AFNI program: 3dClustSim
Output of -help
Usage: 3dClustSim [options]
Program to estimate the probability of false positive (noise-only) clusters.
An adaptation of Doug Ward's AlphaSim, streamlined for various purposes.
In particular, this program lets you run with multiple p-value thresholds
(the '-pthr' option) and only outputs the cluster size threshold at chosen
values of the alpha significance level (the '-athr' option).
In addition, the program allows the output to be formatted for inclusion
into an AFNI dataset's header, whence it can be used in the AFNI Clusterize
interface to show approximate alpha values for the displayed clusters, where
the per-voxel p-value is taken from the interactive threshold slider in the
AFNI 'Define Overlay' control panel, and then the per-cluster alpha value
is interpolated in this table from 3dClustSim. As you change the threshold
slider, the per-voxel p-value (shown below the slider) changes, and then
the interpolated alpha values are updated.
************* IMPORTANT NOTE [Dec 2015] ***************************************
A completely new method for estimating and using noise smoothness values is
now available in 3dFWHMx and 3dClustSim. This method is implemented in the
'-acf' options to both programs. 'ACF' stands for (spatial) AutoCorrelation
Function, and it is estimated by calculating moments of differences out to
a larger radius than before.
Notably, real FMRI data does not actually have a Gaussian-shaped ACF, so the
estimated ACF is then fit (in 3dFWHMx) to a mixed model (Gaussian plus
mono-exponential) of the form
ACF(r) = a * exp(-r*r/(2*b*b)) + (1-a)*exp(-r/c)
where 'r' is the radius, and 'a', 'b', 'c' are the fitted parameters.
The apparent FWHM from this model is usually somewhat larger in real data
than the FWHM estimated from just the nearest-neighbor differences used
in the 'classic' analysis.
The longer tails provided by the mono-exponential are also significant.
3dClustSim has also been modified to use the ACF model given above to generate
noise random fields.
** The take-away (TL;DR or summary) message is that the 'classic' 3dFWHMx and **
** 3dClustSim analysis, using a pure Gaussian ACF, is not very correct for **
** FMRI data -- I cannot speak for PET or MEG data. **
** IMPORTANT CHANGES -- February 2015 ******************************************
** In the past, 3dClustSim did '1-sided' testing; that is, the random dataset
** of Gaussian noise-only values is generated, and then it is thresholded on
** the positive side so that the N(0,1) upper tail probability is pthr.
** NOW, 3dClustSim does 3 different types of thresholding:
** 1-sided: as above
** 2-sided: where positive and negative values above the threshold
** are included, and then clustered together
** (in this case, the threshold on the Gaussian values is)
** (fixed so that the 1-sided tail probability is pthr/2.)
** bi-sided: where positive values and negative values above the
** threshold are clustered SEPARATELY (with the 2-sided threshold)
** For high levels of smoothness, the results from bi-sided and 2-sided are
** very similar -- since for smooth data, it is unlikely that large clusters of
** positive and negative values will be next to each other. With high smoothness,
** it is also true that the 2-sided results for 2*pthr will be similar to the
** 1-sided results for pthr, for the same reason. Since 3dClustSim is meant to be
** useful when the noise is NOT very smooth, we provide tables for all 3 cases.
** In particular, note that when the AFNI GUI threshold is set to a t-statistic,
** 2-sided testing is what is usually appropriate -- in that case, the cluster
** size thresholds tend to be smaller than the 1-sided case, which means that
** more clusters tend to be significant than in the past.
** In addition, the 3 different NN approaches (NN=1, NN=2, NN=3) are ALL
** always computed now. That is, 9 different tables are produced, each
** of which has its proper place when combined with the AFNI Clusterize GUI.
** The 3 different NN methods are:
** 1 = Use first-nearest neighbor clustering
** * above threshold voxels cluster together if faces touch
** 2 = Use second-nearest neighbor clustering
** * voxels cluster together if faces OR edges touch
** 3 = Use third-nearest neighbor clustering
** * voxels cluster together if faces OR edges OR corners touch
** The clustering method only makes a difference at higher (less significant)
** values of pthr. At small values of pthr (more significant), all three
** clustering methods will give very similar results.
**** PLEASE NOTE that the NIML outputs from this new version are not named the
**** same as those from the older version. Thus, any script that takes the NIML
**** format tables and inserts them into an AFNI dataset header must be modified
**** to match the new names. The 3drefit command fragment output at the end of
**** this program (and echoed into file '3dClustSim.cmd') shows the new form
**** of the names involved.
**** SMOOTHING CHANGE -- May 2015 **********************************************
** It was pointed out to me (by Anders Eklund and Tom Nichols) that smoothing
** the simulated data over a finite volume introduces 2 artifacts, which might
** be called 'edge effects'. To minimize these problems, this program now makes
** extra-large (padded) simulated volumes before blurring, and then trims those
** back down to the desired size, before continuing with the thresholding and
** cluster-counting steps. To run 3dClustSim without this padding added, use
** the new '-nopad' option.
OPTIONS [at least 1 option is required, or you'll get this help message!]
******* Specify the volume over which the simulation will occur *******
-----** (a) Directly give the spatial domain that will be used **-----
-nxyz n1 n2 n3 = Size of 3D grid to use for simulation
[default values = 64 64 32]
-dxyz d1 d2 d3 = give all 3 voxel sizes at once
[default values = 3.5 3.5 3.5]
-BALL = inside the 3D grid, mask off points outside a ball
at the center of the grid and touching the edges;
this will keep about 1/2 the points in the 3D grid.
[default = use all voxels in the 3D grid]
-----** OR: (b) Specify the spatial domain using a dataset mask **-----
-mask mset = Use the 0 sub-brick of dataset 'mset' as a mask
to indicate which voxels to analyze (a sub-brick
selector '' is allowed)
-OKsmallmask = Allow small masks. Normally, a mask volume must have
128 or more nonzero voxels. However, IF you know what
you are doing, and IF you are willing to live life on
the edge of statistical catastrophe, then you can use
this option to allow smaller masks -- in a sense, this
is the 'consent form' for such strange shenanigans.
* If you use this option, it must come BEFORE '-mask'.
* Also read the 'CAUTION and CAVEAT' section, far below.
** '-mask' means that '-nxyz' & '-dxyz' & '-BALL' will be ignored. **
-----** OR: (c) Specify the spatial domain by directly giving simulated volumes **-----
-inset iset [iset ...] = Read the 'iset' dataset(s) and use THESE volumes
as the simulations to threshold and clusterize,
[Feb 2016] rather than create the simulations internally.
* For example, these datasets could come from
3dttest++ -toz -randomsign 1000 -setA ...
* This can be combined with '-mask'.
* Using '-inset' means that '-fwhm', '-acf', '-nopad',
'-niter', and '-ssave' are ignored as meaningless.
---** the remaining options control how the simulation is done **---
-fwhm s = Gaussian filter width (all 3 dimensions) in mm (non-negative)
[default = 0.0 = no smoothing]
* If you wish to set different smoothing amounts for each
axis, you can instead use option
-fwhmxyz sx sy sz
to specify the three values separately.
-acf a b c = Alternative to Gaussian filtering: use the spherical
autocorrelation function parameters output by 3dFWHMx
to do non-Gaussian (long-tailed) filtering.
* Using '-acf' will make '-fwhm' pointless!
* The 'a' parameter must be between 0 and 1.
* The 'b' and 'c' parameters (scale radii) must be positive.
* The spatial autocorrelation function is given by
ACF(r) = a * exp(-r*r/(2*b*b)) + (1-a)*exp(-r/c)
>>---------->>*** Combined with 3dFWHMx, the '-acf' method is now the
recommended way to generate clustering statistics in AFNI!
-nopad = The program now [12 May 2015] adds 'padding' slices along
each face to allow for edge effects of the smoothing process.
If you want to turn this feature off, use the '-nopad' option.
* For example, if you want to compare the 'old' (un-padded)
results with the 'new' (padded) results.
* '-nopad' has no effect when '-acf' is used, since that option
automatically pads the volume when creating it (via FFTs) and
then truncates it back to the desired size for clustering.
-pthr p1 .. pn = list of uncorrected (per voxel) p-values at which to
threshold the simulated images prior to clustering.
[default = 0.05 0.02 0.01 0.005 0.002 0.001 0.0005 0.0002 0.0001]
-athr a1 .. an = list of corrected (whole volume) alpha-values at which
the simulation will print out the cluster size
thresholds. For each 'p' and 'a', the smallest cluster
size C(p,a) for which the probability of the 'p'-thresholded
image having a noise-only cluster of size C is less than 'a'
is the output (cf. the sample output, below)
[default = 0.10 0.05 0.02 0.01]
** Both lists '-pthr' and '-athr' (of values between 0 and 0.2) **
** should be given in DESCENDING order. They will be sorted to be **
** that way in any case, and such is how the output will be given. **
** The list of values following '-pthr' or '-athr' can be replaced **
** with the single word 'LOTS', which will tell the program to use **
** a longer list of values for these probabilities [try it & see!] **
** (i.e., '-pthr LOTS' and/or '-athr LOTS' are legal options) **
-LOTS = the same as using '-pthr LOTS -athr LOTS'
-MEGA = adds even MORE values to the '-pthr' and '-athr' grids.
-iter n = number of Monte Carlo simulations [default = 10000]
-nodec = normally, the program prints the cluster size threshold to
1 decimal place (e.g., 27.2). Of course, clusters only come
with an integer number of voxels -- this fractional value
is interpolated to give the desired alpha level. If you
want no decimal places (so that 27.2 becomes 28), use '-nodec'.
-seed S = random number seed [default seed = 123456789]
* if seed=0, then program will quasi-randomize it
-niml = Output the table in an XML/NIML format, rather than a .1D format.
* This option is for use with other software programs;
see the NOTES section below for details.
* '-niml' also implicitly means '-LOTS'.
-both = Output the table in XML/NIML format AND in .1D format.
* You probably want to use '-prefix' with this option!
Otherwise, everything is mixed together on stdout.
* '-both' implies 'niml' which implies '-LOTS'.
So '-pthr' (if desired) should follow '-both'/'-niml'
-prefix ppp = Write output for NN method #k to file 'ppp.NNk_Xsided.1D',
for k=1, 2, 3, and for X=1sided, 2sided, bisided.
* If '-prefix is not used, results go to standard output.
* If '-niml' is used, the filename is 'ppp.NNk_Xsided.niml'.
To be clear, the 9 files that will be named
ppp.NN1_1sided.niml ppp.NN1_2sided.niml ppp.NN1_bisided.niml
ppp.NN2_1sided.niml ppp.NN2_2sided.niml ppp.NN2_bisided.niml
ppp.NN3_1sided.niml ppp.NN3_2sided.niml ppp.NN3_bisided.niml
* If '-niml' AND '-mask' are both used, then a compressed ASCII
encoding of the mask volume is stored into file 'ppp.mask'.
This string can be stored into a dataset header as an attribute
with name AFNI_CLUSTSIM_MASK, and will be used in the AFNI
Clusterize GUI, if present, to mask out above-threshold voxels
before the clusterizing is done (which is how the mask is used
here in 3dClustSim).
* If the ASCII mask string is NOT stored into the statistics dataset
header, then the Clusterize GUI will try to find the original
mask dataset and use that instead. If that fails, then masking
won't be done in the Clusterize process.
-quiet = Don't print out the progress reports, etc.
* Put this option first to silence most informational messages.
-ssave:TYPE ssprefix = Save the un-thresholded generated random volumes into
datasets ('-iter' of them). Here, 'TYPE' is one of these:
* blurred == save the blurred 3D volume before masking
* masked == save the blurred volume after masking
The output datasets will actually get prefixes generated
with the string 'ssprefix' being appended by a 6 digit
integer (the iteration index), starting at 000000.
(You can use SOMETHING.nii as a prefix; it will work OK.)
N.B.: This option will slow the program down a lot,
and is intended to help just one specific user.
* This program is like running AlphaSim once for each '-pthr' value and then
extracting the relevant information from its 'Alpha' output column.
++ One reason for 3dClustSim to be used in place of AlphaSim is that it will
be faster than running AlphaSim multiple times.
++ Another reason is that the resulting table can be stored in an AFNI
dataset's header, and used in the AFNI Clusterize GUI to see estimated
cluster significance (alpha) levels.
* To be clear, the C(p,alpha) thresholds that are calculated are for
alpha = probability of a noise-only smooth random field, after masking
and then thresholding at the given per-voxel p value, producing a cluster
of voxels at least this big.
++ So if your cluster is larger than the C(p,0.01) threshold in size (say),
then it is very unlikely that noise BY ITSELF produced this result.
++ This statement does not mean that ALL the voxels in the cluster are
'truly' active -- it means that at least SOME of them are (very probably)
active. The statement of low probability (0.01 in this example) of a
false positive result applies to the cluster as a whole, not to each
voxel within the cluster.
* To add the cluster simulation C(p,alpha) table to the header of an AFNI
dataset, something like the following can be done [tcsh syntax]:
set fwhm = ( `3dFWHMx -combine -detrend time_series_dataset+orig` )
3dClustSim -mask mask+orig -fwhm $fwhm -niml -prefix CStemp
3drefit -atrstring AFNI_CLUSTSIM_NN1_1sided file:CStemp.NN1_1sided.niml \
-atrstring AFNI_CLUSTSIM_MASK file:CStemp.mask \
rm -f CStemp.*
AFNI's Clusterize GUI makes use of these attributes, if stored in a
statistics dataset (e.g., something from 3dDeconvolve, 3dREMLfit, etc.).
** Nota Bene: afni_proc.py will automatically run 3dClustSim, and **
*** put the results into the statistical results dataset for you. ***
**** Another reason to use afni_proc.py for single-subject analyses! ****
* 3dClustSim will print (to stderr) a 3drefit command fragment, similar
to the one above, that you can use to add cluster tables to any
relevant statistical datasets you have lolling about.
* The C(p,alpha) table will be used in Clusterize to provide the cluster
level alpha value when the AFNI GUI is set so that the Overlay threshold
sub-brick is a statistical parameter (e.g., a t- or F-statistic), from which
a per-voxel p-value can be calculated, so that Clusterize can interpolate
in the C(p,alpha) table.
++ To be clear, the per-voxel p-value is taken from the AFNI GUI threshold
slider (the p-value is shown beneath the slider), and then the C(p,alpha)
table is inverse-interpolated to find the per-cluster alpha value for
each different cluster size.
++ As you move the AFNI threshold slider, the per-voxel (uncorrected for
multiple comparisons) p-value changes, the cluster sizes change (as fewer
or more voxels are included), and so the reported per-cluster alpha
values change for both reasons -- different p and different cluster size.
++ The alpha values reported are 'per-cluster', and are not themselves
corrected for multiple comparisons ACROSS clusters. These alpha values
are corrected for multiple comparisons WITHIN a cluster.
* AFNI will use the NN1, NN2, NN3 tables as needed in its Clusterize
interface if they are all stored in the statistics dataset header,
depending on the NN level chosen in the Clusterize controller.
* The blur estimates (provided via -fwhm, say) can come from various
1) If '3dmerge -1blur_fwhm SIZE' is used to apply the blur to EPI
data, that blur is on top of what is already in the data. It is
then appropriate to estimate the final blur size using 3dFWHMx on
the residual EPI time series (after regression). The final blur
will generally be a bit larger than SIZE. Consider how this is
done by afni_proc.py.
2) If '3dBlurToFWHM -FWHM SIZE' is used, then one can use SIZE
directly (since the resulting blur is SIZE, it is not on top of
what is in the data to begin with).
3) Some people prefer to estimate the smoothness from the stdev of
error in the given statistical test, rather than the residuals.
CAUTION and CAVEAT: [January 2011]
* If you use a small ROI mask and also have a large FWHM, then it might happen
that it is impossible to find a cluster size threshold C that works for a
given (p,alpha) combination.
* Generally speaking, C(p,alpha) gets smaller as p gets smaller and C(p,alpha)
gets smaller as alpha gets larger. As a result, in a small mask with small p
and large alpha, C(p,alpha) might shrink below 1. But clusters of size C
less than 1 don't make any sense!
* For example, suppose that for p=0.0005 that only 6% of the simulations
have ANY above-threshold voxels inside the ROI mask. In that case,
C(p=0.0005,alpha=0.06) = 1. There is no smaller value of C where 10%
of the simulations have a cluster of size C or larger. Thus, it is
impossible to find the cluster size threshold for the combination of
p=0.0005 and alpha=0.10 in this case.
* 3dClustSim will report a cluster size threshold of C=1 for such cases.
It will also print (to stderr) a warning message for all the (p,alpha)
combinations that had this problem.
* This issue arises because 3dClustSim reports C for a given alpha.
In contrast, AlphaSim reports alpha for each given C, and leaves
you to interpret the resulting table; it doesn't try to find C(p,alpha)
for a given alpha, but finds alpha for various values of C.
* If you wish to see this effect in action, the following commands
can be used as a starting point:
3dClustSim -nxyz 8 8 8 -dxyz 2 2 2 -fwhm 8 -niter 10000
AlphaSim -nxyz 8 8 8 -dxyz 2 2 2 -fwhm 8 -niter 10000 -quiet -fast -pthr 0.0005
From the 3dClustSim command above, you should get a warning message
similar to this, right after the table (only the first 2 lines are shown):
*+ WARNING: Simulation not effective for these cases:
NN=1 pthr= 0.001000 alpha= 0.100 [max simulated alpha= 0.087]
---- RW Cox -- July 2010 ----
SAMPLE OUTPUT from the command '3dClustSim -fwhm 7' [only the NN=1 1-sided results]
# 3dClustSim -fwhm 7
# 1-sided thresholding
# Grid: 64x64x32 3.50x3.50x3.50 mm^3 (131072 voxels)
# CLUSTER SIZE THRESHOLD(pthr,alpha) in Voxels
# -NN 1 | alpha = Prob(Cluster >= given size)
# pthr | 0.100 0.050 0.020 0.010
# ------ | ------ ------ ------ ------
0.050000 162.5 182.2 207.8 225.7
0.020000 64.3 71.0 80.5 88.5
0.010000 40.3 44.7 50.7 55.1
0.005000 28.0 31.2 34.9 38.1
0.002000 19.0 21.2 24.2 26.1
0.001000 14.6 16.3 18.9 20.5
0.000500 11.5 13.0 15.1 16.7
0.000200 8.7 10.0 11.6 12.8
0.000100 7.1 8.3 9.7 10.9
e.g., for this sample volume, if the per-voxel p-value threshold is set
at 0.005, then to keep the probability of getting a single noise-only
cluster at 0.05 or less, the cluster size threshold should be 32 voxels
(the next integer above 31.2).
If you ran the same simulation with the '-nodec' option, then the last
line above would be
0.000100 8 9 10 11
If you set the per voxel p-value to 0.0001 (1e-4), and want the chance
of a noise-only false-positive cluster to be 5% or less, then the cluster
size threshold would be 9 -- that is, you would keep all NN clusters with
9 or more voxels.
The header lines start with the '#' (commenting) character so that the result
is a correctly formatted AFNI .1D file -- it can be used in 1dplot, etc.
* This binary version of 3dClustSim is NOT compiled using OpenMP, a
semi-automatic parallelizer software toolkit, which splits the work
across multiple CPUs/cores on the same shared memory computer.
* However, the source code is modified for OpenMP, and can be compiled
with an OpenMP-capable compiler, such as gcc 4.2+, Intel's icc, and
* If you wish to compile this program with OpenMP, see the man page for
your C compiler, and (if needed) consult the AFNI message board, and
++ Compile date = Feb 10 2016
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