Try the following:
PROC GLIMMIX DATA=new method=laplace empirical;
CLASS sample trt sym tpt;
MODEL Akkermansia= trt|sym|tpt/ link=log dist=negbin ddfm=bw OFFSET=loglib ;
random tpt/ subject=sample type=chol;
LSMEANS trt*sym*tpt/diff ilink;
NLOPTIONS maxiter=500 tech=nrridg;
RUN;
This fits a repeated measures design, where V1, V2 and V3 are repeated measures on the subject, which here is the sample. I think this more closely represents the data and the factors involved. This analysis points to a significant 3 way interaction, so you may want to slice your comparisons for each visit, to look at differences between treatments and whether these are mediated by symptom.
Steve Denham
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