# multiple linear mixed models - multiple comparisons adjustment

I recently started to work on a case-control study using repeated measures over time (Modeling repeated measures data in R - Interpretation and Validation). I have several dependent variables and I would like to fit a linear mixed model on each of them.

My question is: should I adjust the p-values of the coefficients obtained from each model, and how would I do that? Additionally, as I am reporting simple contrasts to display differences between groups for each time point, should I also adjust the p-values obtained through the simple contrasts?

As Peter Flom said, there are many reasonable points of view to what one should do in this situation, and no one correct answer. However, since you are after concrete advice, I can say what I'd do in a comparable situation. I'm not a statistician though but a psychology researcher using statistics and this is just what I typically do, not necessarily what you should do.

I understood that you have a dataset with several dependent variables and you want to run separate linear models with two categorical predictors and their interaction as predictors and the interaction results are what you are mainly interested in. I think you mentioned in some question you have 36(?) different outcomes. In a situation like this, I 1) run the interaction contrasts in emmeans without any adjustment, and 2) take all the p-values from these interaction contrasts and run them through Benjamini-Hochberg correction. In R

pvalues<-c(p1, p2, ... pn) #in order from smallest to largest. Edited to add: so these would be the p-values from healthy vs. patient within each time point, i.e. 5 p-values per outcome variable.

• I have 36 different dependent variables so 36 different models and two categorical predictors and their interaction like lmm_model: Response ~ Group * Timepoint + (1 | SubjectID), where Timepoint can have 4 levels. So if I run simple contrasts by Timepoint I obtain 36x4=144 pvalues. The FDR-BH procedure would then use 144 as a denominator. However, in some papers (jstor.org/stable/40835672) the Bonferroni's correction is performed with n=number of outcomes. In my circumstances using Bonferroni with n=36 lead to slightly less stringent p-values than FDR. Am I missing something? Commented Feb 16 at 16:11