bama | R Documentation |
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 )
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,
Y | A, M, C and M | A, C. For the outcome model, bama
uses
Y = M β_M + A * β_A + C* β_C + ε_Y
For the mediator model, bama
uses the model
M = A * α_A + C * α_C + ε_M
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)
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