Description Usage Arguments Details Value Author(s) References Examples

`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.

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

`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 |

`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.

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

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

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]
``` |

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

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