# [SPSS - Mixed Models] Repeated measurements data from randomised controlled trial

#### Flightpete

##### New Member
I am analyzing data from a randomized clinical trial, with 2 intervention groups (placebo and intervention) and repeated measurements over time. I am planning to use linear mixed effects modeling to analyze this longitudinal data and determine whether the intervention causes a change in response over time compared to the control.

More specifically, the outcome variable “six_min_wd” is the walking distance in a standardized walking test (6-minute walking test). I hypothesized that the walking distance will increase in the intervention group over time compared to the control group.

I’ve tested this hypothesis using the following syntax in SPSS:

MIXED six_min_wd BY treatment WITH visit
/FIXED=treatment visit treatment*visit
/METHOD=ML
/PRINT=SOLUTION TESTCOV
/RANDOM=INTERCEPT | SUBJECT(id) COVTYPE(UN)
/REPEATED=visit | SUBJECT(id) COVTYPE(UN).​

“Treatment” is a binary variable for the two intervention groups (0=control, 1=intervention) and “visit” a continuous variable for the three repeated measures (at baseline (0), week 1 (1) and week 8 (8)). A significant interaction term “treatment*visit” would tell me that the two intervention groups significantly differ over time. Are those assumptions correct?

Is the /RANDOM subcommand required in this context? From what I understand the /REPEATED subcommand should suffice?

Secondly, I know that my outcome variable (walking distance) is also affected by other variables, such as age (walking distance expected to decrease with age) or BMI (decrease expected with higher BMI). My approach to controlling for these covariates would be to include those variables as additional terms in the /FIXED subcommand:

MIXED six_min_wd BY treatment WITH visit bmi age
/FIXED=treatment visit treatment*visit bmi age
/METHOD=ML
/PRINT=SOLUTION TESTCOV
/RANDOM=INTERCEPT | SUBJECT(id) COVTYPE(UN)
/REPEATED=visit | SUBJECT(id) COVTYPE(UN).​

Is this the appropriate way to control for these variables?

I spent quite a lot of time reading about mixed effects models, but a review of the actual approach to my situation would be greatly appreciated, since I might miss something and be completely off with my planned analysis. Many thanks.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
I don't use SPSS, but everything seems correct to me. You may experiment with different COVTYPEs to see if there may be a better fit then unstructured, but that may be trivial issue.

#### Flightpete

##### New Member
A follow-up question: If one parameter appears to initially increase, then decrease, inclusion of a squared time variable would be adequate to account for the potential of a curvilinear realtionship. I would therefore include the following fixed effects:

/FIXED=treatment visit treatment*visit visit_squared treatment*visit_squared

Assuming both interaction terms are significant, how do I report the results from this model? Do I report the p-value of the treatment*visit interaction, or the treatment*visit_squared if my intention is to show a difference over time in the two treatment groups?

Any help is massively appreciated.

#### Flightpete

##### New Member
I briefly wanted to see if anyone else could comment on this? I would appreciate any comments especially in regards to adjustment for baseline (wether to include as outcome like I did or adjust as covariate) and inclusion of continuous vs. discrete time variable. Many thanks

#### GretaGarbo

##### Human
I would not be surprised if walking distance is a skewed distribution so that taking the square root or taking logs would cure som of that (or change from normal distribution to a skewed distribution, like maybe the gamma distribution?).

Also taking visits as 0, 1 and 8 seems that you have an hypothesis of a sort "multiplicative" development. So maybe taking a square root of these number, could make it more symmetric. Or why not take the third root (What is it called in English?) that is 8^(1/3) = 2. So that 2*2*2 = 8. Then you would have visits = 0, 1, 2. (0 and 1 are the same but 8 is scaled down to 2.) That would make the repeated measurement symmetric.

It is difficult to understand you system just by looking at the spss commands. (Few people here use spss.) If you write down the equations it might be easier to say something.

I believe that it would be correct to include age and BMI in the fixed explanatory variables.
But what about the visit effect? I can't see this clearly right now.

#### Flightpete

##### New Member
Thank you very much. Walking distance is actually (fairly) normally distributed.

I actually deliberately coded visits as 0, 1 and 8 on a continuous scale to account for the different time differences between visits. I do not want it to be symmetric as you suggest with 0, 1, 2 as that would imply equal time differences if that makes sense.

I am still not sure how to best handle the baseline value though; whether to include it as a covariate or as timepoint 0.