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I'm analyzing multisite clinical trial data with mixed models. I have (a) a continuous DV, (b) a grouping variable (treatment vs control), (c) baseline scores for the DV, (d) a time variable (baseline, and three additional measurement occasions), and (e) subjects who are nested within sites.

My model (run in lme4) is as follows:

DV ~ Group + Time + Group*Time + BaselineScore + BaselineScore*Time + (1|Subject) + (1|Site)

My time variable is coded as continuous.

I've been doing some digging on controlling for baseline scores in mixed models and feel a little lost. I found several answers here, including this one, that suggest to use the baseline score as a covariate in the model but that it's also acceptable to use random effects: Baseline adjustment in mixed models

On the other hand, some answers suggest that while variation between individuals is handled by the random effects, they may not be handled at the group assignment level: Linear mixed model in clinical trials - only one is feasible?

Can random effects, like those in the model I'm proposing to use, adequately control for baseline differences, thereby eliminating the need for the fixed effects of Baselinescore, or is it advantageous to include baseline as a covariate on its own?

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Yes you absolutely should continue to adjust for the pre-treatment baseline as a covariate as one would do with an ANCOVA analysis. AND model the effect of treatment and the treatment-by-time interaction using a repeated measures analysis with a random intercept for subject and site effects. This is the most power and most general model specification. This significantly reduces the residual variation. The rationale for including random effects is that they integrate the contributions of possibly hundreds of unmeasured factors that are constant within an individual. But for a single and strongly prognostic factor like the baseline response, there's no rationale to exclude it.

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