Table 1.

Comparison of selected methods for outcome-wide analysis in exposome research.

	GFLasso	GroupRemMap	MTL_L21	mRRR	sRRR	MBSP
Group	Regularized multivariate regression framework	Regularized multivariate regression framework	Multitask Learning based on regularized regression	Dimensionality reduction techniques	Dimensionality reduction techniques	Sparse multivariate Bayesian estimation with shrinkage priors
Goal	Uses penalties to promote the selection of exposures affecting multiple outcomes.	Uses penalties to promote the selection of exposures affecting the majority of the outcomes.	Uses cross-task regularization to promote the selection of exposures affecting all outcomes.	Promotes the selection of exposures affecting all the outcomes.	Promotes the selection of exposures affecting all the outcomes.	Promotes the selection of only few exposures affecting the majority of the outcomes.
Strategy	It considers the correlation structure existing among outcomes encouraging similar (or dissimilar) responses to be explained by a similar (or dissimilar) predictors.	It considers the correlation structure existing among predictors favoring the selection of groups of related exposures affecting multiple outcomes rather than single variables.	It also allows considering the correlation structure existing among predictors favoring the selection of groups of correlated exposures affecting all outcomes.	Assume that all the outcomes and exposures are associated through a shared low dimensional subspace. It allows considering the correlation structure existing among outcomes.	Assume that all the outcomes and exposures are associated through a shared low dimensional subspace. It allows considering the correlation structure existing among outcomes.	It considers the correlation structure existing among outcomes encouraging similar (or dissimilar) responses to exhibit similar (or dissimilar) coefficients for the same predictor.
Type of outcomes	Only continuous	Only continuous	All continuous or All binary	Mixed outcomes	Only continuous	Only continuous
Missing data in Outcomes	No	No	No	Yes	No	No
Variable Selection	Yes	Yes	Yes	No	Yes	Yes
Allow adjusting for the effect of confounders	Yes (functionality added)	Yes	No (partialling-out as an alternative)	Yes	Yes (functionality added)	Yes (functionality added)
Quantification of uncertainty	No	No	No	No	No	Yes (95 % credible intervals)
Level of sparsity	Low	High	Medium	Low	Medium	High
Reference	Kim et al. (2009) Bioinformatics	Wang et al. (2015) Stat Biosciences	Han et al. (2018) Bioinformatics	C. Luo et al. (2018) Journal of Multivariate Analysis	Chen et al. (2012) Journal of the American Statistical Association	R Bai et al. (2018) Journal of Multivariate Analysis