Roughly a third of these tests are specific to data elements (i.e., you would use #6 if you had a covariate that had a different value at time X and time Y, hence "time-varying covariate"), but the rest of your decision-making has to do with what your research question is (and/or, what null hypothesis you are testing).  In general, is your RQ about whether the average trajectory differs between groups? whether the average trajectory differs over time period?  whether individual characteristics make a difference to the average trajectory? whether group characteristics make a difference to the average trajectory? etc...

Thanks Julia. The idea was to test the trajectory of usage of some painkillers (continuous, in daily dosages) over time (first three timepoints before the intervention and other three after that). If there are several clusters then I will test if there are some differences in demographics between them (gender - binary, SES or occupation  - categorical). Even gender alone would probably be sufficient for this first try.

Did I understand correctly that this GBTM is a little bit like factor analysis? I mean its logic - first, the "exploratory" part with e.g. censored normal model and then "confirmatory" one with e.g. group membership probabilities?

I really appreciate any help. I like the idea of GBTM very much. I am a specialist in PM&R and the most of our evidence is based on rather follow-up than RCT data. So, any new approach is of great value.

So, your primary question concerns the actual shape of the trajectory, with the additional question of whether the trajectory changes significantly from before to after treatment.  Do you have participants who do not undergo the intervention, or is the primary point of comparison a time-based comparison?

   This information rules out joint trajectory models, as that approach is what you use when you have two measures that may shift jointly (like, cortisol level and prolactin level), whereas you have a single outcome that may shift differently depending on the event horizon of your analysis (primarily before and after intervention).  It also rules out multi-trajectory models, as that approach is what you use when you want to identify clusters by differences in overall trajectories, which does not seem to be the primary focus (although it may be relevant to testing hypotheses on your IV).  The Nagin and Odgers 2010 article addresses the issue of identifying groups based on trajectories (attached).

   Yes, the process is what you understand, shifting from exploratory to confirmatory. 

Thank you very much. I have to think and to read. The primary point is a time-based comparison. All the participants have underwent the intervention. 

Hi Mikhail, I have used GBTM in my research project (Traj command in Stata) for the analysis of house price trajectories. The GBTM would be an ideal tool for your analysis, with 6 time points - it is perfect fine with missing values, and you do not have many anyway. 

1-13 is not completely mutually exclusive, and 1 is where the dependent variable is continuous, which from my understand is the daily dosages of pain killer (?). And if you are interested in including some demographic factors in (gender - binary, SES or occupation - categorical), I would recommend using 4 by including those time-invariant factors, or risk factors (unless your 6 time points are much further apart and SES have changed dramatically, you may consider using 6 and treat them as time-varying). 

Form my experience, the tricky part is the trial and error of the trajectory shape, but given the size of your data, it should be relative fast (mine is N=25k, and 14 times points and took a long time to converge). 

Another model you may be interested in investigating is Growth Mixture Model (using Mplus). The two are similar to a degree and I have used both in my analysis and compared the results differences (some publication goes into details as to their conceptual differences)

Happy to answer any more questions you may still have, or if you need any references! Will also keep you posted if I found anything more.