Package 'hdmed' reference manual

Title:	Methods for Mediation Analysis with High-Dimensional Mediators
Description:	A suite of functions for performing mediation analysis with high-dimensional mediators. In addition to centralizing code from several existing packages for high-dimensional mediation analysis, we provide organized, well-documented functions for a handle of methods which, though programmed their original authors, have not previously been formalized into R packages or been made presentable for public use. The methods we include cover a broad array of approaches and objectives, and are described in detail by both our companion manuscript---"Methods for Mediation Analysis with High-Dimensional DNA Methylation Data: Possible Choices and Comparison"---and the original publications that proposed them. The specific methods offered by our package include the Bayesian sparse linear mixed model (BSLMM) by Song et al. (2019); high-dimensional mediation analysis (HDMA) by Gao et al. (2019); high-dimensional multivariate mediation (HDMM) by Chén et al. (2018); high-dimensional linear mediation analysis (HILMA) by Zhou et al. (2020); high-dimensional mediation analysis (HIMA) by Zhang et al. (2016); latent variable mediation analysis (LVMA) by Derkach et al. (2019); mediation by fixed-effect model (MedFix) by Zhang (2021); pathway LASSO by Zhao & Luo (2022); principal component mediation analysis (PCMA) by Huang & Pan (2016); and sparse principal component mediation analysis (SPCMA) by Zhao et al. (2020). Citations for the corresponding papers can be found in their respective functions.
Authors:	Dylan Clark-Boucher [aut, cre], Mike Kleinsasser [aut]
Maintainer:	Dylan Clark-Boucher <[email protected]>
License:	GPL (>= 3)
Version:	1.0.1
Built:	2024-12-12 06:55:57 UTC
Source:	CRAN

Mediation Example Dataset

Description

A toy dataset for demonstrating mediation analysis in settings where there are multiple mediators

Usage

med_dat
med_dat

Format

`med_dat`

A list with three items:

Y: numeric vector containing the outcome variable
M: numeric matrix of 20 continuous mediators
A: numeric vector containing the exposure variable

...

Bayesian Sparse Linear Mixed Model

Description

mediate_bslmm fits the Bayesian sparse linear mixed model proposed by Song et al. (2020) for high-dimensional mediation analysis, estimating the mediation contributions of potential mediators.

Usage

mediate_bslmm(
  A,
  M,
  Y,
  C1 = NULL,
  C2 = C1,
  burnin = 30000,
  ndraws = 5000,
  ci_level = 0.95,
  weights = NULL,
  k = 2,
  lm0 = 1e-04,
  lm1 = 1,
  lma1 = 1,
  l = 1
)
mediate_bslmm(
  A,
  M,
  Y,
  C1 = NULL,
  C2 = C1,
  burnin = 30000,
  ndraws = 5000,
  ci_level = 0.95,
  weights = NULL,
  k = 2,
  lm0 = 1e-04,
  lm1 = 1,
  lma1 = 1,
  l = 1
)

Arguments

`A`	length `n` numeric vector containing exposure variable
`M`	`n x p` numeric matrix of high-dimensional mediators.
`Y`	length `n` numeric vector containing continuous outcome variable.
`C1`	optional numeric matrix of covariates to include in the outcome model.
`C2`	optional numeric matrix of covariates to include in the mediator model. Default is `C1`.
`burnin`	number of MCMC draws prior to sampling.
`ndraws`	number of MCMC draws after burn-in.
`ci_level`	the desired credible interval level. Default is 0.95.
`weights`	optional numeric vector of observation weights.
`k`	shape parameter for the inverse gamma priors. Default is 2.
`lm0`	scale parameter for the inverse gamma prior on the variance of the smaller-variance normal components. Default is `1e-4`. If `k=2`, this parameter equals the prior mean on the smaller normal variance.
`lm1`	scale parameter for the inverse gamma prior on the variance of the larger-variance components of `beta_m`. Default is 1. If `k=2`, this parameter equals the prior mean on the larger normal variance of the mediator-outcome associations.
`lma1`	scale parameter for the inverse gamma prior on the variance of the larger-variance components of `alpha_a`. Default is 1. If `k=2`, this parameter equals the prior mean on the larger normal variance of the exposure-mediator associations.
`l`	scale parameter for the other inverse gamma priors.

Details

mediate_bslmm is a wrapper function for the "BSLMM" option from bama::bama(), which fits a Bayesian sparse linear mixed model for performing mediation analysis with high-dimensional mediators. The model assumes that the mediator-outcome associations ( $\beta_m$ ) and the exposure-mediator associations ( $\alpha_a$ ) independently follow a mixture of small-variance and high-variance normal distributions, and that if a mediator $M_j$ has both $(\beta_m)_j$ and $(\alpha_a)_j$ belonging to the larger-variance distribution, it has a notably large mediation contribution compared to the others. The posterior inclusion probability (PIP) of belonging to both larger-variance distributions is reported for each mediator as ab_pip.

Value

A list containing:

contributions: a data frame containing the estimates, Bayesian credible intervals, and posterior inclusion probabilities of the mediation contributions
effects: a data frame containing the estimated direct, global mediation, and total effects.

References

Song, Y. et al. Bayesian shrinkage estimation of high dimensional causal mediation effects in omics studies. Biometrics 76, 700-710 (2020).

Examples

A <- med_dat$A
M <- med_dat$M
Y <- med_dat$Y

# Toy example with small burnin and ndraws
out <- mediate_bslmm(A, M, Y, burnin = 100, ndraws = 10)
out$effects
head(out$contributions)


A <- med_dat$A
M <- med_dat$M
Y <- med_dat$Y

# Toy example with small burnin and ndraws
out <- mediate_bslmm(A, M, Y, burnin = 100, ndraws = 10)
out$effects
head(out$contributions)

High-Dimensional Mediation Analysis

Description

mediate_hdma fits a high-dimensional mediation model with the de-biased LASSO approach as proposed by Gao et al. (2022), estimating the mediation contributions of potential mediators.

Usage

mediate_hdma(
  A,
  M,
  Y,
  C1 = NULL,
  C2 = NULL,
  binary_y = FALSE,
  n_include = NULL,
  ...
)
mediate_hdma(
  A,
  M,
  Y,
  C1 = NULL,
  C2 = NULL,
  binary_y = FALSE,
  n_include = NULL,
  ...
)

Arguments

`A`	length `n` numeric vector containing exposure variable
`M`	`n x p` numeric matrix of high-dimensional mediators.
`Y`	length `n` numeric vector containing continuous or binary outcome variable.
`C1`	optional numeric matrix of covariates to include in the outcome model.
`C2`	optional numeric matrix of covariates to include in the mediator model.
`binary_y`	logical flag for whether `Y` should be interpreted as a binary variable with 1/0 coding rather than as continuous. Default is `FALSE`.
`n_include`	integer specifying the number of top markers from sure independent screening to be included. Default is `NULL`, in which case `n_include` will be either `ceiling(n/log(n))` if `binary_Y = F`, or `ceiling(n/(2*log(n)))` if `binary_Y = T`. If `n_include >= p`, all mediators are included with no screening. Note that if `binary_y = F`, screening is performed based on the single-mediator outcome model p-values, and if `binary_y = F`, screening is based on the the mediator model p-values.
`...`	other arguments passed to `hdi::hdi()`.

Details

The first step in HDMA is to perform sure independence screening (SIS) to choose the n_include mediators that are most associated with the outcome (when Y is continuous) or the exposure (when Y is binary), based on p-values from linear regression. The second step is to fit the outcome model for the remaining mediators using de-sparsified (A.K.A de-biased) LASSO, which as asymptotic properties allowing for computation of p-values by the hdi package. HDMA then fits the mediator models using linear regression among those mediators that have both survived SIS (in step 1) and been identified by the LASSO (in step 2), obtaining p-values for the mediation contributions by taking the maximum of the $\alpha_a$ and $\beta_m$ p-values. The global indirect effect is estimated by summing the mediation contributions, and the direct effect is estimated by subtracting the global indirect effect from an estimate of the total effect. See References for more detail.

Value

A list containing:

contributions: a data frame containing the estimates and p-values of the mediation contributions.
effects: a data frame containing the estimated direct, global mediation, and total effects.

Source

https://github.com/YuzhaoGao/High-dimensional-mediation-analysis-R

References

Gao, Y. et al. Testing Mediation Effects in High-Dimensional Epigenetic Studies. Front. Genet. 10, 1195 (2019).

Fan, J. & Lv, J. Sure independence screening for ultrahigh dimensional feature space. J. R. Stat. Soc. 70, 849-911 (2008)

Examples

A <- med_dat$A
M <- med_dat$M
Y <- med_dat$Y

# Fit hdma with continuous outcomes
out <- mediate_hdma(A, M, Y)
head(out$contributions)
out$effects

A <- med_dat$A
M <- med_dat$M
Y <- med_dat$Y

# Fit hdma with continuous outcomes
out <- mediate_hdma(A, M, Y)
head(out$contributions)
out$effects

High-dimensional Multivariate Mediation Analysis with Principal Directions of Mediation

Description

mediate_hdmm estimates the first "direction of mediation" in the causal mediation mechanism of an exposure A, an outcome Y, and high-dimensional mediators M as proposed by Chén et al. (2018).

Usage

mediate_hdmm(
  A,
  M,
  Y,
  sims = 1000,
  boot_ci_type = "bca",
  ci_level = 0.95,
  tol = 10^-5,
  theta = rep(1, 5),
  w1 = rep(1, ncol(M)),
  interval = 10^6,
  step = 10^4,
  imax = 100
)
mediate_hdmm(
  A,
  M,
  Y,
  sims = 1000,
  boot_ci_type = "bca",
  ci_level = 0.95,
  tol = 10^-5,
  theta = rep(1, 5),
  w1 = rep(1, ncol(M)),
  interval = 10^6,
  step = 10^4,
  imax = 100
)

Arguments

`A`	numeric vector containing exposure variable.
`M`	numeric matrix of high-dimensional mediators. It is not recommended to supply a matrix with more mediators than observations.
`Y`	numeric vector containing continuous outcome variable.
`sims`	number of Monte Carlo draws for nonparametric bootstrap or quasi-Bayesian approximation. See `mediate`. Default is 1000.
`boot_ci_type`	a character string indicating the type of bootstrap confidence intervals for when `boot = TRUE`. If `"bca"`, bias-corrected and accelerated (BCa) confidence intervals will be estimated. If `"perc"`, percentile confidence intervals will be estimated (see `mediation::mediate()`). Default is "bca".
`ci_level`	the designated confidence level. Default 0.95.
`tol`	tolerance. Default 10^-5.
`theta`	numeric vector of length 5 describing starting value of pathway coefficients. Default is a vector of 1's.
`w1`	numeric vector of the same length of `A` specifying PDM starting values. Default is a vector of 1's.
`interval`	numeric vector proportional to the intervals from where the smoothing parameter is searched. Default is 10^6.
`step`	numerical number specifying step width for smoothing parameter search. Default is 10^4.
`imax`	integer specifying the maximum number of iterations allowed. Default is 100.

Details

HDMM provides latent variable approach to high-dimensional mediation analysis. The function mediate_hdmm uses a likelihood-based approach to compute principal directions of mediation (PDMs), which are loading weights used to linearly combine the inputted mediators to form a single, latent variable that replaces the original mediators in the analysis. Though HDMM cannot be used to estimate the global mediation effect or the contributions of specific mediators, it can still can be useful for inferring whether there is mediation occurring through the set of mediators as a joint system. See the provided reference for more details.

Value

A list containing:

pdm: the first direction of mediation by which mediators are weighted.
mediator: the latent mediator corresponding to the first direction of mediation.
effects: a data frame containing the estimates, confidence intervals, and p-values of the mediation effects.

Source

https://github.com/oliverychen/PDM

References

Chén, O. Y. et al. High-dimensional multivariate mediation with application to neuroimaging data. Biostatistics 19, 121-136 (2018).

Examples

A <- as.numeric(scale(med_dat$A)) # can help to standardize
M <- scale(med_dat$M[,1:8])
Y <- as.numeric(scale(med_dat$Y))

out <- mediate_hdmm(A, M, Y, sims = 5, tol = 10^-3, imax = 50)
out$effects

A <- as.numeric(scale(med_dat$A)) # can help to standardize
M <- scale(med_dat$M[,1:8])
Y <- as.numeric(scale(med_dat$Y))

out <- mediate_hdmm(A, M, Y, sims = 5, tol = 10^-3, imax = 50)
out$effects

High-Dimensional Linear Mediation Analysis

Description

mediate_hilma applies high-dimensional linear mediation analysis (HILMA) as proposed by Zhou et al. (2020).

Usage

mediate_hilma(
  A,
  M,
  Y,
  aic_tuning = FALSE,
  nlambda = 5,
  lambda_minmax_ratio = 0.1,
  center = TRUE
)
mediate_hilma(
  A,
  M,
  Y,
  aic_tuning = FALSE,
  nlambda = 5,
  lambda_minmax_ratio = 0.1,
  center = TRUE
)

Arguments

`A`	length `n` numeric vector containing a single exposure variable or size `n x q` numeric matrix containing multiple exposures. If a matrix, should be low-dimensional (`q << n`).
`M`	`n x p` numeric matrix of high-dimensional mediators.
`Y`	length `n` numeric vector containing continuous outcome variable.
`aic_tuning`	logical flag for whether to select the tuning parameter using AIC. Default is `FALSE` as this was not the preferred approach by the HILMA authors (see references for more detail).
`nlambda`	number of candidate lambdas for AIC tuning. Default is 5. If `aic_tuning=F` this parameter is ignored.
`lambda_minmax_ratio`	ratio of the minimum lambda attempted in AIC tuning to the maximum. If `aic_tuning=F`, ignored.
`center`	logical flag for whether the variables should be centered. Default is `TRUE`.

Details

mediate_hilma is a wrapper function for the freebird::hilma() function, which fits the "high-dimensional linear mediation analysis" model proposed by Zhou et al. (2020) for mediation settings when there are high-dimensional mediators and one or several exposures. The function returns estimates of the direct effect, total effect, and global mediation effect, the last of which is tested for statistical significance with a reported p-value. For additional detail, see the attached reference as well as the freebird::hilma() documentation.

Value

A list containing, for each exposure, a data frame of the estimated direct, total, and global mediation effects. A p-value is provided for the global mediation effect.

References

Zhou, R. R., Wang, L. & Zhao, S. D. Estimation and inference for the indirect effect in high-dimensional linear mediation models. Biometrika 107, 573-589 (2020)

Examples

A <- med_dat$A
M <- med_dat$M
Y <- med_dat$Y

# Implement HILMA with one exposure
out <- mediate_hilma(A, M, Y)
out$a1



A <- med_dat$A
M <- med_dat$M
Y <- med_dat$Y

# Implement HILMA with one exposure
out <- mediate_hilma(A, M, Y)
out$a1

High-Dimensional Mediation Analysis

Description

mediate_hima fits a high-dimensional mediation model with the minimax concave penalty as proposed by Zhang et al. (2016), estimating the mediation contributions of potential mediators.

Usage

mediate_hima(
  A,
  M,
  Y,
  C1 = NULL,
  C2 = NULL,
  binary_y = FALSE,
  n_include = NULL,
  ...
)
mediate_hima(
  A,
  M,
  Y,
  C1 = NULL,
  C2 = NULL,
  binary_y = FALSE,
  n_include = NULL,
  ...
)

Arguments

`A`	length `n` numeric vector containing exposure variable
`M`	`n x p` numeric matrix of high-dimensional mediators.
`Y`	length `n` numeric vector containing continuous or binary outcome variable.
`C1`	optional numeric matrix of covariates to include in the outcome model.
`C2`	optional numeric matrix of covariates to include in the mediator model.
`binary_y`	logical flag for whether `Y` should be interpreted as a binary variable with 1/0 coding rather than as continuous. Default is `FALSE`.
`n_include`	integer specifying the number of top markers from sure independent screening to be included. Default is `NULL`, in which case `n_include` will be either `ceiling(n/log(n))` if `binary_Y = F`, or `ceiling(n/(2*log(n)))` if `binary_Y = T`. If `n_include >= p`, all mediators are included with no screening. Note that if `binary_y = F`, screening is performed based on the single-mediator outcome model p-values, and if `binary_y = F`, screening is based on the the mediator model p-values.
`...`	other arguments passed to `hdi`.

Details

The first step in HIMA is to perform sure independence screening (SIS) to choose the n_include mediators that are most associated with the outcome (when Y is continuous) or the exposure (when Y is binary), based on p-values from linear regression. The second step is to fit the outcome model for the remaining mediators with the minimax concave penalty. HIMA then fits the mediator models using linear regression among those mediators that have both survived SIS (in step 1) and been selected by the MCP (in step 2), which enables estimation of the mediation contributions. The global indirect effect is estimated by summing these contributions, and the direct effect is estimated by subtracting the global indirect effect from an estimate of the total effect. We compute p-values for the mediation contributions by taking the maximum of the $\alpha_a$ and $\beta_m$ p-values, where the beta p-values are obtained via a second, unpenalized generalized linear model containing only the mediators selected by the MCP. We include this p-value computation so that our function replicates the behavior of the HIMA function from HIMA package, the function on which ours is based, but we caution that the beta p-values may be over-optimistic due to double-dipping, since the mediators tested in the unpenalized model are only those chosen by the penalized model. Note also that the HIMA authors apply Bonferroni correction to the final, maxed p-values to account for multiple testing, which we choose to leave up to the user. For more information, see the "HIMA" R package along with the provided reference.

Value

A list containing:

contributions: a data frame containing the estimates and p-values of the mediation contributions.
effects: a data frame containing the estimated direct, global mediation, and total effects.

References

Zhang, H. et al. Estimating and testing high-dimensional mediation effects in epigenetic studies. Bioinformatics 32, 3150-3154 (2016).

Examples

A <- med_dat$A
M <- med_dat$M
Y <- med_dat$Y

# Fit hima with continuous outcome
out <- mediate_hima(A, M, Y)
head(out$contributions)
out$effects

# Fit hima with binary outcome
Y1 <- as.numeric(Y > mean(Y))
out1 <- mediate_hima(A, M, Y1, binary_y = TRUE)
head(out1$contributions)
out1$effects

A <- med_dat$A
M <- med_dat$M
Y <- med_dat$Y

# Fit hima with continuous outcome
out <- mediate_hima(A, M, Y)
head(out$contributions)
out$effects

# Fit hima with binary outcome
Y1 <- as.numeric(Y > mean(Y))
out1 <- mediate_hima(A, M, Y1, binary_y = TRUE)
head(out1$contributions)
out1$effects

Latent Variable Mediation Analysis

Description

mediate_lvma fits a high-dimensional mediation model described by Derkach et al. (2019), in which a small number of latent, unmeasured mediators replace the original mediators in the model.

Usage

mediate_lvma(A, M, Y, q, rhoLM, rhoEL, rhoLY, scale = TRUE, imax = 5000)
mediate_lvma(A, M, Y, q, rhoLM, rhoEL, rhoLY, scale = TRUE, imax = 5000)

Arguments

`A`	length `n` numeric vector representing the exposure variable
`M`	`n x p` numeric matrix of high-dimensional mediators.
`Y`	length `n` numeric vector representing the continuous outcome variable.
`q`	number of latent mediators
`rhoLM`	numeric vector of candidate penalty parameters for the latent mediator-mediator associations in the joint likelihood. Default is a short toy sequence.
`rhoEL`	numeric vector of candidate penalty parameters for the exposure-latent mediator associations in the joint likelihood. Default is a short toy sequence.
`rhoLY`	numeric vector of candidate penalty parameters for the latent mediator-outcome associations in the joint likelihood. Default is a short toy sequence.
`scale`	logical flag for whether the inputted mediators should be standardized prior to the analysis. Default is `FALSE`, but `TRUE` may be worth attempting in case of errors.
`imax`	integer specifying the maximum number of iterations allowed. Default is 5000.

Details

LVMA is a latent variable mediation model which assumes, contrary to standard assumptions, that the inputted set of candidate mediators do not affect the outcome through the exposure on their own, but rather, occur as result of latent, unmeasured mediators which themselves transmit effects from the exposure to outcome. The required parameters for fitting this model are rhoLE, a regularization parameter for effects of the latent mediators on the inputted mediators; rhoEL, a regularization parameter for the effects of the exposure on the latent mediators; and rhoLY, a regularization parameter for the effects of the latent mediators on the exposure. These parameters should ideally be supplied by the user as vectors, so that each combination of the three parameters can be attempted in the estimation. However, this can be intensely computation costly, and for simplicity our default values are vectors of length 4, corresponding to a 64 by 64 parameter grid. In practice, Derkach et al. use a much larger grid with 5 values of rhoLM (ranging from 6 to 8.5), 40 values of rhoEY (ranging from 0 to 40), and 40 values of rhoLY (ranging from 0 to 75). Supplying longer parameter vectors makes the fit more flexible, but more computationally costly, and to reliably implement LVMA on real data one should use a larger parameter grid with parallel computation on a remote computing cluster, as did the authors. For more information on the likelihood, parameters, and mediation model, see the referenced article and/or its supplement files.

Value

A list containing the selected models based on AIC, BIC, and EBIC (recommended) as three sub-lists. The sub-lists include objects indicating the penalty set that was used (penalty), the values of the chosen parameters (e.g., EBIC), the exposure-latent mediator effects (AL_effects), the latent mediator-mediator effects (LM_effects, a data frame), the direct effect of the exposure on the outcome (AY_direct_effect), the the latent mediator-outcome effects (LY_effects), and binary vector indicating whether each mediator was determined to be active. Here, active mediators are those which are associated with a latent mediator that itself is associated with both A and Y.

Source

https://pubmed.ncbi.nlm.nih.gov/30859548/

References

Derkach, A., Pfeiffer, R. M., Chen, T.-H. & Sampson, J. N. High dimensional mediation analysis with latent variables. Biometrics 75, 745-756 (2019).

Examples

A <- med_dat$A
M <- med_dat$M
Y <- med_dat$Y

# Perform latent variable mediation analsis with 4 latent mediators and print
# whether the original 20 mediators are "actively" related to mediation
out <- mediate_lvma(A, M, Y, q = 4, rhoLM = 2, rhoEL = 2, rhoLY = 2, imax = 50)
table(out$EBIC_out$mediator_active)

A <- med_dat$A
M <- med_dat$M
Y <- med_dat$Y

# Perform latent variable mediation analsis with 4 latent mediators and print
# whether the original 20 mediators are "actively" related to mediation
out <- mediate_lvma(A, M, Y, q = 4, rhoLM = 2, rhoEL = 2, rhoLY = 2, imax = 50)
table(out$EBIC_out$mediator_active)

Mediation Analysis via Fixed Effects Model

Description

mediate_medfix fits a high-dimensional mediation model with the adaptive LASSO approach as proposed by Zhang (2021) for the special case of MedFix that there is only one exposure variable.

Usage

mediate_medfix(
  A,
  M,
  Y,
  C1 = NULL,
  C2 = C1,
  nlambda = 100,
  nlambda2 = 50,
  nfolds = 10,
  seed = 1
)
mediate_medfix(
  A,
  M,
  Y,
  C1 = NULL,
  C2 = C1,
  nlambda = 100,
  nlambda2 = 50,
  nfolds = 10,
  seed = 1
)

Arguments

`A`	length `n` numeric vector representing the exposure variable
`M`	`n x p` numeric matrix of high-dimensional mediators.
`Y`	length `n` numeric vector representing the continuous outcome variable.
`C1`	optional numeric matrix of covariates to include in the outcome model. Default is `NULL`.
`C2`	optional numeric matrix of covariates to include in the mediator model. Default is `C1`.
`nlambda`	number of lambdas attempted in the adaptive LASSO. See `gcdnet::cv.gcdnet()`. The specific sequence of `lambda`s is chosen by the `cv.gcdnet()` function.
`nlambda2`	number of `lambda2`s attempted in the initial elastic net used for computing adaptive weights prior to adaptive LASSO. Default is `50`. See `gcdnet::cv.gcdnet()` for details on elastic net regression. If `0`, `lambda2=0` is fed to `cv.gcdnet()` and the initial fit is based on standard LASSO, not elastic net. If not `0)`, the specific sequence of `lambda2`s is given by `exp(seq(1e-4,0.02,length.out=nlambda2))`, and the `lambda2` with the least cross-validated error is chosen.
`nfolds`	number of folds for cross-validation. See `gcdnet::cv.gcdnet()`. Default is `10`.
`seed`	numeric random seed.

Details

MedFix performs mediation analysis when there are multiple mediators by applying adaptive LASSO to the outcome model. In order to fit the adaptive LASSO, we first obtain an initial model fit using either LASSO (which deploys the L1 penalty) or elastic net (which deploys both the L1 and L2 penalties) depending on the provided nlambda2. Estimates from this fit are then used to compute the adaptive weights used in the adaptive LASSO. Once the final adaptive LASSO estimates ( $\beta_m$ ) are obtained for the outcome model, estimates for the p mediator models ( $\alpha_a$ ) are obtained by linear regression. The mediation contributions are computed as $\alpha_a$ times $\beta_m$ , and the p-value is taken as the maximum of the $\alpha_a$ and $beta_m$ p-values. Last, the global indirect effect is estimated by summing the mediation contributions, and the direct effect is estimated by subtracting the global indirect effect from an estimate of the total effect. This function is specific to applying MedFix to the special case that there is only one exposure; for details on how to apply MedFix when the exposures are high-dimensional, as proposed by the authors, see the supplemental files of the referenced manuscript.

Value

A list containing:

contributions: a data frame containing the estimates and p-values of the mediation contributions.
effects: a data frame containing the estimated direct, global mediation, and total effects.

References

Zhang, Q. High-Dimensional Mediation Analysis with Applications to Causal Gene Identification. Stat. Biosci. 14, 432-451 (2021).

Examples

A <- med_dat$Y
M <- med_dat$M
Y <- med_dat$Y

out <- mediate_medfix(A, M, Y, nlambda = 10, nlambda2 = 5, seed = 1)
out$effects
head(out$contributions)

A <- med_dat$Y
M <- med_dat$M
Y <- med_dat$Y

out <- mediate_medfix(A, M, Y, nlambda = 10, nlambda2 = 5, seed = 1)
out$effects
head(out$contributions)

Principal Component Mediation Analysis for High-dimensional Mediators

Description

mediate_pcma applies principal component mediation analysis (Huang and Pan, 2013) to mediation settings in which the mediators are high-dimensional.

Usage

mediate_pcma(
  A,
  M,
  Y,
  var_per = 0.8,
  n_pc = NULL,
  sims = 1000,
  boot_ci_type = "bca",
  ci_level = 0.95,
  seed = 1
)
mediate_pcma(
  A,
  M,
  Y,
  var_per = 0.8,
  n_pc = NULL,
  sims = 1000,
  boot_ci_type = "bca",
  ci_level = 0.95,
  seed = 1
)

Arguments

`A`	length `n` numeric vector containing exposure variable
`M`	`n x p` numeric matrix of high-dimensional mediators.
`Y`	length `n` numeric vector containing continuous outcome variable.
`var_per`	a numeric variable with the desired proportion of variance explained. Default is 0.8.
`n_pc`	optional numeric variable with the desired number of PCs, in which case `var_per` is ignored. Default is `NULL` and the number of PCs is determined based on the desired proportion of variance explained.
`sims`	number of Monte Carlo draws for nonparametric bootstrap or quasi-Bayesian approximation (see `mediation::mediate()`). Default is 1000.
`boot_ci_type`	a character string indicating the type of bootstrap confidence intervals for when `boot = TRUE`. If `"bca"`, bias-corrected and accelerated (BCa) confidence intervals will be estimated. If `"perc"`, percentile confidence intervals will be estimated (see `mediation::mediate()`). Default is "bca".
`ci_level`	the desired confidence level. Default is 0.95.
`seed`	seed used for fitting single-mediator models after PCA

Details

Principal component mediation analysis (PCMA) is a method for estimating mediation effects when the mediators are high-dimensional. The first step is to compute the residuals of mediator models ( $M|A$ ), then perform PCA on those residuals to reduce them to a smaller number of mediators that efficiently explain the residual variance. Then, since those mediators are linearly independent conditional on A, one can trivially perform single-mediator mediation analysis for each PC on its own, in this case by using the mediation::mediate() function. The global mediation effect is estimated by summing the mediation effects of the individual PCs.

Value

A list containing:

loadings: a matrix of the PC loadings.
pcs: a matrix of the PCs.
var_explained: the cumulative proportion of variance explained by the PCs.
contributions: a data frame containing the estimates, confidence intervals, and p-values of the mediation contributions.
effects: a data frame containing the estimated direct, global mediation, and total effects.

Source

https://rdrr.io/github/zhaoyi1026/spcma

References

Huang, Y.-T. & Pan, W.-C. Hypothesis test of mediation effect in causal mediation model with high-dimensional continuous mediators. Biometrics 72, 402-413 (2016).

Examples

A <- med_dat$A
M <- med_dat$M
Y <- med_dat$Y
# Fit PCMA with 3 principal components and print the effects. In practice one
# should choose n_pc (or var_per) and the number sims to be larger
out <- mediate_pcma(A, M, Y, n_pc = 3, sims = 10)
out$effects



A <- med_dat$A
M <- med_dat$M
Y <- med_dat$Y
# Fit PCMA with 3 principal components and print the effects. In practice one
# should choose n_pc (or var_per) and the number sims to be larger
out <- mediate_pcma(A, M, Y, n_pc = 3, sims = 10)
out$effects

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
)
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)


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)

Sparse Principal Component Mediation Analysis for High-Dimensional Mediators

Description

mediate_spcma applies sparse principal component mediation analysis to mediation settings in which the mediators are high-dimensional.

Usage

mediate_spcma(
  A,
  M,
  Y,
  var_per = 0.8,
  n_pc = NULL,
  sims = 1000,
  boot_ci_type = "bca",
  ci_level = 0.95,
  fused = FALSE,
  gamma = 0,
  per_jump = 0.7,
  eps = 1e-04,
  maxsteps = 2000,
  seed = 1
)
mediate_spcma(
  A,
  M,
  Y,
  var_per = 0.8,
  n_pc = NULL,
  sims = 1000,
  boot_ci_type = "bca",
  ci_level = 0.95,
  fused = FALSE,
  gamma = 0,
  per_jump = 0.7,
  eps = 1e-04,
  maxsteps = 2000,
  seed = 1
)

Arguments

`A`	length `n` numeric vector containing exposure variable
`M`	`n x p` numeric matrix of high-dimensional mediators.
`Y`	length `n` numeric vector containing continuous outcome variable.
`var_per`	a numeric variable with the desired proportion of variance explained. Default is 0.8.
`n_pc`	optional numeric variable with the desired number of PCs, in which case `var_per` is ignored. Default is `NULL` and the number of PCs is determined based on the desired proportion of variance explained.
`sims`	number of Monte Carlo draws for nonparametric bootstrap or quasi-Bayesian approximation (see `mediation::mediate()`). Default is 1000.
`boot_ci_type`	character string indicating the type of bootstrap confidence intervals for when `boot = TRUE`. If `"bca"`, bias-corrected and accelerated (BCa) confidence intervals will be estimated. If `"perc"`, percentile confidence intervals will be estimated (see `mediation::mediate()`). Default is "bca".
`ci_level`	the designated confidence level. Default 0.95.
`fused`	logical variable for whether the fused LASSO should be used instead of the ordinary LASSO. Default is `FALSE`.
`gamma`	numeric variable `>=0` indicating the ratio of the standard LASSO penalty to the fusion penalty (see `genlasso::genlasso()`). Ignored if `fused = FALSE`. Default is 0, meaning there is no standard penalty. Larger values result in more shrinkage and sparser PCs.
`per_jump`	numeric value used for tuning parameter selection - the quantile cut-off for total variance change under different `lambda` values in the LASSO. Default is 0.7. Larger values result in more shrinkage and sparser PCs
`eps`	numeric variable indicating the multiplier for the ridge penalty in case `X` is rank deficient (see `genlasso::genlasso()`). Default is `1e-4`.
`maxsteps`	an integer specifying the maximum number of steps for the algorithm before termination (see `genlasso::genlasso()`). Default is 2000.
`seed`	seed used for fitting single-mediator models after PCA

Details

mediate_spcma performs principal component mediation analysis, comparable to mediate_pcma, with the modification that the PC loadings are sparsified by a flexible LASSO penalty. This has the potential make the PCs more interpretable, since, unlike in PCA, they are only linear combinations of a subset of mediators rather than all of them. The choice of LASSO penalties is determined by the fused argument - which, when set to TRUE, deploys a fused LASSO penalty that encourages the model to give consecutive mediators similar loadings. The default is fused = FALSE, and the standard LASSO penalty is used instead of the fusion penalty. Once the sparse PCs are computed, inference proceeds exactly like in PCMA, and the PC-mediators are evaluated with methods from the mediate package.

Value

A list containing:

loadings: a matrix of the PC loadings.
pcs: a matrix of the PCs.
var_explained: the cumulative proportion of variance explained by the PCs.
contributions: a data frame containing the estimates, confidence intervals, and p-values of the mediation contributions.
effects: a data frame containing the estimated direct, global mediation, and total effects.

Source

https://rdrr.io/github/zhaoyi1026/spcma

References

Zhao, Y., Lindquist, M. A. & Caffo, B. S. Sparse principal component based high-dimensional mediation analysis. Comput. Stat. Data Anal. 142, 106835 (2020).

Examples

A <- med_dat$A
M <- med_dat$M
Y <- med_dat$Y

# Fit SPCMA with the fused LASSO penalty while choosing the number of PCs based
# on the variance they explain. In practice, var_per and sims should be higher.
out <- mediate_spcma(A, M, Y, var_per = 0.25, fused = TRUE, gamma = 2, sims = 10)
out$effects

A <- med_dat$A
M <- med_dat$M
Y <- med_dat$Y

# Fit SPCMA with the fused LASSO penalty while choosing the number of PCs based
# on the variance they explain. In practice, var_per and sims should be higher.
out <- mediate_spcma(A, M, Y, var_per = 0.25, fused = TRUE, gamma = 2, sims = 10)
out$effects

Package 'hdmed'

Help Index

Mediation Example Dataset

Description

Usage

Format

med_dat

Bayesian Sparse Linear Mixed Model

Description

Usage

Arguments

Details

Value

References

Examples

High-Dimensional Mediation Analysis

Description

Usage

Arguments

Details

Value

Source

References

Examples

High-dimensional Multivariate Mediation Analysis with Principal Directions of Mediation

Description

Usage

Arguments

Details

Value

Source

References

Examples

High-Dimensional Linear Mediation Analysis

Description

Usage

Arguments

Details

Value

References

Examples

High-Dimensional Mediation Analysis

Description

Usage

Arguments

Details

Value

References

Examples

Latent Variable Mediation Analysis

Description

Usage

Arguments

Details

Value

Source

References

Examples

Mediation Analysis via Fixed Effects Model

Description

Usage

Arguments

Details

Value

References

Examples

Principal Component Mediation Analysis for High-dimensional Mediators

Description

Usage

Arguments

Details

Value

Source

References

Examples

Pathway LASSO for Mediation Analysis with High-Dimensional Mediators

Description

Usage

Arguments

Details

`med_dat`