Dear Alfonso and CONN experts

I have a question regarding using separate covariates for each group in a between group comparison, and despite the numerous messages on this topic I am still debating. I have two groups – men and women- and I want to include their total GM as a covariate in second level ROI-ROI between group analysis. I thought that including a separate covariate for each group is better since it allows for possible group by covariate interactions (though I am not interested to test this interaction).
I created three covariates: GM_all (scores for all subjects), GM_women (scores only for women and zeros for men) and GM_men (scores only for men and zeros for women).
I have 2 questions:
1) Do I need to mean-center the scores in the group specific covariates (that is center the scores of the women in GM_women)? I thought that because the scores of the second group (men) are zeroes in this covariate I should not mean-center the scores of the women, because then I will have 2 zero scores with different interpretations, but I am not entirely sure and will appreciate your help.
2) Surprisingly, when controlling for GM as a single covariate for all subjects: "men" "women" "GM_all" and applying the contrast: [1 -1 0] and alternatively when controlling for GM by including the 2 separate covariates for each group (not centered): "men" "women" "GM_men" "GM_women" and applying the contrast: [1 -1 0 0] the results are entirely different. Any thoughts? Is this related to the centering of covariates?

Many thanks for your help and thoughts

Are there significant differences between male and female GM values?  My understanding of the total covariate vs. separate covariate use depends upon your research question and the possible presence of significant differences between groups in those covariates.  Also, I would recommend mean centering the covariates, because not doing so may make it difficult to interpret the results.  There is really no such thing as zero GM volume (uncentered situation).  You would want to control for the average GM volume in your sample (centered situation).  

Hope this helps,
Jeff

Hi Alice,

Jeff is exactly correct, just to expand a bit on his response:

Typically if you want to evaluate whether there are connectivity differences between groups after correcting/taking-into-account those differences that may be already explained (perhaps more simply?) by differences in GM volume between the two groups, the proper analysis would be:
       1) selecting 'men', 'women', and 'GM_all' in your subject-effects list, and entering a [1 -1 0] between-subject contrast

The results of these analyses will be exactly the same whether 'GM_all' is centered or not.

Typically you will do these sort of analyses when you want to evaluate group differences in connectivity, and a) there are reasons to believe that your covariate (GM volume in this case) may be related to your main connectivity measures (e.g. functional correlations); and b) that covariate also shows group differences (e.g. GM volume is different in males vs. females).

If, in addition to these, you also have reasons to believe that the strength of the association between GM volume and connectivity may also vary between groups (note that this is different than simply saying that average GM volume and connectivity may be different between your groups) then that makes comparing the connectivity between your two groups conceptually harder / less-clear. Since the GM-connectivity associations are different between the two groups (think of two regression lines with different slopes in the same GM-by-connectivity scatter plot), the differences in connectivity between the groups will vary depending on your choice of GM reference value (think of the differences between those two regression lines as you move along the x-axis). That makes it difficult to characterize exactly what one means by differences in connectivity between the groups (the two groups may show the same connectivity at some level of GM, when the lines cross, and higher connectivity to one side vs. lower connectivity to the other side of this crossing point). One possible way to conceptually address this is to choose a meaningful a priori GM reference value for the between-groups comparison. In practice, this is often done by choosing the average GM level across all subjects (jointly across both groups) as a reference point for the comparison. These analyses can be implemented by:

     1) creating two group-specific covariates 'GM_men' and 'GM_women' and centering both to the same value (e.g.  if the average across all subjects is 100, then GM_men should contain GM-100 values for men, and 0's for women, and GM_women should contain GM-100 values for women, and 0's for men)

     2) selecting 'men', 'women', 'GM_men', and 'GM_women' in your subject-effects list, and entering a [1 -1 0 0] between-subjects contrast

Note that the results of these analyses will typically depend on the choice of reference value of your covariate (e.g. GM=100 in our example above). 

Hope this helps
Alfonso
Originally posted by Jeff Browndyke:

Dear Alfonso and Jeff

Thank you both for your very helpful answers!
I have a following question regarding centering of covariates that have values for only 1 group:
In this study, I have 2 groups- controls and Parkinson's disease patients. I want to compare the ROI-ROI FC between the groups when accounting for UPDRS-III (motor function scores). The issue is that only the PD patients have UPDRS scores. A level of zero on the UPDRS can be assumed for the controls and therefore I entered zeroes for the controls in the UPDRS covariate.
My question is: do I need to mean-center the UPDRS covariate?
I see that centering has a huge effect on the results and I infer that it is required. However, I thought centering will be problematic since a PD subject with a value of zero (that is, the average UPDRS) will be considered the same as a control with a value of zero.

Many thanks for your answers, it helps a lot!

Dear Alice,

Whether to center or not in this case simply depends on what exactly your would like to evaluate (I am assuming here that you are selecting 'Controls', 'Patients', and 'UPDRS' covariates and entering a [-1 1 0] contrast):

a) when UPDRS values are centered within the patient subgroup; in this case you are evaluating whether the average connectivity in patients is different from the average connectivity in controls. Any association between connectivity and UPDRS within patients is taken into account by the model simply in order to reduce the residual errors (i.e. increase sensitivity) of these between-group analyses. 

b) when UPDRS values are not centered; in this case you are evaluating whether the average connectivity in controls is comparable to the extrapolated connectivity in patients if they had 0 UPDRS values. In other words, you look at the association between UPDRS values and connectivity within patients, extrapolate what the expected connectivity level in patients would be if they had 0 UPDRS values, and then compare that extrapolated connectivity value to the one observed in controls. Typically this is done in order to determine whether there are differences in connectivity between patients and controls that cannot be simply explained by the higher UPDRS values within patients. 

Hope this helps
Alfonso
Originally posted by Alice Yo:

Hi Alfonso,

Thanks for your answer. 

But I have one question on this test you mentioned in this post

"1) creating two group-specific covariates 'GM_men' and 'GM_women' and centering both to the same value (e.g. if the average across all subjects is 100, then GM_men should contain GM-100 values for men, and 0's for women, and GM_women should contain GM-100 values for women, and 0's for men)

2) selecting 'men', 'women', 'GM_men', and 'GM_women' in your subject-effects list, and entering a [1 -1 0 0] between-subjects contrast"

If we perform this test, my understanding is that we are comparing the FC difference between two group men and women with GM controlled (separately in each group). If this is correct, we don't have to center GM_men or GM_women. Is this correct?

If we want to test the association strength (of FC and GM) difference between men and women, the contrast vector would be [0 0 1 -1]. In this case, we will need to center GM_men and GC_women (for example reference to 100 the average of GM of all). Since the association is of interest rather than the affect of the average difference of GM_men and GM_women. 

Look forward to your reply. Many thanks.

Regards,
Rui.

Originally posted by Alfonso Nieto-Castanon:

Hi Rui,

Regarding your first question, yes, those analyses will differ depending on your choice of baseline/centering levels. In particular, in the ['men', 'women', 'GM_men', and 'GM_women'] analyses, the [1 -1 0 0] test would effectively compare connectivity between the 'men' and 'women' groups at the zero-level of the GM variable (and the zero-level of the GM_men and GM_women covariates depends on whether and how you centered them). For example, if you center both variables at the same GM=100 level, then you are comparing connectivity in 'men' with GM=100 to connectivity in 'women' with GM=100 (but note that, since these analyses allow connectivity and GM to be differently associated in men and women, the results of the above analysis will typically be different depending on your choice of GM baseline level, even if choosing the same level across the two groups; e.g. comparing connectivity in mean with GM=50 and women with GM=50 will likely be different that comparing connectivity at the GM=100 level).

Regarding your second question, in contrast to the above case, in these analyses the choice of baseline/centering levels does not affect the results nor their interpretation. In particular, in the ['men', 'women', 'GM_men', and 'GM_women'] analyses, the [0 0 1 -1] test will compare the association between connectivity and GM across the two groups. This analysis is independent of your choice of GM-baseline levels and/or whether you center the GM covariates or not (the results will be identical no matter how/if you center the GM covariates)

Hope this helps
Alfonso



Originally posted by Rui Li:

Thank you so much for your answer.

Regards,
Rui.