Dear SPM ers:

Similar to a past experiment that I did in 1997(text of 5 Aug 1997 from Andrew Holmes is at the bottom of this message)

I have TODAY

PET scanning using a BEHAVIORAL PARADIGM

2 conditions

scan s1 & s2 and respectively

behavioral scores b1 & b2.

I wanted to regress the differences between s1 & s2 against b2. Since b1 is 0 (or almost 0) for all subjects, I used only b2 as a covariate of INTEREST in a similar design as of 5 Aug 1997. An Ancova model was used because this model was found to be appropriate for our studies.

I obtained interesting correlations but in a small cluster in an expected anatomical location (adjacent to the area of absolute change s1>s2.

Since there was a (neurobiological) possibility that 1) score b2 (during s2) OR 2) diff (s1 - s2) could depend on the GLOBAL count s1 (Gs1), I used exactly the same  design as of Aug 1997 

but in ADDITION

I added GLOBAL_s1 as a CONFOUNDING covariate (after mean centering it and entering consecutively

[0 G1subject1 0 G1subject2 ............. G1subjectN]

The correlation are significantly better(with higher Z values and significant increase in size) when the CONFOUNDING covariate is added than when it is not added. 

My questions are then purely statistical (but any comment is appreciated).

1) is this design still valid (by adding a confounding covariate the way I did)

2)Is there any redundancy in it (since Ancova used Gs1 and Gs2 to obtain adjusted values for s1 and s2, and I am again using Gs1 as a counfounding covariate).

3) Is the confounding covariate (centeredGs1) added to the model as written below 

WITH CONFOUNDING covariate

binding s1 = s1 condition effect + subject effect + error;

binding s2 = s2 condition effect +(centered b2)*regression slope + (centeredGs1)  *regression slope + subject effect + error;

Difference is

Delta s2-s1= (CONDs2-CONDs1) + (centered b2)*regression slope + (centeredGs1)  *regression slope + error

PreviouslyWITHOUT CONFOUNDING covariate

binding s1 = s1 condition effect + subject effect + error;

binding s2 = s2 condition effect +(centered b2)*regression slope + subject effect + error;

Difference is

Delta s2-s1= (CONDs2-CONDs1) + (centered b2)*regression slope + error

Thanks for any help

Sincerely,    

Path: <[log in to unmask]>
Sender: [log in to unmask]
Date: Tue, 5 Aug 1997 12:27:24 +0100
From: [log in to unmask] (Andrew Holmes) To: [log in to unmask]
Subject: Re: study design for same day 2 PET replication without and with drug X-Sun-Charset: US-ASCII

Dear Didine,

So, in short, you have 8 subjects, one scan of average specific binding in each of two conditions per subject, B(aseline) & D(rug), and have a covariate (plasma drug level) for the D condition; and you want to regress the difference in regional average specific binding on the plasma drug level.

This can be handled in SPM, though the setup isn't intuitive!

Enter as a "Multi-Subject: different conditions" design. Enter the B & D scans for each subject. Choose a single "Covariate of interest". This will be the plasma level for the D scans, and zero for the B scans. As SPM mean corects (centers) covariates by default, it's probably best to centre the plasma levels manuall before entering them, so you know what's going on:

mean([50, 75, 150, 70, 220, 100, 215, 90]) = 121.25

[50, 75, 150, 70, 220, 100, 215, 90] - 121.25 =
-71.25 -46.25 28.75 -51.25 98.75 -21.25 93.75 -31.25

So, assumming you entered the B scans before the D scans, you'd enter the following values for the covariate:

[0, -71.25, 0, -46.25, 0, 28.75, 0, -51.25, 0,... etc

I'd go for proportional scaling normalisation in this scenario, if any.

The design has two condition effects, one covariate effect, 8 subject effects. The first three are of interest, so contrasts are:
[-1 +1 0] & [+1 -1 0] for the main effect of drug
(adjusted to the mean Drug condition plasma level)
[0 0 +1] & [0 0 -1] for the +ve & -ve regression slopes of the

drug plasma level

The model for the B scans is:

binding = B condition effect + subject effect + error & for the D scans

binding = D condition effect +
(centered drug plasma level) * regression slope +

subject effect + error

If you subtract the D model from the B model, you see how we get a regression for the difference in binding within subject as:
(Bind-D - BindB) = (CondD-CondA) +
(centered drug plasma level) * regression slope
+ error

Hope this helps,

--
Badreddine Bencherif, MD

Department of Radiology
Division of Nuclear Medicine
Johns Hopkins University School of Medicine
601 N. Caroline St. / JHOC 4230
Baltimore, MD 21287-0855

Phone : (410) 614-2787

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