# brainPvals: Permutation p-Values for Brain Imaging In sumSome: Permutation True Discovery Guarantee by Sum-Based Tests

## 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

 ```1 2 3``` ```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

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.

Permutation statistics for brain imaging using t scores: `brainScores`

True discovery guarantee for cluster analysis: `clusterAnalysis`

Suprathreshold clusters: `findClusters`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```# 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) ```

sumSome documentation built on Nov. 24, 2021, 9:06 a.m.