PROC MIXED - Confidence interval and p-value for geometric ratio of log10 transformed outcome

[tatami]

I am running MMRM on log10 transformed outcome. There is some medical reasoning for log10 transformation instead of natural log. I would like to model using SAS PROC MIXED. To get geometric mean and geometric ratio, I would need to reverse the transformation. I understand that direct reverse transformation gives median instead of the expected value (Solved: Non-normal data; PROC GLIMMIX - SAS Support Communities). How should I go about this? I would like to get GMR of treatment versus control at a specific time point.

proc mixed data=final2;
class id trt avisit;
model log10aval=trt avisit log10base trtp*avisit / S;
repeated avisit / subject=id type= UN R;
LSMEANS trt*avisit / PDIFF CL;
estimate "Visit 9 - Week 52" trt 1 -1 trt*avisit 0 0 0 0 1 0 0 0 0 -1 / CL;
run;

[SteveDenham]

If there is a reason for using a log10 transform for this field, then the backtransformed (10**estimate, 10**stderr) values are what you should probably report to be consistent with the literature.  If you truly need the expected value and the standard deviation of the expected value (standard error), there are two methods that we have used.  These are the delta method and the omega method.  The latter is spelled out in the PROC GLIMMIX documentation, referring to a lognormal distribution.  You can use the formulas there, after converting the log10 values to natural logs (multiply by a constant).  For the delta method, it turns out that Wikipedia has good formulas for E(X) and Var(X).

SteveDenham