yicaoting ★ NanKing, China, 20170901 13:09 (1925 d 10:48 ago) Posting: # 17759 Views: 13,272 

Dear all, According to this thread, we know that PHX does not output IntersubjectCV when the Var(Sequence*Subject) is negtive. Using Ln() tranformation of PK data, I have verfified this using the data in the above thread. My results are identical to those obtained by our Helmut. But when I analysis the above data using orignal Cmax data (none Ln transformed), I find that PHX does not output IntersubjectCV even the Var(Sequence*Subject) is positive. Some of my results using PHX WNL 7.0: Dependent Hypothesis DF SS MS F_stat P_value I don't know how to explain this? I notie that PHX WNL produces no Warning Messages in the output resluts. But my manual calculation resluts are: Parameter Item Value For Nontransformed data analysis, I use these formula: InterCV = 100 * Sqr(SigmaS2) / LSMeanR IntraCV = 100 * Sqr(SigmaE2) / LSMeanR It's noted that here LSMeanR = Mean for NoneLntransformed data. they are cited from Page 153 of this book: SheinChung Chow and JenPei Liu, Design and Analysis of Bioavailability and Bioequivalence Studies, Third Edition. CRC Press. 2009. So does PHX WNL miss this? or I am wrong? Can anyone help me to test of this by other software? Can anyone help me to explain why WNL PHX doesn't calculate this for this dataset? or WNL PHX will never ouput this for BE analysis of NoneLntransformed data and why? Be sure, analysis of BE using Original Cmax data without Ln()transformation. Thank you for your help and clarification.  I try this in WNL 5.1.1 It only outputs Var(Sequecen*Subject) and Var(Residual), but Inter CV and Intra CV are both not calculated when using Nonetransformed data. From the comparison of WNL 5.1.1 and PHX 7.0, it seems PHX is improved in this isssue, but still lack of IntersubjectCV.  
mittyri ★★ Russia, 20170902 17:46 (1924 d 06:11 ago) @ yicaoting Posting: # 17764 Views: 12,192 

Hi Zhang Yong, citing the WNL guide: One additional parameter will appear in the Final Variance Parameters worksheet if, in addition to using the default model, the data is not transformed: intrasubject CV = sqrt(Var(Residual)) / RefLSM where RefLSM is the Least Squares Mean of the reference treatment. so that's not a bug For me even the formula above is strange. You are dividing overall standard deviation (calculated for both T and R) by LSMean of reference product only. Does that mean that if we inverse R to T, CV should change too? — Kind regards, Mittyri 
Helmut ★★★ Vienna, Austria, 20170902 17:57 (1924 d 06:00 ago) @ mittyri Posting: # 17765 Views: 12,207 

Hi mittyri, ❝ citing the WNL guide: ❝ intrasubject CV = sqrt(Var(Residual)) / RefLSM ❝ where RefLSM is the Least Squares Mean of the reference treatment. ❝ ❝ For me even the formula above is strange. You are dividing overall standard deviation (calculated for both T and R) by LSMean of reference product only. Does that mean that if we inverse R to T, CV should change too? Not necessarily should but will. I suggest dividing by the (weighted) global mean. — Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
yicaoting ★ NanKing, China, 20170902 19:50 (1924 d 04:07 ago) @ Helmut Posting: # 17766 Views: 12,159 

❝ Not necessarily should but will. I suggest dividing by the (weighted) global mean. Hi Helmut, I prefer the following formula ： intersubject CV = sqrt(Var(Sequence*Subject)) / RefLSM 
Helmut ★★★ Vienna, Austria, 20170902 21:20 (1924 d 02:37 ago) @ yicaoting Posting: # 17767 Views: 12,261 

Hi Yong, ❝ I prefer the following formula ： ❝ intersubject CV = sqrt(Var(Sequence*Subject)) / RefLSM Why? — Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
yicaoting ★ NanKing, China, 20170903 01:26 (1923 d 22:30 ago) (edited by yicaoting on 20170903 08:13) @ Helmut Posting: # 17768 Views: 12,128 

❝ ❝ I prefer the following formula ： ❝ ❝ intersubject CV = sqrt(Var(Sequence*Subject)) / RefLSM ❝ ❝ Why? Because this is also used for ln_transformed data. Like one formula for intrasubject CV for both transformed and none transformed data, I think this formula is generally accepted both for transformed and none transformed data. 
Helmut ★★★ Vienna, Austria, 20170904 15:32 (1922 d 08:24 ago) @ yicaoting Posting: # 17772 Views: 12,245 

Hi Yong, ❝ ❝ ❝ I prefer the following formula ： ❝ ❝ ❝ intersubject CV = sqrt(Var(Sequence*Subject)) / RefLSM ❝ ❝ Why? ❝ Because this is also used for ln_transformed data. No it isn’t! Back to the basics. The model of a 2×2×2 crossover assumes [sic] IID. For logtransformed data: \(\log{(\mu_T / \mu_R)} = \mu_T  \mu_R\), which is estimated by the difference of the LSMs of logtransformed data \(\bar{x}_T  \bar{x}_R\). Now it gets interesting (i.e., the assumption!): In the balanced case for simplicity (where n_{1} = n_{2} and n = n_{1} + n_{2}), \(\bar{x}_T  \bar{x}_R\) follows a normal distribution \(N\left ( \log{(\mu_T / \mu_R)}, 2\sigma^2 / n \right )\). Since σ^{2} is unknown, it is estimated by the MSE from ANOVA. Then we can estimate \(CV = \sqrt{e^{MSE}  1}\). Do you see \(\bar{x}_R\) in this derivation? I don’t. Remember that the normal distribution is described by two parameters, μ and σ^{2}, which are independent. If you are interested in the variance component, please leave the mean(s) completely out of it (as it is correctly done in PHX/WNL for logtransformed data). ❝ Like one formula for intrasubject CV for both transformed and none transformed data, I think this formula is generally accepted both for transformed and none transformed data. I think that for untransformed data dividing MSE by LSM_{R} goes back to Kem Phillips, who wrote* “… σ being expressed as a percentage of a reference mean, that is, as a coefficient of variation; values of the difference in means are expressed as percentages of the same reference mean.” That’s unfortunate and IMHO, not correct at all (Wolfgang Pauli would say: “That is not only not right; it is not even wrong!”). Again: The mean and variance are independent. So, the more I think about it: Even my idea of using the weighted global mean does not make sense. Paraphrasing Stephen Senn: Proving that apples are oranges by comparing the weight.
— Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
yicaoting ★ NanKing, China, 20170905 04:46 (1921 d 19:11 ago) @ Helmut Posting: # 17775 Views: 12,087 

❝ Since σ^{2} is unknown, it is estimated by the MSE from ANOVA. Then we can estimate \(CV = \sqrt{e^{MSE}  1}\). Do you see \(\bar{x}_R\) in this derivation? I don’t. Remember that the normal distribution is described by two parameters, μ and σ^{2}, which are independent. If you are interested in the variance component, please leave the mean(s) completely out of it (as it is correctly done in PHX/WNL for logtransformed data). ❝ Hi Helmut, Good explanation. Now, I think you are right. 
yicaoting ★ NanKing, China, 20170903 10:19 (1923 d 13:38 ago) @ mittyri Posting: # 17769 Views: 12,185 

Hi Mittyri, ❝ citing the WNL guide: ❝ One additional parameter will appear in the Final Variance Parameters worksheet if, in addition to using the default model, the data is not transformed: ❝ intrasubject CV = sqrt(Var(Residual)) / RefLSM Thanks for your citing. But why only one additional parameter (Intra CV)? but not two additional parameters (Inter CV and Intra CV). Since Inter CV is mathematically possible, I don't understand why it's not calculated in PHX. 
mittyri ★★ Russia, 20170903 10:41 (1923 d 13:16 ago) @ yicaoting Posting: # 17770 Views: 12,127 

Hi Zhang Yong, Helmut has asked a contrary question, I will just reformulate it Why do you prefer intrasubject CV = sqrt(Var(Residual)) / RefLSM but not intrasubject CV = sqrt(Var(Residual)) / TestLSM ? Do you see the difference between CVs for untransformed and transformed data? Yes, for untransformed data you need to know some mean, for logtransformed data a variance only. So even formula above is suspicious (see why in my previous post). I know that Chow says Ref, but why not Test or  as Helmut suggested  weighted mean of LSMs? The later is even more reasonable. I think devs just followed Chow here (and there is no interCV for untransformed data in the book). If you really need it you can post a request to Certara support with appropriate justification why do you need this in the next version. By the way nobody stops you to calculate any additional parameters related to any means and variances in DataWizard, right? — Kind regards, Mittyri 
yicaoting ★ NanKing, China, 20170904 13:35 (1922 d 10:22 ago) @ mittyri Posting: # 17771 Views: 12,078 

Thank you Mittyri, ❝ I think devs just followed Chow here (and there is no interCV for untransformed data in the book). If you really need it you can post a request to Certara support with appropriate justification why do you need this in the next version. I think it's better to move this issue to Certara Forum, and see PHX's opnion. Thank you again. 