Table 1.

Overview of the approaches and models for high-dimension analysis reviewed.

Name of approach	Reference	Assumptions, method, comment
Separate consideration of the potential mediators
Successive tests of association of the potential mediators with the exposure followed by the Sobel mediation test	Küpers et al. 2015	Approaches can be used to overcome the limited power of the Sobel test. Assumes lack of uncontrolled confounders and mutual influences between mediators.
Causal inference test	Liu et al. 2013	Assumes lack of uncontrolled confounders.
Permutation test	Boca et al. 2014; Sampson et al. 2018	Tests multiple putative mediators while controlling the family-wise error rate. Replacing Bonferroni correction with a permutation approach improves statistical power (MultiMed R package).
Joint significance test	Huang 2018	Separate tests of exposure–mediator and mediator–outcome associations.
Test for a composite null hypothesis	Huang 2019	Test statistic is derived by accounting for the composite nature of the null hypothesis. It is less conservative than the Sobel test.
Simultaneous consideration of the potential mediators
Inverse probability weighting approach	VanderWeele and Vansteelandt 2014	More efficient if exposure is categorical with a small number of categories. Can accommodate exposure–mediator and mediator–mediator interactions.
R package HIMA dimension reduction approach	Zhang et al. 2016	Uses variable selection to reduce the number of mediators (HIMA R package).
Joint test of a group of mediators	Huang and Pan 2016	Component-wise testing to evaluate several mediators en bloc rather than testing the marginal contribution of each individual mediator. Spectral decomposition of the mediators.
Directions of mediations	Chén et al. 2018	Builds linear combinations among the potential mediators to construct polymediators.
Sparse principal component–based high-dimension mediation analysis	Zhao et al. 2020	Dimension reduction of the potential mediators via sparse principal component analysis.
Mediation analysis for composition data	Sohn and Li 2019	Tests several mediators en bloc; well-suited for compositional data (i.e., proportions of a whole, as can be the case for microbiome data).
Distance-based test for mediation analysis (applied to microbiome data)	Zhang et al. 2018	Reduces multiple testing burden by using a distance-based approach in which all mediators are tested simultaneously. Implies the existence of a relevant distance that can be used between mediators.
Global test for high‐dimension mediation	Djordjilović et al. 2019	Global approach for mediation to test simultaneously a group of mediators.