alphasim_-_extended_uses
Table of Contents
alphasim - extended uses
Motivation
Under certain circumstances, the traditional way to employ alphasim does not provide the user with the appropriate cluster-level thresholds to actually correctly achieve the desired false-positive rate (of maps, FWE/Bonferroni-corrected alpha level):
- the maps that are displayed are the result of a conjunction
- the maps are correlations (sometimes more severe if the IV is heavily skewed)
Requirements
Conjunction case
In case of a conjunction analysis, alphasim currently assumes that the terms entering the contrast themselves are valid statistics (their overall false-positive rate behaves as specified) and are independent (e.g. orthogonal contrasts from separate conditions or groups of subjects).
Correlation case
To simulate the outcome of a specific correlation, both the maps used (e.g. per-subject contrast maps) and the regressor (independent variable, e.g. behavioral measure with one value per subject, such as a questionnaire score) must be given.
Alternatively, if only the maps are specified, alphasim generates random (normally distributed) regressors, which then tests whether any skewing in the contrast maps leads to increased (or decreased) levels of false positives and thus larger (or smaller) cluster-level thresholds.
Function help
alphasim - simulate noise data to estimate cluster threshold
FORMAT: [at = ] alphasim(ddim [, opts])
Input fields:
ddim data dimension (1x3 integer values)
opts optional settings
.clconn connectivity of clusters, ('face', {'edge'}, 'vertex')
.conj conjunction simulation (1x1 double, number of maps)
.fftconv boolean flag, use FFT convolution (default: false)
.fwhm FWHM kernel sizes (default: [2, 2, 2])
.mask boolean mask (size must be == ddim!, default: none)
.niter number of iterations, default: 1000
.pbar either xprogress or xfigure:XProgress object
.regmaps regression maps (e.g. betas, contrasts)
.regmodel regression model (all-1s column will be complemented)
.regrank rank-transform data before useing regression
.srf optional surface (perform surface-based simulation)
.srfsmp surface sampling (from, step, to, along normals,
default: [-3, 1, 1])
.srftrf transformation required to sample surface coordinates
derived from bvcoordconv
.thr applied (raw) threshold(s), default: p<0.001
Output fields:
at optional output table
Note: other than AFNI's AlphaSim, the data is considered to be
iso-voxel for the default kernel, but that can be altered
accordingly by changing the kernel!
to simulate specific regression results, both options, .regmaps
.regmodel must be set; if only .regmaps is given, random numbers
(using randn) will be generated instead of permuting the predictor
Usage examples
Conjunction case
In this example, we assume that the map to be cluster-level thresholded is the result of the conjunction of two independent t-statistics. Further settings
- map is 52-by-50-by-62 voxels in size
- functional resolution is 3mm (iso-voxel)
- smoothing of the underlying maps was 8mm → kernel in functional resolution is 8/3 voxel!
- we hope for very few maps with large clusters, thus we increase the number of iterations
- alphasim supports settings several threshold (by rescaling the simulated maps)
asim_options = struct( ... 'conj', 2, ... 'fwhm', [8/3, 8/3, 8/3], ... 'niter', 2500, ... 'thr', [0.05, 0.02, 0.01, 0.005, 0.002, 0.001]); alphasim([52, 50, 62], asim_options);
Correlation case
Only maps are given
Following the example above, we simply use a different set of options:
- maps are given (see glm.RFX_conmaps for how to obtain those from a RFX-GLM)
- mask is derived from those maps
asim_cons = glm.RFX_conmaps([0, 1, 0, -1, 0]); asim_mask = any(asim_cons ~= 0, 4); % this masks voxels for which all subjects have a 0-value asim_options = struct( ... 'fwhm', [8/3, 8/3, 8/3], ... 'mask', any(asim_cons ~= 0, 4), ... 'niter', 2500, ... 'regmaps', asim_mask, ... 'thr', [0.005, 0.002, 0.001]); alphasim(size(asim_mask), asim_options);
This will simulate a normally distributed regressor.
Maps and regressor are given
In addition to the above example, a regressor can be set in asim_options, in which case a permutation-based simulation is performed:
asim_options.regmodel = ... [0.25; 0.61; 1.24; -0.07; 0.91; 1.41; 3.11; -0.12; 0.77; 0.49; 0.8; 0.04]; alphasim(size(asim_mask), asim_options);
Sample output
In the conjunction case, this is the sample output (using only 100 iterations, taking 94 seconds on my MacBook Pro…):
Uncorrected threshold: p<0.050000
------------------------------------------------------------
Cl Size Frequency CumProbCl p / Voxel MaxFreq Alpha
1 6367 0.4037925 0.0500000 0 1.00000
2 3248 0.6097793 0.0435410 0 1.00000
3 1817 0.7250127 0.0369512 0 1.00000
4 1161 0.7986428 0.0314214 0 1.00000
5 804 0.8496322 0.0267104 0 1.00000
6 602 0.8878108 0.0226323 0 1.00000
7 411 0.9138762 0.0189681 0 1.00000
8 290 0.9322679 0.0160495 0 1.00000
9 233 0.9470446 0.0136960 0 1.00000
10 207 0.9601725 0.0115687 0 1.00000
11 137 0.9688610 0.0094688 0 1.00000
12 105 0.9755200 0.0079401 0 1.00000
13 86 0.9809741 0.0066619 4 1.00000
14 59 0.9847159 0.0055277 3 0.96000
15 46 0.9876332 0.0046898 5 0.93000
16 35 0.9898529 0.0039898 6 0.88000
17 41 0.9924531 0.0034217 10 0.82000
18 20 0.9937215 0.0027147 8 0.72000
19 19 0.9949264 0.0023495 7 0.64000
20 19 0.9961314 0.0019832 8 0.57000
21 10 0.9967656 0.0015978 7 0.49000
22 8 0.9972730 0.0013847 4 0.42000
23 7 0.9977169 0.0012062 5 0.38000
24 4 0.9979706 0.0010429 4 0.33000
25 6 0.9983511 0.0009455 6 0.29000
26 8 0.9988584 0.0007933 8 0.23000
27 2 0.9989853 0.0005823 2 0.15000
28 4 0.9992390 0.0005275 3 0.13000
29 1 0.9993024 0.0004139 0 0.10000
30 1 0.9993658 0.0003845 1 0.10000
32 1 0.9994292 0.0003540 0 0.09000
33 3 0.9996195 0.0003216 3 0.09000
34 1 0.9996829 0.0002211 1 0.06000
35 1 0.9997463 0.0001867 1 0.05000
36 2 0.9998732 0.0001512 2 0.04000
37 1 0.9999366 0.0000781 1 0.02000
40 1 1.0000000 0.0000406 1 0.01000
Uncorrected threshold: p<0.020000
------------------------------------------------------------
Cl Size Frequency CumProbCl p / Voxel MaxFreq Alpha
1 2363 0.4895380 0.0200000 0 1.00000
2 1073 0.7118293 0.0157331 0 1.00000
3 542 0.8241144 0.0118581 0 1.00000
4 331 0.8926870 0.0089220 0 1.00000
5 186 0.9312202 0.0065312 2 1.00000
6 115 0.9550445 0.0048519 10 0.98000
7 67 0.9689248 0.0036060 6 0.88000
8 55 0.9803190 0.0027591 18 0.82000
9 19 0.9842552 0.0019646 11 0.64000
10 24 0.9892273 0.0016558 17 0.53000
11 19 0.9931635 0.0012225 8 0.36000
12 10 0.9952351 0.0008451 6 0.28000
13 5 0.9962710 0.0006284 4 0.22000
14 8 0.9979283 0.0005110 8 0.18000
16 4 0.9987570 0.0003088 4 0.10000
17 2 0.9991713 0.0001932 2 0.06000
18 3 0.9997928 0.0001318 3 0.04000
19 1 1.0000000 0.0000343 1 0.01000
Uncorrected threshold: p<0.010000
------------------------------------------------------------
Cl Size Frequency CumProbCl p / Voxel MaxFreq Alpha
1 1176 0.5613365 0.0100000 0 1.00000
2 480 0.7904535 0.0070754 2 1.00000
3 199 0.8854415 0.0046879 6 0.98000
4 103 0.9346062 0.0032032 16 0.92000
5 51 0.9589499 0.0021786 14 0.76000
6 45 0.9804296 0.0015444 26 0.62000
7 17 0.9885442 0.0008729 13 0.36000
8 9 0.9928401 0.0005770 8 0.23000
9 5 0.9952267 0.0003979 5 0.15000
10 4 0.9971360 0.0002860 4 0.10000
11 2 0.9980907 0.0001865 2 0.06000
13 3 0.9995227 0.0001318 3 0.04000
14 1 1.0000000 0.0000348 1 0.01000
Uncorrected threshold: p<0.005000
------------------------------------------------------------
Cl Size Frequency CumProbCl p / Voxel MaxFreq Alpha
1 508 0.5805714 0.0050000 5 1.00000
2 212 0.8228571 0.0033388 19 0.95000
3 90 0.9257143 0.0019523 32 0.76000
4 27 0.9565714 0.0010693 10 0.44000
5 22 0.9817143 0.0007162 18 0.34000
6 10 0.9931429 0.0003564 10 0.16000
7 2 0.9954286 0.0001602 2 0.06000
8 1 0.9965714 0.0001145 1 0.04000
9 3 1.0000000 0.0000883 3 0.03000
Uncorrected threshold: p<0.002000
------------------------------------------------------------
Cl Size Frequency CumProbCl p / Voxel MaxFreq Alpha
1 196 0.6555184 0.0020000 40 1.00000
2 66 0.8762542 0.0011588 31 0.60000
3 24 0.9565217 0.0005923 17 0.29000
4 7 0.9799331 0.0002833 6 0.12000
5 2 0.9866221 0.0001631 2 0.06000
6 1 0.9899666 0.0001202 1 0.04000
7 2 0.9966555 0.0000944 2 0.03000
8 1 1.0000000 0.0000343 1 0.01000
Uncorrected threshold: p<0.001000
------------------------------------------------------------
Cl Size Frequency CumProbCl p / Voxel MaxFreq Alpha
1 81 0.6750000 0.0010000 68 1.00000
2 28 0.9083333 0.0005424 21 0.32000
3 7 0.9666667 0.0002260 7 0.11000
4 2 0.9833333 0.0001073 2 0.04000
5 1 0.9916667 0.0000621 1 0.02000
6 1 1.0000000 0.0000339 1 0.01000
alphasim_-_extended_uses.txt · Last modified: 2010/05/26 04:35 by jochen