Table 1.

Summary of statistical methods for mediation analysis in the presence of multiple or high-dimensional mediators.

First category: Mediation methods based on dimension reduction or mediator screening
Methods	Test Statistics	Null Distribution	References
correlation-based method	Pmax	permutation	[120]
Huang-Pan method	marginal and component-wise ME based on PCA	Monte Carlo (normal-based or bootstrapping)	[122]
causal inference test (CIT)	Pmax	permutation	[157]
direction of mediation	PCA-based	bootstrapping	[158]
MCP-subset	Pmax	screening followed by multiple comparison procedure	[106]
MCP-subset based on Westfall-Young	Pmax	screening followed by multiple comparison procedure	[106]
MCP-subset based on multivariate	Pmax	screening followed by multiple comparison procedure	[106]
HDMA	Pmax	screening followed by debiased estimation	[159]
gHMA#	ACAT combining gHMA-L and gHMA-NL	screening followed by multiple comparison procedure	[160]
global test + ScreenMin#	Pmin followed by Pmax	screening followed by multiple comparison procedure	[161]
Second category: Mediation methods accounting for the composite nature of the null
Methods	Test Statistics	Null Distribution	References
JTV-comp#	mixture of multiple-mediator based P value without estimating the proportions	composite null	[79]
JT-comp	mixture of single-mediator based P value without estimating the proportions	composite null	[78]
DACT	mixture of single-mediator based P value with estimated proportion	composite null	[109]
JS-mixture	mixture of single-mediator based P value with estimated proportion	composite null	[112]
Third category: Penalization-based mediation regression methods and Bayesian mediation methods
Methods	Prior Effects Assumptions	Optimization Procedure	References
pathway Lasso	penalization based method	ADMM	[162]
HIMA	Pmax	screening followed by minimax concave penalty estimation	[111]
BAMA	spike-and-slab prior	MCMC	[163]
BAMA with joint priors	Gaussian mixture prior and, product threshold Gaussian prior	MCMC	[164]
BAMA with joint priors considering correlation among mediators	the Potts prior and logistic normal prior	MCMC	[165]

Note: we focus primarily on methodological papers and have not listed applied work that employs mediation methods similar to these listed above (e.g., Wu et al. (2018) [166], Luo et al. (2020) [96]). In addition, we only focus on methods that aim to detect active mediators and have not listed mediation methods for effect estimation and decomposition (e.g., VanderWeele and Vansteelandt (2014) [77], Daniel et al. (2015) [121], Huang and Yang (2017) [92], Steen et al. (2017) [167], Taguri et al. (2018) [168], Zhou et al. (2020) [115], and Zhao et al. (2020) [114]. ADMM: alternating direction method of multipliers; MCMC: Markov chain Monte Carlo; BAMA: Bayesian medaition analysis method; gHMA: gene based high-dimensional mediation analysis; PCA: principal component analysis; MCP: multiple comparison procedure; DACT: divide-aggregate composite-null test; HDMA: high-dimensional mediation analysis; ACAT: aggregated Cauchy association test. Above, # denotes a gene-centric mediation method.