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What are the arguments for and against selecting GEE and Linear Mixed Models when the outcome variable is continuous? Are they any circumstances where one performs better than other?

The data I am modelling has these features:

Randomized trial, 910 subjects
15 measurement occasions (no mistimed measurements)
3 treatment groups
Continuous outcome variable but skewed at all occasions in all three groups
Question of interest: Compare mean trajectory over time among the 3 groups
Had lots of missing data with time, but assume missing is at random

Also, does the choice of using baseline measurement as covariate or as part of outcome vector matter when there are large number of repeated measurements, because the effect of baseline can usually decrease over time.

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If you have any missing data, then using generalized estimating equations will require you to conduct multiple imputation (MI) to handle the missingness. If you don't conduct MI, you'll by default use listwise deletion unless you did something else like mean imputation (not recommended) or last observation carried forward (really not recommended).

In contrast, linear mixed models are already compatible with the missing at random assumption out of the box. They don't require you to conduct MI, as discussed in a prior answer on SE. You will need to incorporate the covariates you think are related to missingness in the model, however (just as you would in MI). Linear mixed models will include all pairwise present observations otherwise. In conducting systematic literature reviews, I have noticed some authors use linear mixed models without including covariates. By itself, this does not address concerns that outcome data are missing at random. (note to readers: this is a term of art, and it really means missing conditional on covariates in the model, as opposed to missing completely at random.)

If the outcome is continuous and skewed, a linear model may still be your best choice. If you can find a sensible alternative family and link function that you'd otherwise have used in GEE, you can probably attempt to fit a generalized linear mixed model with that family and link.

Side note: I work with an evidence-based practice center in the US. We conduct systematic literature reviews. Most of the literature we see does not use an appropriate method to handle missing data like mixed model with appropriate covariates or MI, and thus we are forced to mark a lot of studies down unless their attrition was low to begin with. It's pretty important to minimize attrition as part of the initial study plan, anyway. In some sense, the study has already been damaged if it has high attrition. Statistical methods can only ameliorate the damage.

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