Thank you Tom, that does help a lot.

Best regards,

Omar

**From:** **On Behalf Of **Thomas
Nichols

**Sent:** Thursday, February 25, 2010
1:43 AM

**To:** [log in to unmask]

**Subject:** Re: [FSL] Randomize
design and contrast matrix for Fractional Anisotropy

Dear Omar,

The purpose of assigning the individuals a number rather than

assigning the it to the groups is to code the repeated measures nature

of the design. The FSL randomise website explains it as follows: "This

will ensure that permutations will only occur within subject,

respecting the repeated measures structure of the data"

I wish that the true experts would expand on this last quote from the

website. Here is my attempt at it. Typically what randomise would do

is create a null distribution by repeatedly moving single subject's

data from one group (lets say the experimental group) to another group

(let us say the control group) thus "randomising" the results in such

a way that if there is no effect of treatment the resulting observed

distribution should not be different from the randomised distribution.

Great, that is how it would work if you are looking at group

differences. However, when are looking at repeated measures designs,

you end up wanting to create a null distribution that tests the within

subjects effect. So, you treat each subject's set of data (e.g. T1 and

T2 in my data) as a single group. Then you start moving (randomising)

between these multiple groups of within subject data.

That is the best way I can try to explain it. I think the experts

would do a much better job. I probably butchered the terminology and

made some conceptual mistakes.

I'm sorry the documentation wasn't clearer. The basic issue is
that randomise is built on the GLM, which uses OLS for estimation and assumes
each measurement are independent. To the extent we have repeated
measures, we have to start playing tricks with OLS and restricting how
permutation is done to make things work out. There's no universal theory
here; we're doing something naughty (trying to use OLS permutation for repeated
measures) and for each type of design *and* contrast of interest we have to
make sure that we're standing on our heads and spinning the plate the right way
to make sure things work out.

SO, the part of the manual you cite is the part on "ANOVA:
1-factor 4-levels (Repeated Measures)" manual
is considering the case where you have on group of subjects each with 4 scans
(or copes) each. Under the null hypothesis that there is no factor
effect, we can permute within subject (not between subjects, as we allow that
there is intrasubject correlation). This is what the design.grp file
does.

Does this help?

-Tom

Any takers on expanding my explanation.

Omar

On Fri, Feb 12, 2010 at 2:57 PM, Adnan Majid <[log in to unmask]> wrote:

> Hi Gwenaelle, Omar, and all,

> Thanks for all your advice. I still had a few questions concerning setting

> up the design matrix. In Omar's example design matrix below, what is the

> advantage of assigning each of the six subjects an individual group number

> rather than separating into the three groups of the study (control, relapse,

> and abstinent)? Furthermore, how would the subsequent design.grp file be

> incorporated into the randomise analysis - would it have any effect on the

> expected results?

> Thanks so much!

> Adnan

> Group/EV1(control time1)/EV2(control time2)/EV3(relapse time 1)/EV4 (relapse

> time2)/EV5 (abstinent time1)/EV6 (abstinent time2)/

> EV7(subject1)/EV8(sub2)/EV9(sub3)/EV10(sub4)/EV11(sub5)/EV12(sub6)

>

> 1/1/0/0/0/0/0/1/0/0/0/0/0

> 1/0/1/0/0/0/0/1/0/0/0/0/0

> 2/0/0/1/0/0/0/0/1/0/0/0/0

> 2/0/0/0/1/0/0/0/1/0/0/0/0

> 3/0/0/1/0/0/0/0/0/1/0/0/0

> 3/0/0/0/1/0/0/0/0/1/0/0/0

> 4/0/0/0/0/1/0/0/0/0/1/0/0

> 4/0/0/0/0/0/1/0/0/0/1/0/0

> 5/0/0/0/0/1/0/0/0/0/0/1/0

> 5/0/0/0/0/0/1/0/0/0/0/1/0

> 6/0/0/0/0/1/0/0/0/0/0/0/1

> 6/0/0/0/0/0/1/0/0/0/0/0/1

>

> On Wed, Feb 10, 2010 at 5:30 AM, Gwenaëlle DOUAUD <[log in to unmask]>

> wrote:

>>

>> Hi Omar,

>>

>> let's start from scratch. Say you've got n subjects in total and x

>> contrasts.

>>

>> You've got your design matrix design.mat which is right to start with.

>>

>> Then for your contrast design.con (x contrasts=rows, 3*2+n EVs=columns),

>> you need:

>>

>> (EVs: CON1 CON2 ABS1 ABS2 REL1 REL2 subj1 subj2 sub3...)

>> -1 1 1 -1 0 0 0 0 0...

>> -1 1 0 0 1 -1 0 0 0...

>> 0 0 -1 1 1 -1 0 0 0...

>> -1 1 0 0 0 0 0 0 0...

>> 0 0 -1 1 0 0 0 0 0...

>> 0 0 0 0 -1 1 0 0 0...

>>

>> First row = where the changes between controls (increase of FA) are

>> significantly different from the changes in abstinent patients

>> Second row = where the changes between controls (increase of FA) are

>> significantly different from the changes in relapsing patients

>> etc.

>> Fourth row = where the changes between the two time points are significant

>> in the controls

>> etc.

>>

>> What you also want is to answer this question: "overall is there any

>> significant difference between the changes across groups".

>>

>> So you'll need an F-test, with a design.fts (with 1 row, x column):

>> 1 1 0 0 0 0

>>

>> That tells the model to do the F-test for the first two contrasts of the

>> design.con (third one is redundant).

>>

>> So with all that, you'll be able to answer to:

>> * "overall is there any significant difference between the changes across

>> groups", that's the F-test

>> * "is there any significant difference between the changes in CON/ABS

>> (increase of FA) and in ABS/REL", these are the first 3 contrasts of your

>> model

>> and finally:

>> * "is there any significant increase between the two time points in

>> CON/ABS/REL", these are the last 3 contrasts of your model (post-hoc paired

>> t-tests)

>>

>> In practice in the Glm gui: you need x contrasts and one F test and you

>> click on the first 2 boxes of the F-test.

>>

>> and randomise, something like:

>> randomise -i all_FA_skeletonised -m mean_FA_skeleton_mask -o res_FA -d

>> design.mat -t design.con -f design.fts -F 4 -c 2 --T2 -n 1000

>>

>>

>> Hope this helps,

>> Gwenaelle

>>

>>

>>

>>

>>

>>

>>

>>

>>

>>

>

>

--

____________________________________________

Thomas Nichols, PhD

Principal Research Fellow, Head of Neuroimaging Statistics

Department of Statistics & Warwick Manufacturing Group

Email: [log in to unmask]

Phone, Stats: +44 24761 51086, WMG: +44 24761 50752

Fax: +44 24 7652 4532