Dear Doug, Michael,

Thanks for thinking with me. Following the discussion, it seems to me that weighting the contrast matrix in our cohort for our question is alright. Let me describe it again:

- The diseased population typically consists of 75% female.
- We have three groups (HC, diseased without complaints (Dis1), diseased with complaints (Dis2)); each in terms of sex representing a typical diseased population (so consisting of 75% females); and the groups are matched for age.

We would like to know whether the average CTs between the respective groups are different, while controlling for sex and age. So HC vs Dis1, HC vs Dis2 and Dis1 vs Dis2.

Considering Michaels words (Specifically, whether a healthy population of 75%
female differs from a diseased population of 75% female.  In that sense,
are you not really "controlling" for sex any more in the typical sense
of controlling for a non-balanced sample.  (Rather, you are explicitly
hypothesizing a non-balanced sample) ) weighting would be neccessary, right?

Best,
Martijn



On Tue, Jan 10, 2012 at 6:15 PM, Douglas N Greve <greve@nmr.mgh.harvard.edu> wrote:
Thanks to both Donald and Michael for catching my mistake about recommending sample-size weighting within the contrast (both responses are below). Depending upon the hypothesis being tested it is ok, but you're probably not going to be in a situation in which you will want to.
doug



-------------- from Donald McLaren -----------------------------------
Doug,

>From my understanding there are two questions that need to be asked before a decision is made:

(1) Do I want the average across the groups OR Do I want the average of this cohort?

The former should use equal weightings, while the latter should use the weighted average. Typically, people want the average of the groups, rather than the average of the cohort. The average of the cohort can be skewed toward the larger groups' means. An alternative would be to weight males and females based on the ratio of males and females that have the disease, in this way you are estimating the average of diseased individuals that is not prone to sampling bias.

>From the statistical perspective. The typical null hypothesis is that (males+females)/2=0. Thus, one should not weight the groups by the number of subjects.

If the null hypothesis was healthy-diseased=0, then one would use the ratio of the diseased individuals in the population to avoid any bias in the sample.

If the null hypothesis was healthy-diseased=0 in this sample, then one would use the ratio of the diseased individuals in this sample to avoid any bias in the sample.

(2) Dealing with outliers. Small samples can easily have an outlier that would pull the mean away from its true value; however, the variance will be higher and less likely to produce a significant result. When you have very small samples, one might ask, is it worth including that group? In your case, if you only have 3 males, one might consider limiting the study to females.

A final point, if there is a interaction effect, then they should never be averaged. Even if there is not an interaction, you can still gain power by splitting the groups because then you can model the variance of each group separately.



Michael Harms wrote:
Hi Martijn,
Just to elaborate briefly on what Doug wrote, if you weight your
contrast vector by the sex ratio, you are however testing a very
different hypothesis.  Specifically, whether a healthy population of 75%
female differs from a diseased population of 75% female.  In that sense,
are you not really "controlling" for sex any more in the typical sense
of controlling for a non-balanced sample.  (Rather, you are explicitly
hypothesizing a non-balanced sample).  If you want to test the
hypothesis that the healthy and diseased subjects differ in a putative
balanced sample of 50% male/ 50% female, then you should *not* weight
your contrast vectors according to the sex ratio of your particular
sample.

cheers,
-MH

On Mon, 2012-01-09 at 18:13 -0500, Douglas N Greve wrote:
 
Hi Martijn, yes, that is a good thing to do!
doug

Martijn Steenwijk wrote:
   
Hi Doug,

Thanks for your reply again. It's getting more and more clear now.
I've however one question remaining, which is regarding the correction for sex. What I did not tell (my fault ;-) ), is that 75% of the cohort is female. Comparing the sex-corrected results with male-only and female-only results, it appears to me that the relatively small male-group partly 'drives' the results in the sex-corrected results. I guess this is because the males and females are currently equally weighted in the contrast matrices. Shouldn't the differences in sex also be represented in the contrast matrices, like [.25 .75 -.25 -.75 0 0 0 0 0 0 0 0]
[0 0 .25 .75 -.25 -.75 0 0 0 0 0 0]
[ .25  .75 0 0 -.25 -.75 0 0 0 0 0 0]

? Or am I wrong?

Best,
Martijn


On Wed, Dec 21, 2011 at 5:45 PM, Douglas N Greve <greve@nmr.mgh.harvard.edu <mailto:greve@nmr.mgh.harvard.edu>> wrote:


   Hi Martijn, sorry for  the delay. Your contrast matrices look
   correct. The differences between demeaning and not demeaning is
   somewhat expected. When you do not demean, you are testing whether
   there is a difference between groups at age=0 (ie, birth). When
   you demean, you are testing for a difference at age=MeanAge. If
   the slope of each group with respect to age is the same, then this
   will yield the same result since the regression lines will be
   parallel and the distance between parallel lines will always be
   the same. If the slopes differ, then the distance will change with
   age. For example, there will be an age where the lines cross. If
   you test at this age, you are assured not to see a difference! For
   this reason, it is better to test for a difference in the slopes,
   and, if there is no difference, then reanalyze with DOSS which
   forces the lines to be parallel. In your case, you found that
   there is some difference in insula. If this is not the area that
   you are interested in, then I would not worry about it. You should
   just keep in mind that you should not try to draw conclusions from
   this area.
   doug

   Martijn Steenwijk wrote:

       Dear Doug,

       Thanks again for your reply. Based on that I did some further
       work.

       I first demeaned the age of all subjects. Actually, I have a
       third group which I would like to compare to, so my contrast
       matrices will be [.5 .5 -.5 -.5 0 0 0 0 0 0 0 0]
       [0 0 .5 .5 -.5 -.5 0 0 0 0 0 0]
       [.5 .5 0 0 -.5 -.5 0 0 0 0 0 0]
       to test for CT differences between all the groups while
       correcting for age and sex. Surprisingly, I'm observing a big
       difference in the results compared to the results without
       demeaning. Could you explain the reson for this? In the
       FSGD-examples (eg
       http://surfer.nmr.mgh.harvard.edu/fswiki/FsgdFormat), age is
       also not normalized. Does normalizing the variance to 1 also
       influence the results?
       Given this big difference, I started wondering whether it
       would maybe be better to analyze the data in pairs of two
       groups (and then demean by the mean of the two groups). Would
       this be a better approach?

       Concerning your second suggestion: if I test the data for
       differences in group slope, a number of small area's are
       significantly different. Regions popping up are especially in
       the neighborhood of the insula. Unfortunately this suggests
       that I cannot use the DOSS model, or am I wrong?

       Looking forward to your reply,
       With best regards,
       Martijn


       On Sat, Dec 10, 2011 at 7:16 PM, Douglas Greve
       <greve@nmr.mgh.harvard.edu <mailto:greve@nmr.mgh.harvard.edu>
       <mailto:greve@nmr.mgh.harvard.edu
       <mailto:greve@nmr.mgh.harvard.edu>>> wrote:

          Yes, that is correct, though I think your matrix should be
       [.5 .5
          -.5 -.5 0 0 0 0]. You should also remove the mean from the age
          (mean computed from all subjects). Or even better, first test
          whether there is a group difference in age slope with [0 0
       0 0 .5
          .5 -.5 -.5]. If there is nothing that is significant, then
       re-run
          your analysis using the Different Offset Same Slope (DOSS)
       model
          with this contrast [.5 .5 -.5 -.5 0].

          doug


          On 12/10/11 4:15 AM, Martijn Steenwijk wrote:


              Dear all,

                             I’m relatively new with Freesurfer, but slowly getting
           more and
              more used to it’s great possibilities. To be ‘sure’, I’ve a
              question about the design of a GLM.

                             I want to compare CT in Healthy Controls vs Diseased,
           and control
              for age and sex. It appears to me that factors (eg sex)
           cannot be
              used as covariate/variable, which forces me to model
           them as a
              separate class although I’m not interested in sex
           differences.
              This brings me to the following FSGD file:

                             # HcDis.fsgd

              GroupDescriptorFile 1

              Title HcDis

              Class Hc_Male

              Class Hc_Female

              Class Dis_Male

              Class Dis_Female

              Variables Age

              Input subjid1 Hc_Male 35

              Input subjid2 Dis_Female 30

              ….

                             Then the difference between Hc and Dis, corrected for
           age and sex
              is given by the contrast matrix

              #Hc-vs-Dis.mtx

              0.5 0.5 -0.5 -0.5 0 0 0 0 0 0 0 0

                             Is this correct?

                             Best,

              Martijn

                             

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