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.
2) The global values for scan 1 and scan 2 are averaged to yield an 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)
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.
Do I have this right ?
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Steven Grant, Ph.D.
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