roman_max ☆ Russia, 20181210 18:53 (2107 d 07:01 ago) Posting: # 19674 Views: 14,929 

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 bearpackage. 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=4.0973.971=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 AUC0t 105.235 40.376 106.518 39.090 AUC0inf 107.544 40.624 109.815 40.131 ln(Cmax) 4.097 0.494 3.971 0.527 ln(AUC0t) 4.581 0.406 4.597 0.394 ln(AUC0inf) 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    AUC0t 0.099 0.755    AUC0inf 9.612 0.000    ln(Cmax) 2.410 0.002 113.678 98.809 130.785 ln(AUC0t) 10.306 0.000 98.499 92.772 104.580 ln(AUC0inf) 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) 
Ohlbe ★★★ France, 20181211 01:28 (2107 d 00:27 ago) @ roman_max Posting: # 19676 Views: 11,913 

Dear roman_max, ❝ My question is: does PE and GMR represent different metrics, numerically and/or statistically? Yes. ❝ On the one hand GMR by definition is a ratio of LSM T/LSM R No. This is PE. The GMR is the ratio of geometric means, not of LSM (LSMEAN in SASspeak). For more details on how to calculate LSM and the difference between LSM and geometric mean, see this oldie. PE and GMR will be identical if you have a balanced study (same number of subjects in sequence RT and sequence TR). If the study is unbalanced (e.g. if you have a dropout), you'll get different results. The difference is usually minimal, but can be more important if you have an outlier. — Regards Ohlbe 
roman_max ☆ Russia, 20181212 17:31 (2105 d 08:23 ago) @ Ohlbe Posting: # 19683 Views: 11,666 

Dear Ohlbe, thanks a lot for clarification and the post provided. Because I`m using R/bear package seems that terminology in terms of MEANS are similar with SAS (LSMEAN). I`m not familiar with the latter software. Very often I face with that in BE study reports submitted to EMA/FDA by different companies GMR is the metric, not PE (along with its CIs). This is the reason why I interested in what we really "calculate" and why, is it specific of particular software or using of different terminology or something else. In a BE study report there is a summary table for presenting BE results, where geometric means (or LSMEANs?) in natural scale, GMR (%) (or PE(%)?) and CI(%) should be reported. In my example with R/bear for Cmax and log(Cmax) in output file I have the following data (designations "as is" in the output file): Dependent Variable: log(Cmax)  n1(R > T) = 23 n2(T > R) = 22 N(n1+n2) = 45 Lower criteria = 80.000 % Upper criteria = 125.000 % MEANref = 3.970504 MEANtest = 4.097524 MSE = 0.1563787 SE = 0.08338823 Estimate(testref) = 0.1282001 * Classical (Shortest) 90% C.I. for log(Cmax) * Point Estimate CI90 lower CI90 upper 113.678 98.809 130.785 As Yungjin explained me that PE in R/bear is not a direct arithmetic difference, and it is estimated in a specific linear model in ANOVA. MEANref and MEANtest are correspond to each LSMEAN in PK Parameter Summaries, it is OK. << PK Parameter Summaries >> ln(Cmax)  summary Test Ref Ratio LSMEAN 4.097 3.971 1.043 This is for logarithms So, Exp(LSMEAN[T])=60.159 and Exp(LSMEAN[R])=53.038, and these are geometric means, right? So, the ratio of geometric means (GMR) is 60.159/53.038=113.428 Does my understanding correct now? But what to report to authorities? PE or GMR? For balanced study they are equal, but for imbalanced they are slightly different. And what about CIs? Should I construct them for GMR as well? Thanks in advance for further clarifications. 
mittyri ★★ Russia, 20181212 18:40 (2105 d 07:14 ago) @ roman_max Posting: # 19685 Views: 11,672 

Dear roman_max, ❝ Very often I face with that in BE study reports submitted to EMA/FDA by different companies GMR is the metric, not PE (along with its CIs). This is the reason why I interested in what we really "calculate" and why, is it specific of particular software or using of different terminology or something else. Even if you look into EMA guideline: The assessment of bioequivalence is based upon 90% confidence intervals for the ratio of the population geometric means (test/reference) for the parameters under consideration. <...> The geometric mean ratio (GMR) should lie within the conventional acceptance range 80.00125.00%. They are using 'geometric means', 'geometric mean ratio' terms, but adjusted means (aka LSMeans) should be taken into account instead. As an example please see the code and conclusions in EMA PKWP Q&A ❝ In a BE study report there is a summary table for presenting BE results, where geometric means (or LSMEANs?) in natural scale, GMR (%) (or PE(%)?) and CI(%) should be reported. ❝ MEANref = 3.970504 ❝ MEANtest = 4.097524 ❝ MSE = 0.1563787 ❝ SE = 0.08338823 ❝ Estimate(testref) = 0.1282001 ❝ Point Estimate CI90 lower CI90 upper ❝ 113.678 98.809 130.785 ❝ As Yungjin explained me that PE in R/bear is not a direct arithmetic difference, and it is estimated in a specific linear model in ANOVA. Let's wait for Yungjin's comments ❝ << PK Parameter Summaries >> ❝ summary Test Ref Ratio ❝ LSMEAN 4.097 3.971 1.043 MEANtest = 4.097524 which could be rounded to 4.098, not 4.97 ❝ So, Exp(LSMEAN[T])=60.159 and Exp(LSMEAN[R])=53.038, and these are geometric means, right? ❝ Does my understanding correct now? ❝ But what to report to authorities? PE or GMR? For balanced study they are equal, but for imbalanced they are slightly different. You can try to add a footnote and describe somewhere why GeoMeans could be unequal to LSMeans ❝ And what about CIs? Should I construct them for GMR as well? — Kind regards, Mittyri 
yjlee168 ★★★ Kaohsiung, Taiwan, 20181212 19:58 (2105 d 05:57 ago) @ mittyri Posting: # 19686 Views: 11,733 

Dear mittyri & all others, ❝ ❝ As Yungjin explained me that PE in R/bear is not a direct arithmetic difference, and it is estimated in a specific linear model in ANOVA. ❝ Sounds strange to me. Do we have the ratio of LSMeans, the ratio of GeoMeans and something else? ❝ Let's wait for Yungjin's comments Estimate(testref) in bear is not obtained directly from the difference of mean values or lsmean. It is obtained from one of coefficients of lm() function. I cut the outputs from a test run and show it as follows: please browse "Interpreting regression coefficient in R" for more details (the explanations for the coefficient x32). Does anyone know the name of this coefficient in statistics? Thanks. — All the best,  Yungjin Lee bear v2.9.1: created by Hsinya Lee & Yungjin Lee Kaohsiung, Taiwan https://www.pkpd168.com/bear Download link (updated) > here 
mittyri ★★ Russia, 20181212 23:57 (2105 d 01:57 ago) @ yjlee168 Posting: # 19688 Views: 11,900 

Dear Yungjin, Thank you for the explanation. ❝ Estimate(testref) in bear is not obtained directly from the difference of mean values or lsmean. It is obtained from one of coefficients of lm() function. The question is how do you obtain LSMeans or what do you output as MEANref = 7.32951 ❝ please browse "Interpreting regression coefficient in R" for more details (the explanations for the coefficient x32). Does anyone know the name of this coefficient in statistics? Thanks. Here's a little code where I show that the LSMeans difference is a point estimate irrespective of the sequence balance. library(data.table) — Kind regards, Mittyri 
yjlee168 ★★★ Kaohsiung, Taiwan, 20181213 13:20 (2104 d 12:35 ago) (edited by yjlee168 on 20181213 14:19) @ mittyri Posting: # 19689 Views: 11,545 

Dear mittyri, Very sorry about the delay of this replied message. ❝ In your example the dataset is balanced. That's correct. ❝ The question is how do you obtain LSMeans or what do you output as ❝
These two values were simply obtained from mean(LnCmax) . So they were geometric means as defined. Since only balanced crossover studies will be analyzed in bear, so lsmeans are the same as arithmetic means.❝ ❝ please browse "[link=nk]" for more details (the explanations for the coefficient x32). Does anyone know the name of this coefficient in statistics? Thanks. ❝ That is called as a contrast. Ok, thanks a lot. And also I will try your codes later with my test dataset. Your codes show and clarify the differences in calculation of lsmeans and geometric means for an unbalanced crossover study, as well as the contrast is equal to lnPE(I don't know that before!). Please correct me if I do not interpret your codes correctly. Thanks again. — All the best,  Yungjin Lee bear v2.9.1: created by Hsinya Lee & Yungjin Lee Kaohsiung, Taiwan https://www.pkpd168.com/bear Download link (updated) > here 
mittyri ★★ Russia, 20181211 17:30 (2106 d 08:25 ago) @ roman_max Posting: # 19680 Views: 11,762 

Dear roman_max, just some additional questions coninuing Ohlbe's post above: Are you dealing with replicate or simple crossover? Are there any dropouts? I see you included in the analysis 45 subjects. Did they finish the study as planned? — Kind regards, Mittyri 
roman_max ☆ Russia, 20181212 17:41 (2105 d 08:13 ago) @ mittyri Posting: # 19684 Views: 11,648 

Dear mittyri, thank you for the questions. This study was a classic BE with 2x2x2 design. There was 1 dropout, that was excluded from PK and stat.analysis, so I had imbalance in sequences. I've replied to Ohlbe and asked several additional questions. If you also have your opininon please comment on, I have to find out a solution to the uncertainties 
ElMaestro ★★★ Denmark, 20181212 22:39 (2105 d 03:15 ago) @ roman_max Posting: # 19687 Views: 11,645 

Hi roman_max, I am using the terms PE and GMR interchangeably. I am not necessarily happy to do so but there you are. On the log scale we have differences of model effects (what Yungjin mentioned, but with that coding it becomes so difficult to relate it to real life), differences of geometric means, differences of LSMeans and God knows what else. All this boils down to the same thing with balanced designs, and to confusion more generally. Probably someone is too proud to fix it. Semantics is only important when regulators think so. — Pass or fail! ElMaestro 
roman_max ☆ Russia, 20181214 00:11 (2104 d 01:44 ago) @ ElMaestro Posting: # 19690 Views: 11,498 

Hi ElMaestro, Thanks for the opinion. Indeed, no problem when there are no dropouts from the study. And definitely you don't know how a particular software use its sophisticated logic in calculations, applying coefficients, modeling etc. Sometimes I also use SPSS and it's syntax, but it cannot account for disbalance like R lm function. So it depends.. So, as a solution I will make a footnotes to tables to explain "readers" in RA what a particular metrics mean and how they were calculated / estimated. Along with SAP :) Hope it will be sufficient to our regulator not to be knocked down 
mittyri ★★ Russia, 20181214 16:35 (2103 d 09:19 ago) @ roman_max Posting: # 19691 Views: 11,469 

Hi roman_max, ❝ Sometimes I also use SPSS and it's syntax, but it cannot account for disbalance like R lm function. We compared SPSS vs PHX WNL vs SAS vs lm() using PK datasets with replicated designs (including some sophisticated with dropouts) and didn't find any significant deviations. So I think it can. — Kind regards, Mittyri 
roman_max ☆ Russia, 20181215 14:37 (2102 d 11:17 ago) @ mittyri Posting: # 19693 Views: 11,436 

Dear mittyri, Could you please share the SPSS syntax you use for modeling factors in BE study? :) I use GLM UNIANOVA. 
ElMaestro ★★★ Denmark, 20181214 17:11 (2103 d 08:44 ago) @ roman_max Posting: # 19692 Views: 11,441 

Hello roman_max, ❝ And definitely you don't know how a particular software use its sophisticated logic in calculations, applying coefficients, modeling etc. Sometimes I also use SPSS and it's syntax, but it cannot account for disbalance like R lm function. First of all, there is no hidden secret in the way the software applies logic. All this is generally completely documented and clear, albeit not always easy to understand (the part I am currently struggling with is the actual derivation of an LS Mean, generally, for example also in models that are mopre sophisticated than those used for BE like when covariates are in play. I can't say the SAS documentation is very understandable. But that's just me). The issue, as I understood your question, related to more to what we call the output and if there is a discrepancy in the nomenclature. Next, SPSS will definitely be able to account for imbalance, I am sure of it. If it doesn't appear so when you run the model then this may be a case of garbage in, garbage out. — Pass or fail! ElMaestro 