mediate_plasso {hdmed}

Pathway LASSO for Mediation Analysis with High-Dimensional Mediators

Description

mediate_plasso fits a high-dimensional mediation model with the penalized likelihood described by Zhao and Luo (2022), estimating the mediation contributions of each site.

Usage

mediate_plasso(
  A,
  M,
  Y,
  lambdas = NULL,
  select_lambda = FALSE,
  vss_rep = 5,
  vss_cutoff = 0.1,
  omega_ratio = 1,
  phi = 2,
  maxit = 5000,
  tol = 1e-06
)

Arguments

A

numeric vector containing exposure variable.

M

numeric matrix of high-dimensional mediators.

Y

numeric vector containing continuous outcome variable.

lambdas

numeric vector of tuning parameters lambda for which model is fitted. Default is a vector of length 50 ranging from 10^-5 to 10^4, with more density in the lower range.

select_lambda

logical flag indicating whether to conduct a tuning parameter selection using the Variable Selection Stability Criterion described by Sun et al. (2013). Default is FALSE.

vss_rep

if select_lambda is TRUE, number of VSSC replications.

vss_cutoff

if select_lambda is TRUE, cutoff used for VSSC. Default is 0.1.

omega_ratio

ratio of the omega parameter to lambda parameter in the likelihood penalty. Default is 1.

phi

value of the phi parameter in the likelihood penalty. Default is 2. Cannot be less than 1/2.

maxit

the maximum number of iterations. Default is 5000.

tol

convergence tolerance. Default is 10^-6.

Details

Pathway LASSO fits a high-dimensional mediation model with a likelihood that directly penalizes the mediator-outcome effects, exposure-mediator effects, and mediation contributions (i.e., the mediation "pathways"). The shrinkage of the model is determined by three parameters–phi, omega, and lambda–with higher values tending to result in more sparsity. Mediation results are returned for every unique value in the inputted lambdas argument, in increasing order, excluding potentially any for which the estimation was unsuccessful. For details on the exact likelihood, see the first reference.

When implementing multiple lambdas (i.e., using either the default argument to lambdas or specifying one's own vector), there is an option to perform a tuning parameter selection using the Variable Selection Stability Criterion proposed by Sun et al. (2013), which chooses the parameter for which the variable selection is most stable in repeated data-splitting. However, implementing this can be computationally costly, especially with a long list of tuning parameters, since it involves re-fitting pathway LASSO many times.

Value

A list containing:

• lambdas: the lambdas attempted in the same order as the objects in all_fits.

• all_fits: a list containing, for each lambda, a data.frame of the estimated mediation effects.

• chosen_lambda: if select_lambda is TRUE, the lambda chosen by VSSC.

• chosen_fit: if select_lambda is TRUE, the fit corresponding to the chosen lambda.

• vss: if select_lambda isTRUE, a data.frame containing the variable selection stabilities.

Source

https://github.com/zhaoyi1026/PathwayLasso

References

Zhao, Y. & Luo, X. Pathway LASSO: pathway estimation and selection with high-dimensional mediators. Stat. Interface 15, 39-50 (2022).

Sun, W., Wang, J. & Fang, Y. Consistent selection of tuning parameters via variable selection stability. J. Mach. Learn. Res. 14, 3419-3440 (2013).

Examples

A <- med_dat$A
M <- med_dat$M[,1:8]
Y <- med_dat$Y
# fit pathway LASSO for two tuning parameters and retrieve their fits
out <- mediate_plasso(A, M, Y, lambdas = c(10^-3, 10^-2), tol = 1e-4)
head(out$all_fits$lambda1)
head(out$all_fits$lambda2)