High-dimensional confounding in causal mediation: a comparison study of double machine learning and regularized partial correlation network

In causal mediation analyses, of interest are the direct or indirect pathways from exposure to an outcome variable. For observation studies, massive baseline characteristics are collected as potential confounders to mitigate selection bias, possibly approaching or exceeding the sample size. Accordingly, flexible machine learning approaches are promising in filtering a subset of relevant confounders, along with estimation using the efficient influence function to avoid overfitting. Among various confounding selection strategies, two attract growing attention. One is the popular debiased, or double machine learning (DML), and another is the penalized partial correlation via fitting a Gaussian graphical network model between the confounders and the response variable. Nonetheless, for causal mediation analyses when encountering high-dimensional confounders, there is a gap in determining the best strategy for confounding selection. Therefore, we exemplify a motivating study on the human microbiome, where the dimensions of mediator and confounders approach or exceed the sample size to compare possible combinations of confounding selection methods. By deriving the multiply robust causal direct and indirect effects across various hypotheses, our comprehensive illustrations offer methodological implications on how the confounding selection impacts the final causal target parameter estimation while generating causality insights in demystifying the "gut-brain axis". Our results highlighted the practicality and necessity of the discussed methods, which not only guide real-world applications for practitioners but also motivate future advancements for this crucial topic in the era of big data.