All-Resolution Inference (ARI) for brain imaging is an R-package to estimate True Discovery Proportions (TDP) for brain imaging analysis derived clusters of functional MRI activation. The TDP gives the lower-bound (with a certain confidence, usually 95%) of the number of truly active voxels within each cluster.
ARIbrain is the R-package for All-Resolution Inference (ARI) in neuroscience. It allows researchers to estimate the True Discovery Proportion (TDP) of any cluster in a statistical map derived from a (functional) MRI experiment. Statistical maps can be derived using your favorite fMRI analysis package (e.g. SPM, FSL, AFNI). It is convenient for the output to be in NIfti format, as this can be read in by the package. Alternatively you could use an R array as input as well (as the nifti files will be converted to an array internally).
ARIbrain can be used in two different 'modes'. Using ARI, we show how to compute lower bound for proportion of active voxels (or any other spatially located units) within given clusters. Alternatively, with ARIcluster, we show how to find maximal clusters under the given threshold of true discovery proportion (TDP).
ARIbrain requires R to run and the 'ARIbrain'-package to be installed. For non R-users the easiest way to install R is in combination with Rstudio. You can find the instructions how to install R and RStudio.
The original paper introducing ARI can be found here: (https://doi.org/10.1016/j.neuroimage.2018.07.060), and the efficient algorithm used to perform ARICluster analysis can be found here: (https://doi.org/10.48550/arXiv.2206.13587).
Go here to download R and Rstudio from the Posit website (you need the RStudio Desktop FREE version). First install R and then install RStudio.
You can install the stable version of ARIbrain from CRAN, or use the Tools > Install packages option from Rstudio (select CRAN Repository and search for ARIbrain, leave the install dependencies option checked), or use the install.packages('ARIbrain') command in R/Rstudio. The development version of ARIbrain can be downloaded from this GitHub repository using the 'devtools' package. First install this package using install.packages('devtools'), and then install ARIbrain using the following command: devtools::install_github('wdweeda/ARIbrain').
After installing, open RStudio (if not already open), and load the ARIbrain package by typing library(ARIbrain). This will load the package for usage. For easy access to the files it is convenient to change to the working directory of where your statistics maps (in Nifti format) of interest are located by typing setwd('workdirpath') where workdirpath is the path to your working directory (e.g. '/Users/wouter/fmri' or 'c:/Users/wouter/fmridir')
There are two main flavors of TDP estimation using ARI either providing clusters to the analysis and estimating TDPs for these clusters, or the other way around, setting a minimal TDP level and letting ARI estimate the largest clusters wit at least that TDP level.
ARI can caluculate TDPs for any cluster provided (with full FWER control). These can be clusters defined by, for example, a cluster-forming threshold, or clusters from an anatomical atlas. The basic input for ARI is a map of (2-sided) p-values and a map of cluster indices (0's for non-clusters and integer values for each voxel that belong to a specific clusters, e.g. 1's for cluster 1, 2's for cluster 2, etc.)
If you are familiar with neuroimaging analysis is R here is the main syntax for the R function ARI (type ?ARIbrain::ARI for more details). Below the syntax we will continue with an example of a 'standard' analysis.
ARI(Pmap, clusters, mask=NULL, alpha=0.05, Statmap=function(ix) -qnorm(Pmap[ix]), summary_stat=c("max", "center-of-mass"), silent=FALSE)
The main input parameters of ARI() are:
Pmap: the map of p-values,clusters: the map of cluster indices.
Others optional maps (parameters) are:
mask: the map of logicals (not mandatory, but useful),Statmap: the map of statistics (usually z-scores or t-values).
The function accepts input map formats of character file names or 3D arrays. Therefore the minimal syntax is
ARI(Pmap, clusters)
The clusters can be defined a priori, on the basis of previous knowledges or on the basis of anatomical regions. Clusters of such a kind are usually called ROIs. There are no limitations to the number of ROIs that can be evaluated in the same analysis; the lower bounds for each ROI is valid simultaneously for all estimates (i.e. corrected for multiplicity).
Even more interestingly, the clusters can be defined on the basis of the same data. This is valid as ARI allows for circular analysis, still controlling for multiplicity of inferences.
If you have an output z-map (i.e., containing z-statistics) of a contrast/analysis of interest and want to to a 'standard' cluster-extent analysis. We first need to load the statistics file into R and threshold the image at a certain Z value (e.g., 3.1) to form clusters. Make sure your input file is the unthresholded map of statistics. Use the following commands to load the file and threshold the map into clusters.
zdat <- readNifti('zstat1.nii.gz')
clus31 <- ARIbrain::cluster_threshold(zdat>3.1)
The z-statistics data is now loaded into an r-object called zdat, the clusters that are formed based on a z-statistics value larger than 3.1 (zdat>3.1) which are subsequently stored in the clus31 object.
Now we need to calculate the p-values (preferably 2-sided) from the z-values. We can do that using the following command:
pvals2 <- pnorm(abs(zdat), lower.tail = F)*2
Finally, we can estimate the TDPs for the clusters. Best practice is to also give a brain-mask for the in-brain voxels mask = zdat!=0 (else the method will correct over all voxels including the voxels outside the brain).
ari_out <- ARIbrain::ARI(Pmap = pvals2, clusters = clus31, mask=zdat!=0, Statmap = zdat)
The ari_out output object contains a table with the TDPs (in the ActiveProp column) for all clusters and include locations for the maximum.
A hommel object for 199918 hypotheses.
Simes inequality is assumed.
Use p.adjust(), discoveries() or localtest() to access this object.
With 0.95 confidence: at least 25616 discoveries.
1588 hypotheses with adjusted p-values below 0.05.
Size FalseNull TrueNull ActiveProp dim1 dim2 dim3 Stat
cl92 4470 2668 1802 0.59686801 24 43 58 6.964157
cl91 2644 1187 1457 0.44894100 58 64 63 5.973241
cl90 2226 991 1235 0.44519317 67 33 15 6.258505
cl89 1903 829 1074 0.43562796 29 35 21 6.346173
cl88 1019 227 792 0.22276742 23 80 53 5.484357
cl87 800 324 476 0.40500000 32 68 65 6.333398
cl86 407 59 348 0.14496314 30 76 38 5.569287
cl85 337 43 294 0.12759644 62 75 39 5.331001
cl84 297 0 297 0.00000000 63 92 46 4.748392
cl83 146 0 146 0.00000000 34 22 27 4.258435
cl82 128 0 128 0.00000000 51 18 37 4.881685
cl81 81 0 81 0.00000000 16 50 27 4.635155
cl80 38 0 38 0.00000000 46 53 42 4.503975
cl0 185422 11120 174302 0.05997131 48 19 30 4.937728
The output also includes cl0 which is a 'null' cluster containing all in-mask voxels that are not in any other cluster. If this gives a TDP > 0 this means that there is some activitiy somewhere in the brain not captured in the clusters. Usually this number is relatively low (<1%) If this number is really high, you might want to redefine clusters, as you might have missed some area of activation.
The following paragraphs contain additional ways to define clusters.
You can also append your FSL cluster analysis with TDPs. For this go the cope directory of interest in your multilevel gfeat analysis in the terminal using cd 'gfeatdir/copedir/', where 'gfeatdir/copedir/' is the cope directory of your multilevel analysis. Also download the get_tdp.R file (for example in the 'download' directory. The command line has the following input
True Discovery Proportions (TDP) using ARIbrain version 1.2.a
Usage:
Rscript get_tdp.R --zstat=<filename> --cluster=<filename> [options]
Compulsory arguments:
--zstat/tstat filename of t/z-statistics file (nifti)
--cluster filename of cluster-index file (nifti)
--df if tstat is specified, df is also needed
Optional arguments:
[method]
--alpha nominal alpha level of TDPs, default is 0.05 (%95 confidence)
[output]
--outfile optional output file of TDP values (nifti)
--outtable optional output table of TDP values (txt)
--intable optional input table (txt) of clusters (TDPs will be added with _tdp)
--inhtml optional input html cluster file (TDPs will be added with _tdp)
[options]
--verbose print additional information on TDPs
--quiet suppresses almost all output to console
--help prints this message
The following command will append your cluster.html file (with extension _tdp.html) and save a text file with TDPs and a nifti file with voxels having the TDP value of the cluster they belong to. In the cope directory run: Rscript /download/get_tdp.R --zstat=./stats/zstat1.nii.gz --cluster=cluster_mask_zstat1.nii.gz --alpha=0.05 --outtable=tdptable.txt --outfile=tdpclus.nii.gz --inhtml=cluster_zstat1_std.html
Ouput will look approximately like this:
True Discovery Proportions (TDP) using ARIbrain version 1.2.a
Calculated assuming Simes' inequality with 95% confidence.
> converted z-stats to 2-sided p-values
> writing TDP table
> writing cluster nifti with TDP values
> adding TDPs to cluster html
<TDP output>
Size FalseNull TrueNull ActiveProp dim1 dim2 dim3 Stat
cl5 9161 7134 2027 0.77873595 15 60 37 10.095283
cl4 8851 6531 2320 0.73788273 77 58 39 10.245214
cl3 555 40 515 0.07207207 36 65 41 5.100245
cl2 380 67 313 0.17631579 69 70 50 5.211789
cl1 195 53 142 0.27179487 72 61 62 5.915697
cl0 146612 7048 139564 0.04807246 44 87 29 3.539190
Here we show an analysis where clusters are defined by a TDP threshold. Using a sufficiently high TDP threshold leads to achieving better spatial localisation. In contrast to classical cluster inference by providing a fixed cluster-forming threshold (CFT), ARICluster uses flexible CFTs, each defind by the TDP threshold, and ensures all derived clusters are maximal and obtain the TDP meeting or exceeding the pre-specified TDP threshold.
The syntax of the function includes two steps:
-
Create an ARIBrainCluster object (type
?ARIbrain::ARIBrainClusterfor more details).ARIBrainCluster(Pmap, mask, conn=18, alpha=0.05)The main input parameter of
ARIBrainCluster()is:Pmap: the map of p-values.
Others optional maps (parameters) are:
mask: the map of numerics/logicals (not mandatory, but useful),conn: the connectivity criterion: face (8), edge (18) and vertex (26),alpha: the significance level.
The output of
ARIBrainCluster()is:ARIBrainCluster: the ARIBrainCluster object.
-
Answer queries given a TDP threshold (type
?ARIbrain::TDPQueryfor more details).TDPQuery(ARIBrainCluster, threshold)The input parameters of
TDPQuery()are:ARIBrainCluster: the ARIBrainCluster object,threshold: the TDP threshold.
The output of
TDPQuery()is:TDPBrainClusters: the TDPBrainClusters object.
The function accepts input map formats of character file names or 3D arrays. Therefore the minimal syntax is
aricluster <- ARIBrainCluster(Pmap)
tdpclusters <- TDPQuery(aricluster, threshold)
Others methods can be used to show the resulting cluster information:
summary(TDPBrainClusters, rest=FALSE)# summarize cluster information & show summary tableprint(TDPBrainClusters)# print summary tableshow(TDPBrainClusters)# display summary tablelength(TDPBrainClusters)# compute the number of clustersTDPBrainClusters[[i]]# obtain 3D voxel indices of the ith largest clusterTDPBrainClusters[1:i]# obtain 3D voxel indices of the top i largest cluster
and to write out the cluster image
writeClusters(TDPBrainClusters, file, template)
Finding clusters with non-zero TDP threshold threshold indicates the presence of some signal in each cluster, however, threshold of 40%, 70% and 90% could be characterized as weak, moderate and strong spatial localisation, respectively.
You simply need to run on the shell:
cluster -z zstat1.nii.gz -t 3.2 -o cluster.nii.gz
This will create cluster.nii.gz that you need.
hint: In case it retun an error message like
cluster: error while loading shared libraries: libutils.so: cannot open shared object file: No such file or directory
type into the shell (replacing the path with your own path of the file fsl.sh):
source /etc/fsl/5.0/fsl.sh
and try again.
Get a complete help for FSL at
https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/Cluster
library(RNifti)
library(hommel)
library(ARIbrain)
Tmap <- RNifti::readNifti(system.file("extdata", "zstat.nii.gz", package="ARIbrain"))
Pmap <- RNifti::readNifti(system.file("extdata", "pvalue.nii.gz", package="ARIbrain"))
mask <- RNifti::readNifti(system.file("extdata", "mask.nii.gz", package="ARIbrain"))
mask <- mask!=0
# compute p-value threshold (thr_p) and z-score threshold (thr_z)
hom <- hommel::hommel(Pmap[mask])
thr_p <- hommel::concentration(hom)
thr_z <- -qnorm(thr_p)
# define clusters
Tmap[!mask] <- 0
clstr <- cluster_threshold(Tmap>thr_z)
table(clstr)
library(ARIbrain)
pvalue_name <- system.file("extdata", "pvalue.nii.gz", package="ARIbrain")
cluster_name <- system.file("extdata", "cluster_th_3.2.nii.gz", package="ARIbrain")
zstat_name <- system.file("extdata", "zstat.nii.gz", package="ARIbrain")
mask_name <- system.file("extdata", "mask.nii.gz", package="ARIbrain")
res_ARI <- ARI(Pmap=pvalue_name, clusters=cluster_name, mask=mask_name, Statmap=zstat_name)
str(res_ARI)
library(RNifti)
library(ARIbrain)
Tmap <- RNifti::readNifti(system.file("extdata", "zstat.nii.gz", package="ARIbrain"))
# compute p-values from test statistic (refering to Normal distribution, right-side alternative)
Pmap <- pnorm(-Tmap)
# read the mask file
mask <- RNifti::readNifti(system.file("extdata", "mask.nii.gz", package="ARIbrain"))
# make sure that mask is a logical map
mask <- mask!=0
# create clusters using a threshold equal to 3.2
Tmap[!mask] <- 0
clstr <- cluster_threshold(Tmap>3.2)
table(clstr)
res_ARI <- ARI(Pmap, clusters=clstr, mask=mask, Statmap=Tmap)
str(res_ARI)