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alphasim_-_extended_uses [2010/05/26 06:35] (current)
jochen created
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 +====== 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 =====
 +<​code>​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</​code>​
 +
 +===== 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)
 +
 +<code matlab>​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);</​code>​
 +
 +==== 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
 +
 +<code matlab>​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);</​code>​
 +
 +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:
 +
 +<code matlab>​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);</​code>​
 +
 +===== Sample output =====
 +In the conjunction case, this is the sample output (using only 100 iterations, taking 94 seconds on my MacBook Pro...):
 +
 +<​code>​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</​code>​
  
alphasim_-_extended_uses.txt ยท Last modified: 2010/05/26 06:35 by jochen