Dear FreeSurfer community,

I have a few questions regarding the usage of the LME matlab tools for 
longitudinal data analyses, and how to set up the model. We have patients and 
control data that we want to compare with respect to cortical changes over time 
(two time points: baseline and follow-up). We are also dealing with several 
cases (100 out of 300) with only one time point. The model is set up with 
“time” between scans, group, group*time, sex, and age as regressors. But, 
dealing with only two time points raised some questions:

1) I have read mixed opinions about fitting random slopes when dealing with two 
time points. Even though it seems to make sense to model individual random 
slopes, a fit through two time points may actually cause a problem. It also 
seems redundant to include 2 random factors (intercept and slope) in that case, 
as fitting random intercepts seems to be sufficient for the covariance 
estimation. So my question: Is it recommended to model only one random factor 
(intercept), or even wrong to model two (intercept and slope), when dealing 
with 2 TPs (especially when dealing with drop outs)?

2) This question is regarding how to set up the time variable. We have a large 
variance in that measure, meaning the follow-up scans were done between 5-7 
years after baseline. As this contributes to the variance of the dependent 
variable, I would like to include the exact time interval as continuous number 
in the model (thus a slightly different number for each participant), rather 
than using time as a two-level factor (e.g. “0” for baseline and “6” for all 
follow-up cases). I am wondering which approach is recommended and whether 
there are any significant benefits of using one method (time as two-level 
factor) over the other (time as continuous) in a LME model with two time points.

3) We have several cases with data at one single time point (ca 100 out of 
300). In the design matrix, I include single rows for drop out cases, with 
time=0. I assume that their number of repeated measures (1) will be handled by 
the ni-vector generated by the sorting procedure (sortData in matlab). However, 
we also have cases who were scanned only during clinical follow-up intervention 
(6 years after the baseline data was collected). Ideally, I would like to avoid 
assigning those to the baseline time point, for several reasons (e.g. treatment 
effects, potential scanner drifts over 6 years, etc). Instead, I want to assign 
them to the follow-up time point. If the better choice in point 2) is to use 
the actual (continuous) numbers for “time”, I am thinking about assigning the 
population median of the time difference between scans to those cases. Is this 
a reasonable approach? Does not seem to be the cleanest way of doing it, as we 
introduce some error, but may be a reasonable trade off to avoid dropping data 
of ca. 50 individuals. What is your opinion on that matter?

Thanks for any help and opinions.
Best,
Christoph

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