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3dFDR

3dFDR is an AFNI program for controlling the multiple comparisons problem in any statistical test (t-test, ANOVA, etc.). It works by generating a new statistical threshold that predicts the percent of false positives at a given p-value. The new threshold, called a q-value, is generated from the distribution of p-values in your data. The output of the program is a sorted list of p-values with a q-value associated with each one. Standard q-value thresholds are .05 or .1, indicating predicted 5% or 10% false positives among all significant voxels. The test is much less conservative than Bonferroni and is easier to implement than family-wise corrections. It is also valid under situations of high positive correlations in a dataset, which we typically have in neighboring SAM voxels. 3dFDR can also be used to give a common threshold for a SAM sliding window dataset using the combined p-values from t-tests at each time slice.

Usage

The help menu incorrectly states that the default -cind option is only valid for independent p-values. This is incorrect; -cind should be used for both independent p-values and cases where positive correlations between p-values are expected (as is the case for SAM datasets). -cdep is more conservative and should only be used for datasets with more complex positive and negative correlations (hardly ever true for SAM).

Here is a sample script for calculating a single FDR threshold for multiple t-tests performed at each window of a SAM sliding window dataset. The sample sliding window data has 38 time points and 20 subjects.

for i in `seq 0 37`;
do
    3dttest -session RESULTS -prefix ttest_${i} -base1 0 \
        -set2 set1+tlrc\[$i] set2+tlrc\[$i] \
              set3+tlrc\[$i] set4+tlrc\[$i] \
              set5+tlrc\[$i] set6+tlrc\[$i] \
              set7+tlrc\[$i] set8+tlrc\[$i] \
              set9+tlrc\[$i] set10+tlrc\[$i] \
              set11+tlrc\[$i] set12+tlrc\[$i] \
              set13+tlrc\[$i] set14+tlrc\[$i] \
              set15+tlrc\[$i] set16+tlrc\[$i] \
              set17+tlrc\[$i] set18+tlrc\[$i] \
              set19+tlrc\[$i] set20+tlrc\[$i] 

    3dcalc -t RESULTS/ttest_${i}+tlrc[1] -expr "fitt_t2p(t,19)" -prefix RESULTS/ttest_${i}_p
    3dmaskdump -noijk -mask N27_mask_newgrid+tlrc RESULTS/ttest_${i}_p+tlrc >> ttest_Pvalues
done

3dFDR -input1D ttest_Pvalues -list -cind > ttest_Qvalues

A trick using brace expansion for generating the 3dttest -set2 list in bash goes like this:

slist={`seq -s, 1 20`}
...
    set2=`eval echo set$slist+tlrc\[$i]`
    eval 3dttest -session RESULTS -prefix ttest_${i} -base1 0 \
        -set2 $set2

A single list of p-values from t-tests at each window is generated in a loop. 3dFDR is then used to associate q-values with the sorted list of p-values. The output file ttest_Qvalues will look something like this:

      Index      p-value      q-value      z-score 
......
       29449     0.020939     0.049972     1.960204 
       10796     0.020943     0.049980     1.960139 
       95533     0.020943     0.049980     1.960139 
       80055     0.020944     0.049981     1.960127 
       10186     0.020945     0.049982     1.960116 
      108282     0.020946     0.049984     1.960104 
       37049     0.020948     0.049986     1.960080 
       45878     0.020948     0.049986     1.960080 
      105672     0.020951     0.049993     1.960028 
       31238     0.020952     0.049993     1.960024 
       64705     0.020952     0.049993     1.960024 
       71425     0.020953     0.049994     1.960013 
       13603     0.020954     0.049996     1.960001 
       51660     0.020957     0.050000     1.959966 
       69209     0.020957     0.050000     1.959966 
      105685     0.020957     0.050000     1.959966 
       22420     0.020958     0.050001     1.959954 
       72279     0.020960     0.050005     1.959922 
       52726     0.020961     0.050006     1.959910 
       27627     0.020964     0.050012     1.959857 
       44890     0.020968     0.050021     1.959784 
       84083     0.020970     0.050025     1.959752
...... 

Here we see that a q-value of .05, representing a 5% chance of a false positive, is associated with a p-value of .020957.