# Baseline adjustment in mixed models with two assessments

I want to exmine whether three interventions have different effects over time on an outcome that has been measured only two times (two assessments before and after treatment: baseline and follow-up) in a RCT. I would like to adjust for baseline differences, but this is kind of tricky because of only two assessments. I have read a lot of articles that suggest to use an ANCOVA approach with only two assessments, but that leads to the problem that cases with missing values are listwise deleted. I would like to use mixed models (in long format) to include all available data (also cases with missing data).

My questions are: 1) Is it reasonable to use baseline and follow-up assessments as the outcome/dependent variable with treatment group (3 groups), time and treatment*time interaction as fixed effects with random intercepts and (at the same time) to adjust for baseline scores as a covariate (also as fixed effects)when using mixed models?

2) If the answer is yes: Should I also include the baseline*time interaction even if I have only one more assessment (follow-up)?

I have found a similar question (Baseline adjustment in mixed models), but I am not sure whether this applies also for only two measurements. In this link I have not found any references showing, that adjusting for baseline scores is allowed while at the same time baseline scores are part of the outcome. I have consulted several statistic books and articles and always found that adjusting for baseline (as a fixed effect) is possible if it is not part of the outcome/dependent measures. It would be great if you have any articles/literature showing that this (baseline as outcome AND as a covariate) is a proper way to do a statistical analysis (if that is actually the case).

## 1 Answer

If you are going to treat both measurements as a repeated measurements outcome and fit a mixed model for it, then you should not also correct in the fixed effects for the baseline measurement.

Moreover, if you are going to include only random intercepts you assume that the variance of the error terms for the baseline measurement is equal to the variance of the error terms of the follow-up measurement. If you want to relax this assumption, you can alternatively fit a multivariate regression model with an unspecified $$2 \times 2$$ variance-covariance matrix.

• Thank you, Dimitris, for your answer. Could you please provide some more details why I should not correct in the fixed effects for the baseline measurement when treating both measurements (pre- and post) as repeated measurements outcome in a mixed model. – Stefan Oct 15 at 14:25