analysis of 2x2 crossover trial

[Kylie Lange]

Hi all,

I have been presented with an analysis of a 2x2 (2 groups x 2 treatment)
crossover design study, based on the syntax provided by SPSS in their
knowledgebase (#26277), which I have copied below. The syntax uses the
GLM procedure to analyse a model with treatment, order and
treatment*order (ie, carryover) effects.

The syntax assumes that the dependent measure is taken at baseline,
after period 1 and after period 2, and that it is the two difference
scores from baseline that are used in the analysis. However, in this
analysis the researcher has kept the three separate measures in the
analysis rather than converting to change scores. Ie, their syntax starts:

GLM baseline placebo treatment BY order ...

Am I correct in assuming that by not converting to change scores that
the analysis is now actually invalid? In particular I would think that
the tests for the period effect and carryover effect would no longer be
testing what we are interested in? In anyone able to confirm that?

Thanks,
Kylie.

------------------------------------------
* The following commands read in a sample data file
from a hypothetical crossover design.
* There are two levels of the between-subjects factor ORDER:
(1) placebo-first and supplement-second; and
(2) supplement-first and placebo-second.
* There are two dependent variables:
(1) PLACEBO, which is the response under the placebo
condition; and
(2) SUPPLMNT, which is the response under the supplement
condition.
* Both dependent variables are deviations from each subject's
baseline measurement.

DATA LIST FREE
/ order placebo supplmnt .
BEGIN DATA
1 -1.0 1.0
1 -0.5 1.0
1 -0.5 0.5
1 -0.5 0.5
1 0.5 1.5
1 0.5 1.0
1 0.5 0.5
1 1.0 1.0
2 -0.5 0.5
2 1.0 1.0
2 0.5 0.5
2 0.0 0.5
2 1.0 1.5
2 1.0 1.0
2 0.5 0.5
2 1.0 1.0
END DATA.
FORMATS order placebo supplmnt(F3.1) .

* Set up a repeated measures model defining one two-level
Within-Subject (WS) factor, named TREATMNT.
* PLACEBO and SUPPLMNT are the dependent measures and
ORDER is the between-subjects factor.

GLM
placebo supplmnt BY order
/WSFACTOR = treatmnt 2 Polynomial
/METHOD = SSTYPE(3)
/PLOT = PROFILE( treatmnt*order )
/CRITERIA = ALPHA(.05)
/WSDESIGN = treatmnt
/DESIGN = order .

* There is a significant main effect for TREATMNT,
F(1,14) = 16.2, p < .001.
* Inspection of the Profile Plot shows that both groups
had higher average values for the dependent variable
following the supplement condition (TREATMNT = 2) than
following the placebo condition (TREATMNT = 1).
* The TREATMNT*ORDER interaction is significant,
F(1,14) = 5.0, p < .05.
* Further inspection of the Profile Plot suggests that
subjects in the ORDER = 2 group--for which the supplement
condition preceded the placebo condition--showed a higher
average response following the placebo condition than did
the ORDER = 1 group.
* This finding suggests that there was a carryover of
benefits from initial administration of the supplement.
------------------------------------------

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