Bayesian Mediation Analysis

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) and Song et al (2020), 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.

Installation

You can install bama via CRAN

install.packages("bama")

Or devtools

devtools::install_github("umich-cphds/bama", build_opts = c())

The Github version may contain new features or bug fixes not yet present on CRAN, so if you are experiencing issues, you may want to try the Github version of the package.

If you wish to install the package via devtools, you will need a C++ compiler installed. This can be accomplished by installing Rtools on Windows and Xcode on MacOS.

Example

This example is taken from the bama help file to help you get started using the method. Please check the documentation of the function by typing ?bama::bama, and the vignette by typing vingette("bama") in R.

bama includes an example dataset, bama.data. It is a data.frame with a numeric response y, numeric exposure a and 100 numeric mediators named m1, m2, ..., m100.

We recommend using much larger numbers for burnin and ndraws, for example (30000, 35000).

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 = 1000, ndraws = 1100, weights = NULL, inits = NULL, 
            control = list(k = 2, lm0 = 1e-04, lm1 = 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 = 1000, ndraws = 1100, 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)

# Gaussian Mixture Model
gmmmod = bama(Y = Y, A = A, M = M, C1 = C1, C2 = C2, method = "GMM", seed = 1234,
              burnin = 1000, ndraws = 1100, weights = NULL, inits = NULL, 
              control = list(phi0 = 0.01, phi1 = 0.01))

mean(gmmmod$beta.a)
apply(gmmmod$beta.m, 2, mean)
apply(gmmmod$alpha.a, 2, mean)

mean(gmmmod$sigma.sq.a)
mean(gmmmod$sigma.sq.e)
mean(gmmmod$sigma.sq.g)

References

Song, Y, Zhou, X, Zhang, M, et al. Bayesian shrinkage estimation of high dimensional causal mediation effects in omics studies. Biometrics. 2019; 1-11.

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).