BHMSMA {BHMSMAfMRI}

Bayesian hierarchical multi-subject multiscale analysis (BHMSMA) of functional MRI data or other multiscale data

Description

BHMSMA is the main function that performs BHMSMA (Sanyal & Ferreira, 2012) of fMRI data, or other multiscale data, using wavelet-based prior that borrows strength across subjects and provides posterior smooth estimates of the effect sizes. Specifically, BHMSMA constructs a 2D regression coefficient map (e.g., corresponding to a single brain slice) of a given regressor and returns its posterior smoothed version based on multi-subject or single subject analyses.

Usage

BHMSMA(n, grid, data, designmat, k, analysis="multi", 
  truecoef=NULL, wave.family="DaubLeAsymm", filter.number=6, 
  bc="periodic")

Arguments

n

Number of subjects.

grid

The number of voxels in one row (or column) of the brain slice of interest. Must be a power of 2. The total number of voxels is grid^2. The maximum value of grid for this package is 512.

data

The data in the form of an array with dimension (n,grid,grid,ntime), where ntime is the size of the time series for each voxel. The rows (first dimension) must correspond to n.

designmat

The design matrix used to generate the data. The rows must correspond to n. It should include an intercept column if desired. No intercept column will be added by the function. The GLM fit will include all the columns of designmat.

k

Index of the regressor chosen for analysis, consistently with designmat. After fitting GLM, the regression coefficients of this regressor will be considered for the rest of the analysis.

analysis

"MSA" or "SSA", depending on whether performing multi-subject analysis or single subject analysis.

truecoef

If available, the true GLM coefficients in the form of an array with dimension (n,grid,grid). NULL by default.

wave.family

The family of wavelets to use - "DaubExPhase" or "DaubLeAsymm". Default is "DaubLeAsymm".

filter.number

The number of vanishing moments of the wavelet. Default is 6.

bc

The boundary condition to use - "periodic" or "symmetric". Default is "periodic".

Details

The wavelet computations are performed by using the R package wavethresh.

Value

A list containing the following.

GLMCoefStandardized

An array of dimension (n,grid,grid), containing for each subject the standardized GLM coefficients obtained by fitting GLM to the time-series corresponding to the voxels.

GLMCoefSE

An array of dimension (n,grid,grid), containing for each subject the estimated standard errors of the GLM coefficients.

WaveletCoefficientMatrix

A matrix of dimension (n,grid^2-1), containing for each subject the wavelet coefficients of all levels stacked together (by the increasing order of resolution level).

hyperparam

A vector containing the estimates of the six hyperparameters.

hyperparamVar

Estimated covariance matrix of the hyperparameters.

posteriorMixProb

A matrix of dimension (n,grid^2-1), containing the piklj.bar values (see Reference for details).

PostMeanWaveletCoef

A matrix of size (n,grid^2-1), containing for each subject the posterior mean of the wavelet coefficients of all levels stacked together (by the increasing order of resolution level).

GLMcoefposterior

An array of dimension (n,grid,grid), containing for each subject the posterior means of the standardized GLM coefficients.

MSE

MSE of the posterior estimates of the GLM coefficients, if the true values of the GLM coefficients are available.

Author(s)

Nilotpal Sanyal, Marco Ferreira

Maintainer: Nilotpal Sanyal <[e-mail]>

References

Sanyal, Nilotpal, and Ferreira, Marco A.R. (2012). Bayesian hierarchical multi-subject multiscale analysis of functional MRI data. Neuroimage, 63, 3, 1519-1531.

See Also

readfmridata, glmcoef, waveletcoef, hyperparamest, postmixprob, postwaveletcoef, substituteWaveletCoef, postglmcoef, imwd, imwr

Examples

# BHMSMA multi-subject analysis for simulated (fMRI) 
# data at 4 timepoints over an 8x8 grid (of a brain 
# slice) for 3 subjects
set.seed(1)
n <- 3
grid <- 8
ntime <- 4
data <- array(rnorm(n*grid*grid*ntime),
  dim=c(n,grid,grid,ntime))
designmat <- cbind(c(1,1,1,1),c(1,0,1,0))
k <- 2
analysis <- "multi"
BHMSMAmulti <- BHMSMA(n, grid, data, designmat, 
  k, analysis)

zlim = c(0,max(abs(BHMSMAmulti$GLMCoefStandardized)))
par(mfrow=c(1,2))
image( abs(BHMSMAmulti$GLMCoefStandardized[1,,,k]),
  col=heat.colors(12),zlim=zlim,main="GLM coef map")
image( abs(BHMSMAmulti$GLMcoefposterior[1,,]),
  col=heat.colors(12),zlim=zlim,main="GLM coef posterior map")


## Not run: 
# BHMSMA multi-subject analysis for simulated (fMRI) 
# data at 100 timepoints over an 64x64 grid (of a 
# brain slice) for 15 subjects
# (takes ~12s in a 2.8 GHz Quad-Core Intel Core i7 processor)
set.seed(1)
n <- 15
grid <- 64
ntime <- 100
data <- array(rnorm(n*grid*grid*ntime),
          dim=c(n,grid,grid,ntime))
designmat <- cbind(rep(1,ntime),runif(ntime))
k <- 2
analysis <- "multi"
system.time({BHMSMAmulti <- BHMSMA(n,grid,data, 
  designmat,k,analysis)})

## End(Not run)