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Georgette Asherman
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I took the longitudinal data course with Geert and Geert a few years back and on a few occasions used these methods.
There are reasons to 1) analyze the data at each time point and 2)use an AUC and calculate the difference of AUCs. My experience was with pre-clinical toxicology and dermatology. I am sure there are other areas as well. With some protocols, even an unstructured within-subject correlation structure for within subjects won't converge. For example, the products have different thresholds in different subjects. So a mixed model of AUC with subject as a random effect gives a sense of overall product differences. Yes it is true that the same AUC value can have different shapes but it does get across the sense of moving away from baseline. Separate mixed models at each time for the response variable show when product effects have impact without looking for any attempt at defining a temporal relationship.
I hear the research statisticians asking me 'why are you even doing work with stuff so weird?' but at early stages studies taking several measurements does not always imply longitudinal research.