Hi,

I would advocate the non-paired approach as what you've got are not truly pairs, they are just matched for age and sex.  So if you adjust for the effects of age and sex as covariates within an unpaired model, then you are already taking into account anything that varies with these, and this seems a more natural way of modelling it to me.

Also, as you pointed out in your follow-up email, you should demean your covariates.

All the best,
	Mark




On 27 Jan 2014, at 12:39, Anders Hougaard <[log in to unmask]> wrote:

> Dear all,
> 
> I realize that this post is actually off-topic as it really concerns
> (very basic) general statistics and not FSL specifically, I just
> happen to be using FSL for the analysis. My apologies for this.
> 
> I am comparing fMRI results from a group of subjects with a condition
> that may or may not affect the results, and a group of individually
> age- sex matched control subjects.
> 
> I would like to test if the presence of the condition affects the fMRI
> results, and if/how this effect depends on the severity of the
> condition.
> The condition is expected to be associated with subtle changes of the
> results only.
> I cannot rule out, that other subject-specific parameters, such as
> BMI, cerebral volume or IQ, could affect the results.
> I would like to do as sensitive an analysis as possible.
> 
> Would it be OK to apply a paired/longitudinal design for this purpose?
> 
> Consider the two groups of subjects:
> A - subjects with condition
> B - matched subjects without condition
> 
> Group A
> subj scan_results severity age gender
> 1 X1 3 29 2
> 2 X2 5 25 1
> 3 X3 4 33 2
> 4 X4 7 28 2
> 
> where, in the gender column, 2 is female, 1 is male, and
> 
> Group B
> subj scan_results severity age gender
> 1 Y1 0 29 2
> 2 Y2 0 25 1
> 3 Y3 0 33 2
> 4 Y4 0 28 2
> 
> I imagine doing testing the differences between groups in a paired fashion:
> 
> Differences
> scan_diff severity_diff age_diff gender_diff
> X1-Y1 3 0 0
> X2-Y2 5 0 0
> X3-Y3 4 0 0
> X4-Y4 7 0 0
> 
> To do this, I would use a GLM like this:
> 
> scan_diff = mean + severity_diff
> 
> Could I even control for the (small) age differences by adding this as
> another confound:
> 
> scan_diff = mean + severity_diff + age_diff ?
> 
> Another approach would be to do an unpaired design, in which the
> dependent variable would be a column of scan results from all
> subjects:
> 
> scan_results severity age gender
> X1 3 29 2
> X2 5 25 1
> X3 4 33 2
> X4 7 28 2
> Y1 0 29 2
> Y2 0 25 1
> Y3 0 33 2
> Y4 0 28 2
> 
> And to correct for differences due to age and gender, the model would be:
> 
> scan_results = mean + severity + age + gender
> 
> What are the principal differences between these two approaches and
> which one would you consider most appropriate and most sensitive for
> this purpose?
> 
> Best,
> Anders