# Proper methods for this case of repeated measures?

I am measuring hormone changes in animals. I have three groups: Groups A, B, and C. In each group, blood was collected from the SAME individuals for hormone assay at 0, 15, 30, and 60 min. This was done in males and in females and I would like to keep in mind sex differences.

My question: do the changes we see in hormones over time differ between groups A,B, and C? And if so, how?

Does the variation of hormone change over time differ between groups A,B, and C?

I would like to analyze in one big model, but I'm not exactly confident in the test(s) I'm using. Any advice?

A graphical overview of the data would help inform which model to fit, however a possible fit would be as follows:

Fixed: the interaction between group and time. If the changes over time are not very linear, then time should be used as a factor. If time is a factor, then an intercept would not need to be included.

Random: random slopes with respect to time. Again, time could be a factor or numeric. If time is numeric, then random intercepts could be added if the starting point in each animal is different. If time is a factor, then an assumption will need to be made about correlations between the random effects at different time points.

Finally, if your sample size is small, then it may not be worthwhile fitting any model at all and a graphical/tabular overview should be used.

A basic model like this can be estimated using lme4 in R by running the following:

lmer(y ~ group:time + (time|animal))

If you want to have a specific variance structure for the random effects, then you'll need nlme instead of lme4

I've no idea about how to do this in JMP/SAS