Analysing change scores via linear mixed effects model with baseline adjustment? I am still trying to find a model for a large dataset, approximately 1-5 measurements per patient (over time), one is the baseline value at t=0. The researcher is interested in the change over time and in the effect of the baseline value on that change. I want to set up a LMEM with random intercept+slope and I want to account for the baseline by adding this as a covariate.
However, I have read some literature and it seems that it is not correct due to the dependency which is created by this. Nevertheless I read more than one paper where this model was performed.
So basically I mean something like this:
$$ z_{i,j}=y_{i,j}-y_{i,0}=(\beta_0+b_{i,0})+(\beta_1+b_{1,0})\cdot t_{i,j}+\beta_3 y_{i,0}+...(\text{other covariates})+\epsilon_{i,j} $$
and it appears strange to me. So basically change scores are used for pre/post experiments but for several patients I have more than one post value, this might also be a problem? Furthermore I'm not sure whether we should really consider the change as the response because I also read that these types of model in general have some undesired properties.
Maybe anyone can help? Thanks!
 A: The fact that many studies erroneously model change scores as a function of baseline does not remove the inherent problem with that approach. See this answer among many links on this site. It's important for the researcher to understand that.
If you are expecting a linear change in the measurement values over time, as your model implies, then random effects with the actual measurement as the outcome variable nicely accommodate both the baseline value and multiple measurements over time. You code the baseline value to have a measurement time of 0. Depending on how you set up the model, it can incorporate correlations between random intercepts and slopes. The model then can provide any desired estimates of value differences between measurement times.
All the data for a patient will be used this way, partially pooled with information from other patients, to estimate the random intercept and slope. That avoids putting undue extra weight on any (potentially uncertain) single baseline value.
A potential practical problem will be having too few data points to fit a model of desired complexity. For example, if there's only 1 value for some patients then you can't estimate a slope over time for them. But that would be a problem even if the researcher were to insist on modeling change scores, as such patients wouldn't have any.
