Mixed model cLDA adjusting baseline score

[xuyi]

I am analyzing data from a randomized cluster trial (6 clinics in control and 7 clinics in intervention) to examine whether the intervention have effect over time on an outcome (continuous variable ‘score’). The score was measured two times (baseline and 12-month follow-up). I would like to adjust for baseline measurement (there was significant mean difference between intervention group and control group by t-test at baseline for some reason).
proc mixed data=combine1 NOCLPRINT=10 covtest;
class subject_ID clinic group visit;
model Score=baseline_score visit group*visit/s cl;
random intercept/subject=clinic type=vc;
random intercept/subject=subject_ID (clinic) type=vc;
lsmeans group*visit/diff e cl;
title 'MIXED model-clinic and patient as random effect';
run;
I would like to use mixed model (in long format) to include all available data (also cases with missing data).

My questions are:
1. Is the above model reasonable that I use baseline and follow-up assessment as the outcome vector; group, visit and group*visit interaction as fixed effect; and adjust for baseline measurement as a covariate (also as fixed effect) when using mixed models? I have subject and clinic as random effects.
2. Is this model equivalent to the cLDA (constraint Longitudinal Data Analysis) model? My understanding is the model above used baseline mean to calculate LS means, and cLDA model forced baseline to be equal in two groups. I got different results between two models, and I am not sure whether this cLDA model is correct (TrtVisit12 is a dummy variable. It is 1 when intervention group=1 and visit=12; else=0)
proc mixed data=combine1 NOCLPRINT=10 covtest;
class subject_ID clinic group visit(ref='0');
model Score=visit TrtVisit12/s cl;
random intercept/subject=clinic type=vc;
random intercept/subject=subject_ID (clinic) type=vc;
title 'cLDA MIXED model-clinic and patient as random effect';
run;
3. Does it still make sense to compare baseline score between two groups (model based), since we have adjusted the baseline score?
Thank you!

[StatsMan]

Your model would be reasonable with multiple follow-up visits. With a single non-baseline response, you will have difficulty estimating the random effect for subject_ID(clinic). If you get a message that the g-matrix is non-positive definite, then you should consider dropping that RANDOM statement. 

For a good write-up on approaches to this kind of data, see https://www.lexjansen.com/phuse/2017/as/AS07_ppt.pdf.

The cLDA model works well when you have multiple follow-up visits. I am not sure of its effectiveness with a single follow-up.

[xuyi]

Thank you so much for your response. I studied the link you provided, which is very helpful.

My first model is not as same as the longitudinal ANCOVA model since I have baseline value as a covariate and also in the outcome vector. I expected the two models I built should have similar LS means, since they both forced baseline to be the same. However, they are quite different as below, which was my concern, although the difference between two groups at 12 months wasn't significantly different in either methods.

and here below is the LS  means from cLDA mode:

Could you please provide any insight into why they are so different?

Thank you so much?

[SteveDenham]

If you fit a model with a covariate equal to the response variable, odd things can happen, mostly because you are fitting some sort of adjusted response - essentially the response being fit is now equal to response_variable - response_variable * beta_hat, where beta_hat reflects a slope estimate. Since your means are relatively close, I suspect beta_hat is near, but not equal to, zero.

SteveDenham