Many important exposure-response relationships, such as diet and weight, can be influenced by intermediates, such as the gut microbiome. Understanding the role of these intermediates, the mediators, is important in refining cause-effect theories and discovering additional medical interventions (e.g., probiotics, prebiotics). Mediation analysis has been at the heart of behavioral health research, rapidly gaining popularity with the biomedical sciences in the last decade. A specific analytic challenge is being able to incorporate an entire 'omics assay as a mediator. To address this challenge, we propose a hypothesis testing framework for multivariate omnibus distance mediation analysis (MODIMA). We use the power of energy statistics, such as partial distance correlation, to allow for analysis of multivariate exposure-mediator-response triples. Our simulation results demonstrate the favorable statistical properties of our approach relative to the available alternatives. Finally, we demonstrate the application of the proposed methods in two previously published microbiome datasets. Our framework adds a new tool to the toolbox of approaches to the integration of 'omics big data.
Keywords: causal inference; direct effect; distance correlation; indirect effect; multivariate analysis; multivariate causal mediation.