clusterAnalysis {sumSome}

True Discovery Guarantee for Cluster Analysis

Description

This function determines a true discovery guarantee for fMRI cluster analysis. It computes confidence bounds for the number of true discoveries and the true discovery proportion within each cluster. The bounds are simultaneous over all sets, and remain valid under post-hoc selection.

Usage

clusterAnalysis(sumBrain, clusters, nMax = 50, silent = FALSE)

Arguments

sumBrain

an object of class sumBrain, as returned by the functions brainScores and brainPvals.

clusters

3D numeric array of cluster indices, or character for a Nifti file name. If NULL, the whole brain is considered.

nMax

maximum number of iterations per cluster.

silent

logical, FALSE to print the summary.

Value

clusterAnalysis returns a list containing summary (matrix) and TDPmap (3D numeric array of the true discovery proportions). The matrix summary contains, for each cluster,

• size: size

• TD: lower (1-alpha)-confidence bound for the number of true discoveries

• maxTD: maximum value of TD that could be found under convergence of the algorithm

• TDP: lower (1-alpha)-confidence bound for the true discovery proportion

• maxTD: maximum value of TDP that could be found under convergence of the algorithm

• dim1, dim2, dim3: coordinates of the center of mass.

Author(s)

Anna Vesely.

References

Goeman, J. J. and Solari, A. (2011). Multiple testing for exploratory research. Statistical Science, 26(4):584-597.

Hemerik, J. and Goeman, J. J. (2018). False discovery proportion estimation by permutations: confidence for significance analysis of microarrays. JRSS B, 80(1):137-155.

Vesely, A., Finos, L., and Goeman, J. J. (2020). Permutation-based true discovery guarantee by sum tests. Pre-print arXiv:2102.11759.

See Also

Permutation statistics for brain imaging: brainScores, brainPvals

Suprathreshold clusters: findClusters

Examples

# simulate 20 copes with dimensions 10x10x10
set.seed(42)
copes <- list()
for(i in seq(20)){copes[[i]] <- array(rnorm(10^3, mean = -10, sd = 30), dim=c(10,10,10))}

# cluster map where t scores are grater than 2.8, in absolute value
thr <- 2.8
cl <- findClusters(copes = copes, thr = thr)

# create object of class sumBrain
res <- brainScores(copes = copes, alpha = 0.2, seed = 42, truncFrom = thr)
res
summary(res)

# confidence bound for the number of true discoveries and the TDP within clusters
out <- clusterAnalysis(res, clusters = cl$clusters)