EDIT: I forgot to say that your PROC MIXED approach is quite good.  I wouldn't shift to REG.  The Type3 tests are whether at least one time point mean differs from all the rest.  That may not be a trend, so...   If you want to look at a trend in time, use an LSMESTIMATE statement.   lsmestimate 'linear time' time -1 0 1; lsmestimate 'quadratic time' time 1 -2 1; Note that with 3 time points, for linear time the middle time point has no effect, which is why looking at the quadratic time (or deviation from linearity) is useful.   SteveDenham   ... View more

Consider this code:   proc glimmix data=have; ods output lsmeans=lsmeans; class bmi time; model concentration = bmi time bmi*time/dist=lognormal ddfm=satterthwaite; random _residual_/group=bmi; lsmeans bmi time bmi*time/cl; run; If you have the first and second observation for each subject, you could change this to:   proc glimmix data=have; ods output lsmeans=lsmeans; class bmi time sub_ID; model concentration = bmi time bmi*time/dist=lognormal ddfm=satterthwait; random _residual_/group=bmi subject=sub_ID; lsmeans bmi time bmi*time/cl; run; This requires a "long" version of the data, where each line has one subject_ID, one BMI and one time.  You could add in a test for homogeneity of variance, but these two blocks are closer to the assumption in a Welch's t test of unequal variances.  If the variances are grossly different by group, that Satterthwaite approximation for the denominator degrees of freedom is appropriate.   So this results in a dataset that has the estimates and the 95% confidence bounds on the natural log scale.  To get geometric means and bounds, simply exponentiate these values in a DATA step.   SteveDenham   ... View more

The Friedman test depends on the time factor being measured within subject, so I don't think that it is quite what would fit this design.  There is a test called the "aligned ranks transformation".  This link provides a SAS approach: https://libres.uncg.edu/ir/uncg/f/S_Richter_C463_2002.pdf    This will allow you to correctly test for a time by treatment interaction, although probably not as powerfully as a transformed or generalized linear model.   SteveDenham   PS Here is another paper that isn't so SAS-centric. https://www.researchgate.net/publication/221514774_The_Aligned_Rank_Transform_for_Nonparametric_Factorial_Analyses_Using_Only_ANOVA_Procedures  ... View more