Thanks Anderson for that thoughtful and thorough response !

Cheers, raj 

-----Original Message-----
From: FSL - FMRIB's Software Library [mailto:[log in to unmask]] On Behalf
Of Anderson Winkler
Sent: Saturday, July 02, 2011 12:08 PM
To: [log in to unmask]
Subject: Re: [FSL] Permutation testing - combining significance levels

Dear Raj,

I'm afraid it might be safer to this all again using the original data,
rather than try to combine. The reasons are:
a) Each study may have slightly different skeletons, which won't be the same
as a global skeleton that combines everyone. This, alone, may already hinder
the per-voxel comparison or combination you'd like to do.
b) If you are not using covariates (e.g. age, sex, maybe some clinical
scores, etc), or if you regressed them out beforehand, it's possible to
produce a combined statistic without having to refit the model. However,
this depends on the sample size for each group and on the availability of
the parameter estimates, as well as on some non-standard processing you'd
have to do with FSL tools.
c) Once you manage to produce a new statistic, you'd still have to permute
again, even if you had the empirical distributions for each of the two
initial studies, because there is no guarantee that these empirical
distributions would be identical one to another everywhere in the brain,
neither that the distribution of the combined statistic would be the same as
these distributions combined (pooled).

Having said that, except for the different skeletons (item "a" above), in
principle you could use still the Fisher's method to combine the p-values
(http://en.wikipedia.org/wiki/Fisher%27s_method) as long as you handle the
non-independence between the two studies. This may seem trivial at first,
but it's actually not, because the two control groups seem to differ in
different parts of the brain, suggesting that the degree of dependence
varies spatially.

So, again, I'd suggest rather to spend time trying to combine this data,
that you spend time trying to obtain the original images, and run TBSS
again.

Hope this helps!

All the best,

Anderson


On 07/01/2011 08:07 PM, Rajendra Morey wrote:
> Hi
>
> I have results from two studies that both used TBSS. Both studies, 
> lets call them ST-1 and ST-2, compare patients to controls and have 
> significant between-group differences obtained from 5,000 
> permutations. The results of the two stduies are grossly consistent 
> i.e. voxels in the same general area are lighting up but there are also a
lot of differences.
>
> I want to combine results of p-values from the two studies. Basic 
> probabilty theory says that the probability of getting two 
> proabilities of 0.01 and
> 0.01 is the joint probability which is 0.0001. My question is if this 
> is the right way to combine the p-values from my two studies. Second, 
> because these p-values were obtained from a probability distribution 
> obtained by permutations, does this change the way we compute the joint
probability.
>
> Finally, the results of ST-1 and ST-2 may not be completely indpendent 
> because they actually have the same patient group, but two completely 
> separate control groups. How might this change the calculation of the 
> joint probability?
>
> Raj
> Duke Univeristy
>
>