brainPvals {sumSome}

Permutation p-Values for Brain Imaging

Description

This function computes p-value combinations for different permutations of brain imaging data. A voxel's p-value is calculated by performing the one-sample t test for the null hypothesis that its mean contrast over the different subjects is zero.

Usage

brainPvals(copes, mask = NULL, alternative = "two.sided", alpha = 0.05, B = 200, 
           seed = NULL, truncFrom = NULL, truncTo = 0.5,
           type = "vovk.wang", r = 0, rand = FALSE)

Arguments

copes

list of 3D numeric arrays (contrasts maps for each subject).

mask

3D logical array, where TRUE values correspond to voxels inside the brain, or character for a Nifti file name.

alternative

direction of the alternative hypothesis (greater, lower, two.sided).

alpha

significance level.

B

number of permutations, including the identity.

seed

seed.

truncFrom

truncation parameter: values greater than truncFrom are truncated. If NULL, it is set to alpha.

truncTo

truncation parameter: truncated values are set to truncTo. If NULL, p-values are not truncated.

type

p-value combination among edgington, fisher, pearson, liptak, cauchy, vovk.wang (see details).

r

parameter for Vovk and Wang's p-value combination.

rand

logical, TRUE to compute p-values by permutation distribution.

Details

A p-value p is transformed as following.

• Edgington: -p

• Fisher: -log(p)

• Pearson: log(1-p)

• Liptak: -qnorm(p)

• Cauchy: tan(0.5 - p)/p

• Vovk and Wang: - sign(r)p^r

An error message is returned if the transformation produces infinite values.

Truncation parameters should be such that truncTo is not smaller than truncFrom. As Pearson's and Liptak's transformations produce infinite values in 1, for such methods truncTo should be strictly smaller than 1.

The significance level alpha should be in the interval [1/B, 1).

Value

brainPvals returns an object of class sumBrain, containing

• statistics: numeric matrix of p-values, where columns correspond to voxels inside the brain, and rows to permutations. The first permutation is the identity

• mask: 3D logical array, where TRUE values correspond to voxels inside the brain

• alpha: significance level

• truncFrom: transformed first truncation parameter

• truncTo: transformed second truncation parameter

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 using t scores: brainScores

True discovery guarantee for cluster analysis: clusterAnalysis

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 (combination: Cauchy)
res <- brainPvals(copes = copes, alpha = 0.2, seed = 42, type = "cauchy")
res
summary(res)

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