# High Dimensional Bayesian Mediation Analysis in R

hdbm is a Bayesian inference method that uses continuous shrinkage priors for high-dimensional mediation analysis, developed by Song et al (2018). hdbm provides estimates for the regression coefficients as well as the posterior inclusion probability for ranking mediators.

# Installation

You can install hdbm from CRAN

install.packages("hdbm")

or from github via devtools

# install.packages(devtools)
devtools::install_github("umich-cphds/hdbm", built_opts = c())

hdbm requires the R packages Rcpp and RcppArmadillo, so you may want to install / update them before downloading. If you decide to install hdbm from source (eg github), you will need a C++ compiler that supports C++11. On Windows this can accomplished by installing Rtools, and Xcode on MacOS.

# Example problem

hdbm contains a semi-synthetic example data set, hdbm.data that is used in this example. hdbm.data contains a continuous response y and a continuous exposure a that is mediated by 100 mediators, m[1:100].

library(hdbm)
# print just the first 10 columns
#>            y          a          m1         m2          m3         m4
#> 1 -0.5077701  1.3979467 -0.75395346 -0.2787043 -0.04471833  0.3422936
#> 2 -0.3239898 -0.2311032 -1.20208195  0.4210638  0.93175992 -0.3699733
#> 3 -1.8553536 -2.4647028 -0.65712133  0.3285993  0.59144748 -0.1307554
#> 4  0.1685455  0.1119932  0.04982723  0.6816996 -0.12956715 -0.8348541
#> 5  0.9070900  0.4994626 -0.99964057 -0.7660710  1.53962908 -0.9308951
#> 6 -1.0357105  0.6359685  1.06954128 -0.2441489 -1.52176072  0.4657214
#>            m5          m6          m7           m8
#> 1 -0.66227113 -0.30925865  1.58001664  0.008326522
#> 2  1.09811497 -0.09969085  1.02369272  0.045104531
#> 3 -0.30196963  0.38853526 -0.05841533 -0.436429826
#> 4  0.08936191 -0.69699157  0.41615473  0.973411472
#> 5  1.12107670  1.07603088  0.37449777 -0.289794580
#> 6 -1.55992443 -0.42705075 -0.98761802 -0.639473238

The mediators have an internal correlation structure that is based off the covariance matrix from the Multi-Ethnic Study of Atherosclerosis (MESA) data. However, hdbm does not model internal correlation between mediators. Instead, hdbm employs continuous Bayesian shrinkage priors to select mediators and assumes that all the potential mediators contribute small effects in mediating the exposure-outcome relationship, but only a small proportion of mediators exhibit large effects.

We use no adjustment covariates in this example, so we just include the intercept. Also, in a real world situation, it may be beneficial to normalize the input data.


Y <- hdbm.data$y A <- hdbm.data$a

# grab the mediators from the example data.frame
M <- as.matrix(hdbm.data[, paste0("m", 1:100)], nrow(hdbm.data))

# We just include the intercept term in this example.
C <- matrix(1, nrow(M), 1)

# Initial guesses for coefficients
beta.m  <- rep(0, ncol(M))
alpha.a <- rep(0, ncol(M))

set.seed(12345)
# It is recommended to pick a larger number for burnin.
hdbm.out <- hdbm(Y, A, M, C, C, beta.m, alpha.a,
burnin = 1000, ndraws = 100)

# Which mediators are active?
active <- which(colSums(hdbm.out$r1 * hdbm.out$r3) > 100 / 2)
colnames(M)[active]
#> [1] "m12" "m65" "m89"

Here, we calculate the posterior inclusion probability r1 = r3 = 1 | Data, and classify a mediator as active if its posterior probability is greater than 0.5.

# Reference

Yanyi Song, Xiang Zhou et al. Bayesian Shrinkage Estimation of High Dimensional Causal Mediation Effects in Omics Studies. bioRxiv 10.1101/467399

## Contact information

If you would like to report a bug, ask questions, or suggest something, please e-mail Alexander Rix at alexrix@umich.edu.