Author: Alexander Rix

# High Dimensional Bayesian Mediation Analysis in R

#### Alexander Rix

`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
    head(hdbm.data[,1:10])
    #>            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`.