Bioequivalence and Bioavailability Forum

Dear all,

some time ago almost the same question was posted on the forum, but for me this problem persist so far. My question is: does PE and GMR represent different metrics, numerically and/or statistically?

I have posted it under the R for BE/BA category because I faced with this when I performed NCA/stat analysis utilizing bear-package.

On the one hand GMR by definition is a ratio of LSM T/LSM R, or in log scale Mean(lnCmaxT) minus Mean(lnCmaxR)
On the other hand PE is a sqrt(LL*UL)

In my example for Cmax below GMR=4.097-3.971=0.126, after exponentiation =1.1343
PE=sqrt(0.98809*1.30785=1.13678, which correspond to the table data.

So the results for GMR and PE are slightly different: 1.1343 for GMR and 1.13678 for PE. But why? Is my logic somewhere wrong?

The example output data:
Stat. Summaries for Pivotal Parameters of Bioequivalence (N = 45 )
----------------------------------------------------------------

Parameters Test_Mean Test_SD Ref_Mean Ref_SD
Cmax 67.390 31.872 60.398 31.526
AUC0-t 105.235 40.376 106.518 39.090
AUC0-inf 107.544 40.624 109.815 40.131
ln(Cmax) 4.097 0.494 3.971 0.527
ln(AUC0-t) 4.581 0.406 4.597 0.394
ln(AUC0-inf) 4.605 0.397 4.629 0.389


Statistical Summaries for Pivotal Parameters of Bioequivalence (N = 45 )
(cont'd)
----------------------------------------------------------------

Parameters F values P values PE (%) Lo 90%CI Up 90%CI
Cmax 1.492 0.229 - - -
AUC0-t 0.099 0.755 - - -
AUC0-inf 9.612 0.000 - - -
ln(Cmax) 2.410 0.002 113.678 98.809 130.785
ln(AUC0-t) 10.306 0.000 98.499 92.772 104.580
ln(AUC0-inf) 10.564 0.000 97.757 92.232 103.614

-------------------------------------------
Both F values and P values were obtained
from ANOVA respectively.
90%CI: 90% confidence interval
PE(%): point estimate; = squared root of
(lower 90%CI * upper 90%CI)