Dear Wolfgang,
|We have problems with a simple activation task for two groups: patients
|and healthy controls. We are using a block-design with alternating rest
|and activation condition (Tr=3s, 100 measurements, 10 measurements per
|epoch). Everything was preprocessed and put in one big statistical
|matrix. The individual contrasts show that the healthy controls have
|activation in brain regions where the patients don't activate. I get
|corresponding results when I set up contrasts like 0 0 0 0 1 1 1 1 where
|all patients are set to one and the controls are set to zero and vice
|versa. Also contrasts like -1 -1 -1 -1 1 1 1 1 seem to give me good
|results for interaction. Now, is this method valid?
This depends on the inference you want to make from the comparisons. You
are describing a fixed effects model, so the statistical inference is
restricted to the specific group of patients and specific group of
controls you are studying. Usually in comparing patients and controls you
would like to generalise your inferences to the population of patients and
controls. This can be implemented in SPM by the 'second level' analysis
you describe, effecting a random effects model where the error variance is
solely the inter-subject (i.e. intra-population) variance.
|When I do a second level analysis with the individual contrast images
|(what information contain these images anyway ?????)
The contrast images represent spatially distributed images of the
weighted sum of the parameter estimates for that particular contrast. In
essence and for your particular case, it's like a difference image for
(activation-rest). You need one contrast image for each patient and each
control. By doing that you are collapsing over intra-subject variability
(to only one image per contrast per subject) and the image-to-image
residual variability is now between subject variance alone.
| with a two-sample
|t-test or with one-sample t-tests for each group I get really strange
|results. Suddenly the patients are activating more then the controls in
|brain regions where not even one patient activated individually. Things
|change again dramatically (and get even stranger) when I use
|proportional scaling in the first level analysis. Now I would like to
|know, what exactly the second - level analysis tells me and whether it
|is valid just to work with the first level analysis.
There are many possible reasons for the differences, which are basically
telling you that the error map for the fixed and random
effects models are different (as might be expected). Usually
proportional scaling would be used in the first level of analysis,
because you want the contrast images entering into the second level of
analysis to be on the same scale. You don't tell us how many
subjects are in each group, but I infer from the fixed effect
contrasts that you have four subjects in each group. In this case, you
will not have very many degrees of freedom for the second level of
analysis and therefore lack power. In general, the recommendation would be
to use 10-12 subjects per group for a second level analysis so adding
subjects will help considerably.
As to which method is 'valid', that depends on the nature of the
statistical inference you wish to make. In general for comparisons
between patient populations and control populations a random effects
model will be more appropriate, as one would like to generalise the
result beyond the specific individuals studied to the population. You
might be interested in the excellent summary of the rfx discussions
prepared by Darren Gitelman, which is at
http://www.brain.nwu.edu/fmri/spm/ranfx.html
Best wishes,
Geraint
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Dr. Geraint Rees
Wellcome Advanced Fellow Lecturer
California Institute of Technology Institute of Neurology
Division of Biology 139-74 University College London
Pasadena 12 Queen Square
California 91125 London WC1N 3BG
voice (626) 395-2880 voice (171) 833-7472
fax (626) 796-8876 fax (171) 813-1420
http://www.klab.caltech.edu/~geraint [log in to unmask]
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