Why aren’t GARCH and VAR models used as frequently as GEE or Mixed effects in modeling clinical trial data? Why are VAR models and GARCH models used in forecasting for economics and stocks but not in analyzing clinical trial data? The most common for clinical trial is mixed effects or GEE. Are they bad for making inferences or require too much data?
 A: Are clinical trials data multivariate time series that display autoregressive and cross-autoregressive patterns in the conditional mean? Or do they display autoregressive conditional heteroskedasticity? (VAR(X) and GARCH models, respectively, were designed specifically to deal with such patterns.) If not, why would you use VAR(X) or GARCH for them?
I know very little about clinical trials, but here is my attempt of an example. If the dependent variables are some feature of multiple patients, a VAR(X) model would imply the historical values of that feature for patient $i$ explains the current value of that feature for patient $j$. I doubt the history of John's blood pressure has much to say about the current blood pressure of Mary, whether or not they are taking some medicine for hyperthesion. Thus I doubt the relevance of a VARX model, where X would be some medical intervention such as taking hypertension medicine in some periods. I wonder if changing the medical condition of interest could make this type of relationship plausible. It probably could if the patients had some connection and the condition were contagious, as suggested in the comment by @Germania.
Another issue is dimensionality vs. sample size. Unless the number of time periods is much greater than the number of patients, estimating the parameters of a VARX model with any precision would be impossible.
