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I have data on a repeated measures study with measurements on various outcomes taken at 0,6 and 12 weeks. An issue I have run into is that baseline values for various outcomes are not similar between treatments even though individuals were randomly assigned to the two treatment groups. I made a mistake earlier where I did not randomize based on outcomes, whats done is done.

I realize that mixed effects model or an ANCOVA can allow for analysis in-spite of baseline differences. I have used mixed effect model to analyze my data.

Here is my question: as I understand, in a mixed effect model the use of random intercept for each participant in the study (time | subject) takes care of different baseline values of outcome for a given set of participants.

This is what my main effect model looks like

outcome_a ~ age + sex + treatment + time + time * treatment + (time | subject)

Where 'outcome_a' has a higher mean baseline value in treatment 'a' as compared to treatment 'b'

What I am wondering is, is there way to have a random intercepts set in such a way that outcome_a random intercepts are set higher just for treatment 'a' as compared to treatment 'b' random intercepts.

Would this account for

a) differences in baseline across groups (treatment 'a' having higher mean value for outcomes as compared to treatment 'b'), and as well as b) general differences in baseline within all participants?

And if yes, how would one go about setting up such a model?

I hope I am clear with this, please let me know if there are any questions.

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    $\begingroup$ If you just want a random intercept, then (1 | subject) already takes care of that. (time | subject) is like saying there is a baseline effect and subjects responds differently to the effect of time. As for random intercepts 'set higher' for one treatment than the other, how does this differ from a fixed effect for treatment? $\endgroup$ – Frans Rodenburg Aug 29 '18 at 1:23
  • $\begingroup$ @FransRodenburg I see. I understand this better now. Thanks. $\endgroup$ – DiscoStat Aug 29 '18 at 14:51
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Check the paper by Stephen Senn on baseline imbalances between treatments.

Moreover, because you have the main effect of treatment in your model, you already account for treatment differences at baseline. That is, that the outcome has a different mean for treatment ‘a’ and for treatment ‘b’ at baseline.

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