| Title: | High Dimensional Bayesian Mediation Analysis |
|---|---|
| Description: | Perform mediation analysis in the presence of high-dimensional mediators based on the potential outcome framework. Bayesian Mediation Analysis (BAMA), developed by Song et al (2019) <doi:10.1111/biom.13189> and Song et al (2020) <arXiv:2009.11409>, relies on two Bayesian sparse linear mixed models to simultaneously analyze a relatively large number of mediators for a continuous exposure and outcome assuming a small number of mediators are truly active. This sparsity assumption also allows the extension of univariate mediator analysis by casting the identification of active mediators as a variable selection problem and applying Bayesian methods with continuous shrinkage priors on the effects. |
| Authors: | Alexander Rix [aut], Mike Kleinsasser [aut, cre], Yanyi Song [aut] |
| Maintainer: | Mike Kleinsasser <[email protected]> |
| License: | GPL-3 |
| Version: | 1.3.0 |
| Built: | 2024-11-28 06:46:26 UTC |
| Source: | CRAN |
bama is a Bayesian inference method that uses continuous shrinkage priors
for high-dimensional Bayesian mediation analysis, developed by Song et al
(2019, 2020). bama provides estimates for the regression coefficients as
well as the posterior inclusion probability for ranking mediators.
bama( Y, A, M, C1, C2, method, burnin, ndraws, weights = NULL, inits = NULL, control = list(k = 2, lm0 = 1e-04, lm1 = 1, lma1 = 1, l = 1, lambda0 = 0.04, lambda1 = 0.2, lambda2 = 0.2, phi0 = 0.01, phi1 = 0.01, a0 = 0.01 * ncol(M), a1 = 0.05 * ncol(M), a2 = 0.05 * ncol(M), a3 = 0.89 * ncol(M)), seed = NULL )bama( Y, A, M, C1, C2, method, burnin, ndraws, weights = NULL, inits = NULL, control = list(k = 2, lm0 = 1e-04, lm1 = 1, lma1 = 1, l = 1, lambda0 = 0.04, lambda1 = 0.2, lambda2 = 0.2, phi0 = 0.01, phi1 = 0.01, a0 = 0.01 * ncol(M), a1 = 0.05 * ncol(M), a2 = 0.05 * ncol(M), a3 = 0.89 * ncol(M)), seed = NULL )
Y |
Length |
A |
Length |
M |
|
C1 |
|
C2 |
|
method |
String indicating which method to use. Options are
|
burnin |
number of iterations to run the MCMC before sampling |
ndraws |
number of draws to take from MCMC (includes burnin draws) |
weights |
Length |
inits |
list of initial values for the Gibbs sampler. Options are
|
control |
list of Gibbs algorithm control options. These include prior
and hyper-prior parameters. Options vary by method selection. If
If
If
|
seed |
numeric seed for GIBBS sampler |
bama uses two regression models for the two conditional relationships,
and . For the outcome model, bama
uses
For the mediator model, bama uses the model
For high dimensional tractability, bama employs continuous Bayesian
shrinkage priors to select mediators and makes the two following assumptions:
First, it assumes that all the potential mediators contribute small effects
in mediating the exposure-outcome relationship. Second, it assumes
that only a small proportion of mediators exhibit large effects
("active" mediators). bama uses a Metropolis-Hastings within Gibbs
MCMC to generate posterior samples from the model.
NOTE: GMM not currently supported. Instead, use method = 'PTG'.
If method = "BSLMM", then bama returns a object of type "bama" with 12 elements:
ndraws x p matrix containing outcome model mediator
coefficients.
ndraws x p matrix indicating whether or not each beta.m
belongs to the larger normal component (1) or smaller normal
component (0).
ndraws x p matrix containing the mediator model
exposure coefficients.
ndraws x p matrix indicating whether or not each alpha.a
belongs to the larger normal component (1) or smaller normal component (0).
Vector of length ndraws containing the beta.a coefficient.
Vector of length ndraws containing the proportion of
non zero beta.m coefficients.
Vector of length ndraws containing the proportion of
non zero alpha.a coefficients.
Vector of length ndraws containing the standard
deviation of the smaller normal component for mediator-outcome
coefficients (beta.m).
Vector of length ndraws containing standard deviation
of the larger normal component for mediator-outcome coefficients (beta.m).
Vector of length ndraws containing standard
deviation of the smaller normal component for exposure-mediator
coefficients (alpha.a).
Vector of length ndraws containing standard deviation
of the larger normal component for exposure-mediator coefficients
(alpha.a).
The R call that generated the output.
NOTE: GMM not currently supported. Instead, use method = 'PTG'
If method = "GMM", then bama returns a object of type "bama" with:
ndraws x p matrix containing outcome model mediator
coefficients.
ndraws x p matrix containing the mediator model
exposure coefficients.
ndraws x p matrix of 1's and 0's where
item = 1 only if beta.m is non-zero.
ndraws x p matrix of 1's and 0's where
item = 1 only if alpha.a is non-zero.
ndraws x (q2 + p) matrix containing alpha_c coefficients.
Since alpha.c is a matrix of dimension q2 x p, the draws are indexed as
alpha_c(w, j) = w * p + j
ndraws x q1 matrix containing beta_c coefficients.
Since beta.c is a matrix of dimension q1 x p
Vector of length ndraws containing the beta.a coefficient.
Vector of length ndraws variance of beta.a effect
Vector of length ndraws variance of outcome model error
Vector of length ndraws variance of mediator model error
If method = "PTG", then bama returns a object of type "bama" with:
ndraws x p matrix containing outcome model mediator
coefficients.
ndraws x p matrix containing the mediator model
exposure coefficients.
ndraws x (q2 + p) matrix containing alpha_c coefficients.
Since alpha.c is a matrix of dimension q2 x p, the draws are indexed as
alpha_c(w, j) = w * p + j
ndraws x q1 matrix containing beta_c coefficients.
Since beta.c is a matrix of dimension q1 x p
ndraws x p matrix of 1's and 0's where
item = 1 only if beta.m is non-zero.
ndraws x p matrix of 1's and 0's where
item = 1 only if alpha.a is non-zero.
Vector of length ndraws containing the beta.a coefficient.
Vector of length ndraws variance of beta.a effect
Vector of length ndraws variance of outcome model error
Vector of length ndraws variance of mediator model error
Song, Y, Zhou, X, Zhang, M, et al. Bayesian shrinkage estimation of high dimensional causal mediation effects in omics studies. Biometrics. 2019; 1-11. doi:10.1111/biom.13189
Song, Yanyi, Xiang Zhou, Jian Kang, Max T. Aung, Min Zhang, Wei Zhao, Belinda L. Needham et al. "Bayesian Sparse Mediation Analysis with Targeted Penalization of Natural Indirect Effects." arXiv preprint arXiv:2008.06366 (2020).
library(bama) Y <- bama.data$y A <- bama.data$a # grab the mediators from the example data.frame M <- as.matrix(bama.data[, paste0("m", 1:100)], nrow(bama.data)) # We just include the intercept term in this example as we have no covariates C1 <- matrix(1, 1000, 1) C2 <- matrix(1, 1000, 1) beta.m <- rep(0, 100) alpha.a <- rep(0, 100) out <- bama(Y = Y, A = A, M = M, C1 = C1, C2 = C2, method = "BSLMM", seed = 1234, burnin = 100, ndraws = 110, weights = NULL, inits = NULL, control = list(k = 2, lm0 = 1e-04, lm1 = 1, lma1 = 1, l = 1)) # The package includes a function to summarise output from 'bama' summary <- summary(out) head(summary) # Product Threshold Gaussian ptgmod = bama(Y = Y, A = A, M = M, C1 = C1, C2 = C2, method = "PTG", seed = 1234, burnin = 100, ndraws = 110, weights = NULL, inits = NULL, control = list(lambda0 = 0.04, lambda1 = 0.2, lambda2 = 0.2)) mean(ptgmod$beta.a) apply(ptgmod$beta.m, 2, mean) apply(ptgmod$alpha.a, 2, mean) apply(ptgmod$betam_member, 2, mean) apply(ptgmod$alphaa_member, 2, mean)library(bama) Y <- bama.data$y A <- bama.data$a # grab the mediators from the example data.frame M <- as.matrix(bama.data[, paste0("m", 1:100)], nrow(bama.data)) # We just include the intercept term in this example as we have no covariates C1 <- matrix(1, 1000, 1) C2 <- matrix(1, 1000, 1) beta.m <- rep(0, 100) alpha.a <- rep(0, 100) out <- bama(Y = Y, A = A, M = M, C1 = C1, C2 = C2, method = "BSLMM", seed = 1234, burnin = 100, ndraws = 110, weights = NULL, inits = NULL, control = list(k = 2, lm0 = 1e-04, lm1 = 1, lma1 = 1, l = 1)) # The package includes a function to summarise output from 'bama' summary <- summary(out) head(summary) # Product Threshold Gaussian ptgmod = bama(Y = Y, A = A, M = M, C1 = C1, C2 = C2, method = "PTG", seed = 1234, burnin = 100, ndraws = 110, weights = NULL, inits = NULL, control = list(lambda0 = 0.04, lambda1 = 0.2, lambda2 = 0.2)) mean(ptgmod$beta.a) apply(ptgmod$beta.m, 2, mean) apply(ptgmod$alpha.a, 2, mean) apply(ptgmod$betam_member, 2, mean) apply(ptgmod$alphaa_member, 2, mean)
Synthetic example data for bama
bama.databama.data
A data.frame with 1000 observations on 102 variables:
Numeric response variable.
Numeric exposure variable.
Numeric mediator variables
fdr.bama uses the permutation test to estimate the null PIP
distribution for each mediator and determines a threshold (based off of the
fdr parameter) for significance.
fdr.bama( Y, A, M, C1, C2, beta.m, alpha.a, burnin, ndraws, weights = NULL, npermutations = 200, fdr = 0.1, k = 2, lm0 = 1e-04, lm1 = 1, lma1 = 1, l = 1, mc.cores = 1, type = "PSOCK" )fdr.bama( Y, A, M, C1, C2, beta.m, alpha.a, burnin, ndraws, weights = NULL, npermutations = 200, fdr = 0.1, k = 2, lm0 = 1e-04, lm1 = 1, lma1 = 1, l = 1, mc.cores = 1, type = "PSOCK" )
Y |
Length |
A |
Length |
M |
|
C1 |
|
C2 |
|
beta.m |
Length |
alpha.a |
Length |
burnin |
Number of iterations to run the MCMC before sampling |
ndraws |
Number of draws to take from MCMC after the burnin period |
weights |
Length |
npermutations |
The number of permutations to generate while estimating the null pip distribution. Default is 200 |
fdr |
False discovery rate. Default is 0.1 |
k |
Shape parameter prior for inverse gamma. Default is 2.0 |
lm0 |
Scale parameter prior for inverse gamma for the small normal components. Default is 1e-4 |
lm1 |
Scale parameter prior for inverse gamma for the large normal component of beta_m. Default is 1.0 |
lma1 |
Scale parameter prior for inverse gamma for the large normal component of alpha_a. Default is 1.0 |
l |
Scale parameter prior for the other inverse gamma distributions. Default is 1.0 |
mc.cores |
The number of cores to use while running |
type |
Type of cluster to make when |
fdr.bama returns a object of type "fdr.bama" with 5 elements:
Output from the bama run.
A p x npermutations matrices containing the
estimated null PIP distribution for each mediator.
The cutoff significance threshold for each PIP controlling for the false discovery rate.
The false discovery rate used to calculate threshold.
The R call that generated the output.
Alexander Rix
Song, Y, Zhou, X, Zhang, M, et al. Bayesian shrinkage estimation of high dimensional causal mediation effects in omics studies. Biometrics. 2019; 1-11. doi:10.1111/biom.13189
library(bama) Y <- bama.data$y A <- bama.data$a # grab the mediators from the example data.frame M <- as.matrix(bama.data[, paste0("m", 1:100)], nrow(bama.data)) # We just include the intercept term in this example as we have no covariates C1 <- matrix(1, 1000, 1) C2 <- matrix(1, 1000, 1) beta.m <- rep(0, 100) alpha.a <- rep(0, 100) set.seed(12345) out <- fdr.bama(Y, A, M, C1, C2, beta.m, alpha.a, burnin = 100, ndraws = 120, npermutations = 10) # The package includes a function to summarise output from 'fdr.bama' summary(out)library(bama) Y <- bama.data$y A <- bama.data$a # grab the mediators from the example data.frame M <- as.matrix(bama.data[, paste0("m", 1:100)], nrow(bama.data)) # We just include the intercept term in this example as we have no covariates C1 <- matrix(1, 1000, 1) C2 <- matrix(1, 1000, 1) beta.m <- rep(0, 100) alpha.a <- rep(0, 100) set.seed(12345) out <- fdr.bama(Y, A, M, C1, C2, beta.m, alpha.a, burnin = 100, ndraws = 120, npermutations = 10) # The package includes a function to summarise output from 'fdr.bama' summary(out)
Print a bama object.
## S3 method for class 'bama' print(x, ...)## S3 method for class 'bama' print(x, ...)
x |
An object of class 'bama'. |
... |
Additional arguments to pass to print.data.frame or summary.bama |
Print a bama object.
## S3 method for class 'fdr.bama' print(x, ...)## S3 method for class 'fdr.bama' print(x, ...)
x |
An object of class 'bama'. |
... |
Additional arguments to pass to print.data.frame or summary.bama |
summary.bama summarizes the 'beta.m' estimates from bama and generates
an overall estimate, credible interval, and posterior inclusion probability.
## S3 method for class 'bama' summary(object, rank = F, ci = c(0.025, 0.975), ...)## S3 method for class 'bama' summary(object, rank = F, ci = c(0.025, 0.975), ...)
object |
An object of class "bama". |
rank |
Whether or not to rank the output by posterior inclusion probability. Default is TRUE. |
ci |
The credible interval to calculate. |
... |
Additional optional arguments to |
A data.frame with 4 elements. The beta.m estimates, the estimates' credible interval (which by default is 95\ inclusion probability (pip) of each 'beta.m'.
summary.fdr.bama summarizes the beta.m estimates from
fdr.bama and for each mediator generates an overall estimate,
credible interval, posterior inclusion probability (PIP), and PIP threshold
for significance controlling for the specified false discovery rate (FDR).
## S3 method for class 'fdr.bama' summary( object, rank = F, ci = c(0.025, 0.975), fdr = object$fdr, filter = T, ... )## S3 method for class 'fdr.bama' summary( object, rank = F, ci = c(0.025, 0.975), fdr = object$fdr, filter = T, ... )
object |
An object of class "bama". |
rank |
Whether or not to rank the output by posterior inclusion probability. Default is TRUE. |
ci |
The credible interval to calculate. |
fdr |
False discovery rate. By default, it is set to whatever the
|
filter |
Whether or not to filter out mediators with PIP less than the PIP threshold. |
... |
Additional optional arguments to |
A data.frame with 4 elements. The beta.m estimates, the estimates' credible interval (which by default is 95\ inclusion probability (pip) of each 'beta.m'.