I have data from traumatic brain injury patients where EEG (IV) is collected for several days and used to predict a behavioral measure of outcome (DV) 6 months after patients are discharged. So, I have longitudinal data for my IV, but I have static data for my DV. Are mixed models appropriate here? Or does it not work because the DV is static? There are also a few covariates I want to account for, a few of which are static (sex, and age which doesn't really change either because the EEGs are only a few days apart), while other covariates are time-varying (e.g., medications). This would be a random intercept model, i.e., each patient has their own intercept, with fixed effects for EEG and covariates. So, the formula would be OUTCOME ~ 1 + EEG + AGE + SEX + MEDICATION + (1|PATIENT).
An alternative approach I thought of is to randomly sample one observation day per patient N times, enter the observations for each resample into a multiple linear regression, and then take the resample with the median test statistic across all N resamplings and report the results for that resampling (the test statistic in this case being the regression t-stat for EEG). Would this approach be preferable over using a linear mixed model?