# hdbm: High Dimensional Bayesian Mediation In hdbm: High Dimensional Bayesian Mediation Analysis

## Description

`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.

## Usage

 `1` ```hdbm(Y, A, M, C1, C2, beta.m, alpha.a, burnin, ndraws) ```

## Arguments

 `Y` numeric outcome vector. `A` numeric exposure vector. `M` numeric matrix of mediators of Y and A. `C1` numeric matrix of extra covariates in the outcome model `C2` numeric matrix of extra covariates in the mediator model `beta.m` numeric vector of initial beta.m in the outcome model `alpha.a` numeric vector of initial alpha.a in the mediator model `burnin` number of iterations to run the MCMC before sampling `ndraws` number of draws to take from MCMC after the burnin period

## Details

`hdbm` uses two regression models for the two conditional relationships, Y | A, M, C1 and M | A, C2. For the outcome model, `hdbm` uses

Y = M β_M + A * β_A + C1* β_CY + ε_Y

For the mediator model, `hdbm` uses the model

M = A * α_A + C2 * α_C2 + ε_M

For high dimensional tractability, `hdbm` 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). `hdbm` uses a Metropolis-Hastings within Gibbs MCMC to generate posterior samples from the model.

## Value

hdbm returns a list with 11 elements (each of length `ndraws`), sampled from the burned in MCMC:

beta.m

Outcome model mediator coefficients

r1

Whether or not each beta.m belongs to the larger normal component (1) or smaller normal component (0)

alpha.a

Mediator model exposure coefficients

r3

Whether or not each alpha.a belongs to the larger normal component (1) or smaller normal component (0)

beta.a

beta.a coefficient

pi.m

Proportion of non zero beta.m coefficients

pi.a

Proportion of non zero alpha.a coefficients

sigma.m0

standard deviation of the smaller normal component for mediator-outcome coefficients (beta.m)

sigma.m1

standard deviation of the larger normal component for mediator-outcome coefficients (beta.m)

sigma.ma0

Standard deviation of the smaller normal component for exposure-mediator coefficients (alpha.a)

sigma.ma1

Standard deviation of the larger normal component for exposure-mediator coefficients (alpha.a)

Alexander Rix

## References

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```library(hdbm) 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, 1000, 1) beta.m <- rep(0, 100) alpha.a <- rep(0, 100) set.seed(12345) 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) > 50) colnames(M)[active] ```

### Example output

```[1] "m12" "m65" "m89"
```

hdbm documentation built on Aug. 28, 2019, 5:04 p.m.