Are linear mixed models valid for time-varying IV with static DV?

Question

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?

Answer 1

Answered in comments:

If you only measured the DV one time for each patient, then the mixed model will not work, unfortunately. I'll let others weigh in on your proposed OLS approach. Do you have any reason to believe the EEG readings closer in time to the DV are more relevant for predicting the DV? If so, you may just want to use 2 or 3 of those as predictors rather than resampling. Or likewise if the first 2 or 3 are more important.

– Erik Ruzek