Dear Steven,

>I want to compare results from SPM and an ROI analysis. Our ROI data is
>proportionaly normalized, whereas I have been using ANCOVA normalization for
>SPM. This has lead me to an exercise into understanding how SPM performs the
>ANCOVA adjustment for global values. The example in the SPM course book
is for
>a single subject with multiple replications, and the calculation of the
adjusted
>ANCOVA values for a given pixel is clear to me for that type of study.
>
>But I am dealing with FDG data where each subject gets only two scans, one
>under each condition. This is how I understand SPM calculates the ANCOVA
>adjusted values.
>
>1) There is only a single data point for each pixel per subject per
condition.
>Therefore, the beta coeffcient for the regression of the pixel value with the
>global value is taken as 1.0. If there were more than one scan per
condition,
>then the beta coefficient could be calculated and would not be necessarily =
>1.0.
>

The problem you describe here pertains to the situation where one attempts
to fit a separate beta for each subject, which as you correctly have
inferred is not really a sensible thing to do. This would effectively "rob"
you of all your degrees of freedom.
However, the way around this is not that which you have suggested, but
simply to estimate a single beta for each voxel across all subjects. This
means that you assume that a given voxel has the same behaviour with
respect to changes in global flow for all subjects.

>2) The global values for scan 1 and scan 2 are averaged to yield an Global
>Mean.
>

Nope, the global values are averaged across all subjects and scans to yield
a global mean.

>3) The adjusted pixel value for a given scan and subject is calculated as
>Y(adj) = Y(actual) - 1*(Scan Global - Global Mean)
>

Nope, a single beta is estimated based on all scans of the study and
Y(adj) = Y(actual) - beta(Scan Global - Global Mean)
I addition any subject specific effects will be subtracted from the
adjusted values.

>To give an numerical example for a single subject
>
> Scan A Scan B
>Actual Pixel Value 804 906
>Global Value 975 1027
>Beta 1 1
>Global Mean 1001 1001
>
>Adjusted Pixel Scan A = 804 - 1*(975 -1001) = 804 + 26 = 830
>Adjusted Pixel Scan B = 906 - 1*(1027 - 1001) = 906 - 26 = 880
>
>This represents a 6% change across sessions. Just for comparison, after
>proportional normalization would Scan A = 0.825 and Scan B = 0.883, for
a 7 %
>difference.
>
>Issues of smoothing in SPM and averaging within an ROI aside, the main
>differences between the statistical analysis from proportional normalization
>and ANCOVA normalization should mainly be a function of the reduction of a
>degree of freedom in the ANCOVA, and the slightly larger difference in the
>proportionally normalized data.
>

The main differences between ANCOVA proportional normalisation is that the
proportional normalisation will scale the variance whereas ANCOVA will not.
This has some implications regarding the validity of the subsequent
statsistical modelling where it is assumed that each point is associated
with the same experimental uncertainty. It is really not clear what is the
correct model, but as a rule of thumb one can say that if one believes that
the dominating source of variance in the globals is "apparatus dependent"
(i.e. differences in injected dose (PET) or drifts in amplifier electronics
(fMRI) then proportional scaling is clearly more correct. If on the other
hand one believes that the dominating source is "physiological" then the
issue becomes less clear. In your case, quantitative FDG, I would guess
that the latter situation is true.
You should be aware though that all empirical studies comparing ANCOVA and
proportional normalisation have indicated that there is little practical
difference.
 
>Do I have this right ?
>
Well, not quite. I hope this reply have made it a bit clearer though.


Good luck Jesper



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