MIXED model syntax for cross-over trial with repeated measures over time

[rsegurad]

Hi folks,

I've a query about the right syntax to use for a linear mixed model with a bit of a tricky design.

This is a trial of a *treatment*. All participants (indexed by *id*) were randomised to receive treatment A or B. The outcome is a blood marker measured longitudinally on each test occasion, with 6 (unevenly spaced) *time* levels fixed by design. The time course of the *DV* is known to be (very) non-linear, so I will treat time as categorical.

Of primary interest is the treatment effect and the time*treatment interaction.

So far, so good. I could run a random intercept, random slope model within subjects, and estimate fixed time, treatment and interaction effects:

MIXED DV BY time treatment
 /FIXED=INTERCEPT time treatment time*treatment
 /RANDOM=INTERCEPT time | SUBJECT(id).

Here's the complication. The design is actually a cross-over trial. All participants received both treatments, randomised to either receive A first, or B first, so there is now a *sequence* variable, and *id*, *treatment*, and *time* are fully crossed, am I right? Example data (reduced):

id trtmt time seq DV
1 0 1 0 1.2
1 0 2 0 2.3
1 0 3 0 3.4
1 1 1 0 4.3
1 1 2 0 3.2
1 1 3 0 2.1
2 0 1 0 1.0
2 0 2 1 1.9
2 0 3 1 9.8
2 1 1 1 8.7
2 1 2 1 7.6
2 1 3 1 6.5
...


To start with I wanted to get my head around cross-over trial analysis, so I've followed the SPSS mixed model crossover trial Case Study, which gives me:

MIXED DV BY treatment sequence id
 /FIXED=INTERCEPT treatment sequence
 /RANDOM=id(sequence) | COVTYPE(ID).

With a scaled identity covariance structure, so sequence is now a higher level term with zero covariance between ids within levels of sequence, right? Would a treatment*sequence interaction here tell me whether the allocation sequence modified the effect of the treatment? Is that recommended?

Next, I would want to bring in the time-points, within person. So...

MIXED DV BY treatment sequence id time
 /FIXED=INTERCEPT treatment sequence time time*treatment
 /RANDOM=id(sequence) | COVTYPE(ID)
 /RANDOM=INTERCEPT time | SUBJECT(id) COVTYPE(UN).

I admit I'm outside my comfort zone here, and want to be absolutely sure I'm correct, and that I understand it. I'm using two /RANDOM statements: the first to reflect the sequence:id hierarchy with no correlations, and the second to reflect the id:time hierarchy with (for now) unstructured covariance. But otherwise I have just combined the two models. Is this correctly specified, or have I introduced redundant effects?

If anyone can comment or suggest better or correct syntax, I'd very much appreciate it. And please tell me why too, or link to some reading!
Many thanks,
Ric

[parisec]

Hi Ric

I was recently trying to wrap my head around analysis of a crossover design and found this article very helpful .
http://ligarto.org/rdiaz/Papers/cross-over-animal-behaviour.pdf


It shows that you can use GLM or MIXED to correctly analyze the data. I was able to use the data in the article and replicate their results which lead to a much clearer understanding of what the analysis was doing.

Happy crossover friday!

Carol


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of rsegurad
Sent: Friday, July 12, 2013 8:32 AM
To: [hidden email]
Subject: MIXED model syntax for cross-over trial with repeated measures over time

Hi folks,

I've a query about the right syntax to use for a linear mixed model with a bit of a tricky design.

This is a trial of a *treatment*. All participants (indexed by *id*) were randomised to receive treatment A or B. The outcome is a blood marker measured longitudinally on each test occasion, with 6 (unevenly spaced)
*time* levels fixed by design. The time course of the *DV* is known to be
(very) non-linear, so I will treat time as categorical.

Of primary interest is the treatment effect and the time*treatment interaction.

So far, so good. I could run a random intercept, random slope model within subjects, and estimate fixed time, treatment and interaction effects:

MIXED DV BY time treatment
 /FIXED=INTERCEPT time treatment time*treatment  /RANDOM=INTERCEPT time | SUBJECT(id).

Here's the complication. The design is actually a cross-over trial. All participants received both treatments, randomised to either receive A first, or B first, so there is now a *sequence* variable, and *id*, *treatment*, and *time* are fully crossed, am I right? Example data (reduced):

id      trtmt   time    seq     DV
1       0       1       0       1.2
1       0       2       0       2.3
1       0       3       0       3.4
1       1       1       0       4.3
1       1       2       0       3.2
1       1       3       0       2.1
2       0       1       0       1.0
2       0       2       1       1.9
2       0       3       1       9.8
2       1       1       1       8.7
2       1       2       1       7.6
2       1       3       1       6.5
...


To start with I wanted to get my head around cross-over trial analysis, so I've followed  the SPSS mixed model crossover trial Case Study <http://pic.dhe.ibm.com/infocenter/spssstat/v21r0m0/index.jsp?topic=%2Fcom.ibm.spss.statistics.cs%2Fmixed_groc_intro.htm>
, which gives me:

MIXED DV BY treatment sequence id
 /FIXED=INTERCEPT treatment sequence
 /RANDOM=id(sequence) | COVTYPE(ID).

With a scaled identity covariance structure, so sequence is now a higher level term with zero covariance between ids within levels of sequence, right? Would a treatment*sequence interaction here tell me whether the allocation sequence modified the effect of the treatment? Is that recommended?

Next, I would want to bring in the time-points, within person. So...

MIXED DV BY treatment sequence id time
 /FIXED=INTERCEPT treatment sequence time time*treatment
 /RANDOM=id(sequence) | COVTYPE(ID)
 /RANDOM=INTERCEPT time | SUBJECT(id) COVTYPE(UN).

I admit I'm outside my comfort zone here, and want to be absolutely sure I'm correct, and that I understand it. I'm using two /RANDOM statements: the first to reflect the sequence:id hierarchy with no correlations, and the second to reflect the id:time hierarchy with (for now) unstructured covariance. But otherwise I have just combined the two models. Is this correctly specified, or have I introduced redundant effects?

If anyone can comment or suggest better or correct syntax, I'd very much appreciate it. And please tell me why too, or link to some reading!
Many thanks,
Ric




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