Andrew,
In previous postings, you stated that when you wish to do a regression on a
covariate associated with a baseline and an active condition, one must
transform the covariate so that SPM will properly correlate the difference
in the covariate with the difference in the images. This transformation
consisted of
1) computing the differences in the covariate
2) mean centering the difference
3) halving the mean centered difference
4) multiplying the baseline covariate by -1 and the active covariate by +1
This procedure was required in SPM99 so that the +1 contrast on the
covariate would produce subtraction of model [1] for each scan and thereby
result in model [2] :
[1] Y_iq = A_q + C * s_iq + B_i + error
[2] (Y_i2 - Y_i1) = D + C(s_i2-s_i1) + error
You do not mention doing this covariate transformation in your reply to
David Keator. Is this because SPM99 does not require such a transformation
?
Also, one would expect that the baseline/active effect would highly
correlated with the covariate effect since presumably the covariate would be
affected by the drug administration. Therefore, wouldn't model [2] would
greatly underestimate the correlation between the difference in the
covariate and the difference in the scan. Since the covariate and the scan
condition are not orthogonal (i.e. the drug induces a change in both the
scan and the covariate), it is not appropriate to try and partition these
two effect independently of each other.
sg
( Note new e-mail address:
[log in to unmask] )
====================================
Steven Grant, Ph.D.
Cognitive Neuroscience of Addiction Program
Clinical Neurobiology Unit
Div. Treatment Research & Development
National Institute on Drug Abuse
Room 4-4238
6001 Executive Blvd
Bethesda, MD 20892
301 443-4877 (voice) 443-6814 (fax)
-----Original Message-----
From: Andrew Holmes [mailto:[log in to unmask]]
Sent: Thursday, June 01, 2000 12:47 PM
To: Keator, David
Cc: [log in to unmask]
Subject: Re: please help..
Dear David,
At 17:25 16/05/2000 -0700, Keator, David wrote:
| I'm trying to do simple correlations with SPM99..will someone please
| help me, this should be very simple.
|
| I have 2 PET scans per subject, one at baseline and one on drug. I
| have 2 clinical rating scores, one at baseline and one after drug.
| I want to look at increases in GMR after drug correlated with
| increases in the clinical rating. I also want to look at negative
| correlations. What model should I use and how do I define the
| contrasts??
PET/SPECT models: Multi-subject, conditions and covariates. For each
subject, enter the two scans as baseline and then drug. One covariate,
values are the clinical rating scores in the order you selected the scans,
i.e. baseline score for subject 1, drug score for subject 1, baseline score
for subject 2, drug score for subject 2, &c. No interactions for the
covariate. No covariate centering. No nuisance variables. I'd use
proportional scaling global normalisation, if any. (You could use
"straight" Ancova (with grand mean scaling by subject), but SPM99 as only
offers you AnCova by subject, which here would leave you with more
parameters than images, and a completely unestimable model).
Your model (at the voxel level) is:
[1] Y_iq = A_q + C * s_iq + B_i + error
...where:
Y_iq is the baseline (q=1) / drug (q=2) scan on subject i
(i=1,...,n)
A_q is the baseline / drug effect
s_iq is the clinical rating score
C is the slope parameter for the clinical rating score
B_i is the subject effect
...so the design matrix has:
2 columns indicating baseline / drug
1 column of the covariate
n columns indicating the subject
You will have n-1 degrees of freedom.
Taking model [1] and subtracting for q=2 from q=1, you get the equivalent
model:
[2] (Y_i2 - Y_i1) = D + C(s_i2-s_i1) + error
...where D = (A_2 - A_1), the difference in the baseline & drug main
effects.
(Note that this only works when there are only two conditions and one scan
per condition per subject!)
I.e. a simple regression of the difference in voxel value baseline to drug
on the difference in clinical scores, exactly what you want.
----------------
Entering [0 0 1] (or [0 0 -1] as an F-contrast will test the null
hypothesis that there is no covariate effect (after accounting for common
effects across subjects), against the alternative that there is an effect
(either positive *or* negative. I.e., the SPM{F} will pick out areas where
the difference baseline to drug is correlated with the difference in
clinical scores.
[0 0 +1] and [0 0 -1] as t-contrasts will test against one sided
alternatives, being a positive & negative correlation (respectively) of
baseline to drug scan differences with difference in clinical scores. Since
you're interested in both, you should interpret each at a halved
significance level (double the p-values). This will give you the same
inference as the SPM{F} (which is the square of the SPM{t}'s), but with the
advantage of separating +ve & -ve correlations in the glass brain for you.
----------------
Incidentally, the variance term here incorporates both within and between
subject variability, and inference extends to the (hypothetical) population
from which you (randomly!) sampled your subjects from.
----------------
Hope this helps,
-andrew
+ - Dr Andrew Holmes mailto:[log in to unmask]
| Robertson Centre for Biostatistics ( ,) / _)( ,)
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