcome is considered. While there has been significant research on this topic, little work has been done when the set of potential mediators is high-dimensional. A further complication arises when the potential mediators are interrelated. In particular, we assume that the causal structure of the treatment, potential mediators and outcome is a directed acyclic graph. In this setting, we propose novel methods for estimating and testing the influence of a mediator on the outcome for high-dimensional linear structural equation models (linear SEMs). For the estimation of individual mediation effect, we propose a modification of the IDA algorithm that was developed for estimating causal effects from observational data. While most of the approaches for estimating the influence of potential mediators ignore the causal relationship among the mediators, our IDA-based approach estimates the underlying causal graph from data. We derive a high-dimensional consistency result for the IDA-based estimators when the data are generated from a linear SEM with sub-Gaussian errors. Further, we propose a first asymptotically valid testing framework in such a setting, leading to a principled FDR control approach for the identification of the set of true mediators. Finally, we empirically demonstrate the importance of using an estimated causal graph in high-dimensional mediation analysis.