Dear Kath,
At 22:49 08/02/99 -0800, Kath Moores wrote:
| I am analysing data from my functional MRI study using the Medx
| implementation of SPM. The study has 10 subjects, 5 conditions per run
| and 8 runs collected per subject. This gives a total of 640 volumes per
| subject.
OK - firstly I have to say that I have never used nor have access to the
MEDx implementation!
| There are a few issues that I wanted to clarify:
| (1) I had hoped to be able to use the functional MR design within SPM,
| maintaining the time series. As you can see I would end up with 80
| sessions (i.e., 8 runs X 10 subjects). There are two problems with this:
| (a) the volume of data - I don't think the DEC Alpha we are runnning on
| could handle it, and (2) I 'm not sure how this relates to fixed and
| mixed effects.
SPM (and the MEDx implementation) only considers a single source of error
variance. This is the scan to scan residual error. With repeated
measurements on multiple subjects scan to scan is within subject, and the
analysis is fixed effects. You would certainly have problems getting 80
sessions into SPM, especially the MEDx implementation which reads the
entire data set into memory (SPM uses the data in situ on disk as virtual
memory).
| (2) Ideally, for a group analysis I would like to be able to use a
| mixed effects model to account for the condition effects and subject
| variability effects, but I see from the notes accompanying the Random
| Effects Kit that it is preferable not to have repeated measures - and if
| you do you should pool the data for each subject, for each condition
| into one image.
Its not that repeated measures are bad, it's just that in the presence of
repeated measures SPM can only do a fixed effects analysis.
With only one "scan" per subject, scan to scan residual variability is
between subject variance. For balanced designs, by summarising the
individual subject data with an appropriate measure, and then assessing
those measures across subject, a random effects analysis is effected. Using
the within-subject data to compute the summary measure "scan" incorporates
the within-subject error into the summary scans, such that the between
variability between subject of these computed summary "scans" incorporates
both within and between subject variance. It's fairly easy for a balanced
design to show that these are in exactly the right ratio for a random
effects assessment of the overall (population) effect.
Although this second level (between subjects) model is a fixed effects
model, by using summary "scans", the fixed effect is the population effect
(which *is* fixed), and the residual error variance is that appropriate for
assessing that population effect allowing for random subject effects (&
subject by condition interaction).
(Actually, the SPM96 random effects approach would surmise each subject by
two "scans" - adjusted mean condition images for each condition. These
would then be assessed using a paired test, which is the same as testing
the differences of the adjusted means directly. This is for technical
reasons - there are problems (grey matter) thresholding negative images in
SPM96.)
| How does this type of mixed effects model (i.e., random and condition
| effects)relate to the fMRI time series model? Is the fMRI model purely a
| fixed effects model? How does the fMRI design in SPM handle sources of
| variability?
As above. SPM only does fixed effects models. The summary measures approach
to random effects simply recasts a mixed-effects model into a framework
where simple fixed effects procedures give the right answer.
| These issues pertain to my main problem: If I did collapse the data from
| each subject across conditions - clearly I do not have a time series,
| and therefore I forfeit the benefits of the time series approach ( i.e,
| modelling of low frequencu physiological noise etc).
That depends how you construct your summary measure. If you construct your
summary measure from a sophisticated time series model then you retain all
the advantages of the time series approach.
The random effects kit for SPM96 produces summary measures as the fitted
effects from a standard SPM General Linear Model. This is like a
sophisticated adjusted mean. It uses a delayed smoothed box-car model with
"high-pass filter" modelling of low frequency confounds. (Note however that
if a covariate is orthogonal to the effect of interest it has no effect on
the fitted effect.) Don't think MEDx has this (post SPM96) functionality in
it, but I may be wrong.
( nuSPM integrates the random effects kit into the core of SPM,
( enabling any SPM model to be used a first level (within subject) model,
( and any contrast from that model as summary statistic.
| This approach would avoid the data quantitiy problems.
...which sadly seems to be the main reason random effects analyses are
catching on!
----------------
Note that you have an additional "level" of variance - between session
within subject. For inference to the population from which these eight
subjects were chosen you would have to first surmise each session, and then
surmise each subject, resulting in only 8 (sets of) summary "scans" to assess.
----------------
| The other option that was suggested on the SPM list (Cathy Price) was to
| do a single subject fMRI design and do conjunction analysis on the
| resultsing SPM maps (i.e., an across subject conjucntion). I did note
| your veiws on this and the limitation in generalising to the popoulation
| from this type of method.
A fixed effects analysis in the context of subject by condition
interactions (i.e. subject specific activation) only infers about the
average effect for this group of subjects. This is not a problem is you are
only interested in this group of subjects *on average* as a case study, but
clearly *is* a problem is you want to generalize beyond these subjects. The
main problem is that a significant average effect for this group actually
only reflect responses in a few subjects. For example, if ten people do
nothing but one has a huge response, the average group response may well be
significant!
Conjunction analysis (in its current formulation) addresses this issue by
seeking areas where there is a significant average effect but no
(significant) subject by condition interaction. A response significant by
conjunction analysis is then a response shared by all of the subjects in
this group. This is clearly more stringent than the "group on average" of
the simple fixed effects analysis, but is still short of full population
inference.
However, one could then use this kind of information to estimate the
proportion of the population exhibiting the response. This idea is
developed in:
Friston KJ, Holmes AP, Price CJ, Buechel C, Worsley KJ
"Multi-subject fMRI studies and conjunction analyses"
...which is currently under review. You can pick up the manuscript from
ftp://ftp.fil.ion.ucl.ac.uk/out/methods/karl/fMRI_conjunctions/paper.pdf
(This paper also has a comprehensive discussion of random effects issues.)
( Conjunctions in nuSPM has been reformulated simply as activation in all
( contrasts. This is effected in a single SPM by taking the minima of the
( SPMs to be conjoined at each voxel. The above paper describes the
( distributional and random field theory results for such minima SPM.
----------------
Current references for the SPM random effects approach were given in a
recent SPM email:
http://www.mailbase.ac.uk/lists/spm/1999-03/0057.html
----------------
| So at the present time, really I am not sure whether to average the data
| I have and do a PET like analysis procedure or use the fMRI design and
| retain the time series. ANY advice on these matters would be really
| usefull.
Hope this has helped...
-andrew
PS: Sorry to have taken so long to get back to you...
+- Dr Andrew Holmes ------------------ mailto:[log in to unmask] -+
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