Baseline adjustment in mixed models

Question

I am doing mixed model analysis to evaluate (Y=) fruit intake (continuous variable) between two groups (intervention versus control) over time (baseline, year 1, year 2, year 5, year 7 and year 15). My model look like this: Y = group + time + group*time. My question regards the baseline measurements. In my first analysis I was told to transform my data to a long format without the baseline measurements, and include this as a fixed effect to adjust for it. However, I then struggle as I have to interpret the results differently. If I include baseline data when I convert my data to long format,

1. Do I need to adjust for baseline - assume there are baseline differences between groups? I read somewhere that I don't need to adjust for baseline differences in mixed models with interaction terms.

2. Can I then include baseline measurements as a fixed effect or will this create collinearity?

My question is basically, how can I adjust for baseline measurements in mixed model analysis?

Answer 1

I assume this is a parallel group experiment (randomized assignment to just one group or the other, not some kind of cross-over).

Assuming this is a continuous outcome, the purpose of baseline adjustment is to reduce the variability of the treatment difference. Some discussion around this and the conditions under which it is helpful are found in Senn, S. (2006). Change from baseline and analysis of covariance revisited. Statistics in medicine, 25(24), 4334-4344. It does not really make a difference whether it is a mixed model or not. However, if one does include the baseline, it is usually recommended to have a time (as a factor) by baseline interaction, because the importance of the baseline will usually decrease over time. Personally, I would by default include the baseline in any model in the type of trial you are describing (and for the type of mixed model you describe always include the time by baseline interaction).

The most usual way is to indeed include the baseline as a fixed covariate. Using it as a random effect is of course also possible, but less common.

The final option is to use the baseline as yet another observation instead of as a model term. This assumes joint (multivariate-)normality (assuming you are using a normal model) of the error terms across the visits including the baseline. This can work nicely, but tends to be problematic if subjects were only included in the study, if their values were above (or below) a certain threshold (because that induces very strong non-normality due to the truncated distribution of the baseline values). For that reason including it as a model term is more common.