yicaoting
★

NanKing, China,
2017-09-01 11:09
(1239 d 00:40 ago)

(edited by yicaoting on 2017-09-01 11:37)
Posting: # 17759
Views: 12,440

## Lack of IntersubjectCV in PHX [Software]

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 Cmax      Sequence          1   1056.5714   1056.5714   0.017626409   0.89657994 Cmax      Sequence*Subject  12  719310.29   59942.524   1.3991004     0.28488402 Cmax      Formulation       1   37889.286   37889.286   0.8843624     0.36555519 Cmax      Period            1   88706.286   88706.286   2.0704667     0.17574474 Cmax      Error             12  514123.43   42843.619 Cmax   Var(Sequence*Subject)   8549.4524 Cmax   Var(Residual)          42843.6190 Cmax   Intrasubject CV         0.12677478

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 Cmax      Var(Sequence*Subject)     8549.4524 Cmax      Var(Residual)            42843.6190 Cmax      Inter-subject CV(%)        5.6632 Cmax      Intra-subject CV(%)       12.6775
For Non-transformed data analysis, I use these formula:
InterCV = 100 * Sqr(SigmaS2) / LSMeanR
IntraCV = 100 * Sqr(SigmaE2) / LSMeanR
It's noted that here LSMeanR = Mean for None-Ln-transformed data.
they are cited from Page 153 of this book: Shein-Chung Chow and Jen-Pei 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 None-Ln-transformed 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 None-transformed 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,
2017-09-02 15:46
(1237 d 20:03 ago)

@ yicaoting
Posting: # 17764
Views: 11,445

## CVs for untransformed data

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,
2017-09-02 15:57
(1237 d 19:52 ago)

@ mittyri
Posting: # 17765
Views: 11,452

## CVs for untransformed data

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.

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
yicaoting
★

NanKing, China,
2017-09-02 17:50
(1237 d 17:59 ago)

@ Helmut
Posting: # 17766
Views: 11,425

## CVs for untransformed data

» 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,
2017-09-02 19:20
(1237 d 16:29 ago)

@ yicaoting
Posting: # 17767
Views: 11,481

## CVs for untransformed data

Hi Yong,

» I prefer the following formula ：
» intersubject CV = sqrt(Var(Sequence*Subject)) / RefLSM

Why?

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
yicaoting
★

NanKing, China,
2017-09-02 23:26
(1237 d 12:23 ago)

(edited by yicaoting on 2017-09-03 08:13)
@ Helmut
Posting: # 17768
Views: 11,399

## CVs for untransformed data

» » 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,
2017-09-04 13:32
(1235 d 22:17 ago)

@ yicaoting
Posting: # 17772
Views: 11,484

## N(μ, σ²)

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 log-transformed data:
$$\log{(\mu_T / \mu_R)} = \mu_T - \mu_R$$, which is estimated by the difference of the LSMs of log-transformed data $$\bar{x}_T - \bar{x}_R$$. Now it gets interesting (i.e., the assumption!): In the balanced case for simplicity (where n1 = n2 and n = n1 + n2), $$\bar{x}_T - \bar{x}_R$$ follows a normal distribution $$N\left ( \log{(\mu_T / \mu_R)}, 2\sigma^2 / n \right )$$.
Since σ2 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 σ2, 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 log-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.

I think that for untransformed data dividing MSE by LSMR 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.

• Phillips KM. Power of the Two One-Sides Tests Procedure in Bioequivalence. J Pharmacokinet Biopharm. 1990; 18(2): 137–44. doi:10.1007/BF01063556.

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
yicaoting
★

NanKing, China,
2017-09-05 02:46
(1235 d 09:03 ago)

@ Helmut
Posting: # 17775
Views: 11,286

## N(μ, σ²)

» Since σ2 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 σ2, 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 log-transformed data).
»

Hi Helmut,
Good explanation. Now, I think you are right.
yicaoting
★

NanKing, China,
2017-09-03 08:19
(1237 d 03:30 ago)

@ mittyri
Posting: # 17769
Views: 11,428

## CVs for untransformed data

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

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,
2017-09-03 08:41
(1237 d 03:08 ago)

@ yicaoting
Posting: # 17770
Views: 11,389

## CVs for untransformed data

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,
2017-09-04 11:35
(1236 d 00:14 ago)

@ mittyri
Posting: # 17771
Views: 11,345

## CVs for untransformed data

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.