pkpdpkpd
●    

2007-04-03 17:45
(4954 d 05:56 ago)

Posting: # 616
Views: 15,651
 

 BE parallel design [General Sta­tis­tics]

While assessing BE in two-group parallel design study, should one use nominal data or log transformed data. If log transformed, should it be log or ln?

PKPDPKPD
Jaime_R
★★  

Barcelona,
2007-04-03 18:58
(4954 d 04:44 ago)

@ pkpdpkpd
Posting: # 617
Views: 14,365
 

 BE parallel design

Hi PKPDPKPD - what a nick! :cool:

» While assessing BE in two-group parallel design study, should one use nominal data or log transformed data.

Log-transformed if you are applying a multiplicative model (for all clearance based parameters, e.g., for AUC, Cmax,...)
Untransformed for Tmax - if applicable to your formulation.

» If log transformed, should it be log or ln?

Whatever you like (ld - logarithmus dualis - would also do the job), but most people prefer ln.

Regards, Jaime
pkpdpkpd
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2007-04-03 19:07
(4954 d 04:34 ago)

@ Jaime_R
Posting: # 618
Views: 14,151
 

 BE parallel design

Thank you. While using raw data and log data, I have significantly different results. In case of the parallel design, I calculate the ratio taking the mean from one group and the mean of the other group for the raw data and log of the mean from one group and log of the mean from another gruop. Am I true?

--
Edit: Full quote removed. [HS]
Jaime_R
★★  

Barcelona,
2007-04-03 19:41
(4954 d 04:01 ago)

@ pkpdpkpd
Posting: # 619
Views: 14,063
 

 BE parallel design

Hi PKPDPKPD!

» Thank you. While using raw data and log data, I have significantly different results.

That's quite common using transformations on data.
I hope you have a statistical protocol in place, and are not playing around to see which results are meeting your expectations. ;-)

» In case of the parallel design, I calculate the ratio taking the mean from one group and the mean of the other group for the raw data and log of the mean from one group and log of the mean from another gruop. Am I true?

I guess, you are talking of untransformed analysis first and transfomed analysis second?

Let's concentrate only on the transfomed analysis (because this is the one you will need).
  1. Calculate the log (Y1,Y2,...,Yn) of all individual values (X1,X2,...,Xm), where n = number of subjects under test and m = number of subjects under reference
  2. Calculate the arithmetic means form log transfomed data (Y) for the two treatments (YT and YR)
  3. If you want you can antilog these means (= geometric means of the original data)
  4. Calculate the SDs for the two treatments (SDT, SDR)
  5. Calculate the total variance S^2 = [(n-1)*SDT^2 + (m-1)*SDR^2]/(n+m-2)
  6. Calculate the difference Delta = YT - YR
  7. Calculate the point estimate by taking the antilog of Delta
  8. Calculate the upper/lower confidence limit as Delta + t(0.05,n+m-2)*S^2
  9. Calculate the antilogs of these confidence limits

Regards, Jaime
pkpdpkpd
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2007-04-03 20:14
(4954 d 03:27 ago)

@ Jaime_R
Posting: # 620
Views: 14,140
 

 BE parallel design

Jaime,

Thank you for your lesson. I am a beginner PKPDPKPD and am trying to understand the procedure which is normally done by the software. Just few questions to your instructions:
1. delta: should it be a difference of the raw data and log transformed data
2. why shoudl i calculate the difference not ratio

PKPDPKPD

--
Edit: Full quote removed. [HS]
Jaime_R
★★  

Barcelona,
2007-04-03 20:29
(4954 d 03:12 ago)

@ pkpdpkpd
Posting: # 621
Views: 15,565
 

 BE parallel design

Dear PKPDPKPD!

» I am a beginner PKPDPKPD and am trying to understand the procedure which is normally done by the software.

That's the best start of possible ones! ;-)

Never trust in any piece of software you haven't written yourself (and even then you should be cautious…)


» Just few questions to your instructions:
» 1. delta: should it be a difference of the raw data and log transformed data

After you have log-transformed the data, you are only working with these (in my example the Ys and not the Xs)

» 2. why shoudl i calculate the difference not ratio

Since we are now in the log-domain, we have transformed the multiplicative model (which would call for ratios!) into an additive model (therefore we are interested in differences of logs).
May be sound confusing, but once you have applied the transformation, all the nice examples given in statistical textbooks (99% are based on differences!) are working now…

Actually you can boil it down into three steps:
  1. Take logs of individual data (now you have a new data set)
  2. Apply common statistical methods (t-test, ANOVA, GLM, whatsoever,…)
  3. Antilog you results (point estimate, confidence limits)

Regards, Jaime
pkpdpkpd
●    

2007-04-03 21:48
(4954 d 01:53 ago)

@ Jaime_R
Posting: # 622
Views: 14,105
 

 BE parallel design

Should AUC and Cmax be also calculated from the log transformed data?

--
Edit: Full quote removed. Please see this post! [HS]
Jaime_R
★★  

Barcelona,
2007-04-04 15:14
(4953 d 08:27 ago)

@ pkpdpkpd
Posting: # 623
Views: 14,392
 

 BE parallel design

Dear PKPDPKPD!

» Should AUC and Cmax be also calculated from the log transformed data?

See my first post. You should only transform the calculated PK parameters (not the concentrations).
  1. Calculate AUC from your analytical results by any method you like (trapezoidal rule preferred, but not limited to).
  2. Cmax is simply the highest measured concentration.
  3. For the comparison you log-transform AUC and Cmax.
Second an apology: yesterday I was too fast (referring to my memory and not a textbook - I'm also using software and not explicit formulas). Therefore a little correction (valid for unequal group sizes):
Let's misuse Helmut's data (download here) ;-)
Although his data are from a cross-over study, we will use only period 1.
  1. Change the header of the first column from 'Seq' to 'Trt'
  2. Delete the column 'Rand'
  3. Delete the column 'P2'
Now we have data from a parallel study where Trt 1 = reference and Trt 2 = test, Group 1 = Subjects 1-12, Group 2 = Subjects 13-24, and Response (your PK parameter) in column 'P1'.
  1. log-transform 'P1'
  2. calculate separately for each treatment:
    • arithmetic mean: (1: 3.56227, 2: 3.38383)
    • exp(arithmetic mean): (1: 35.24321, 2: 29.48349),
    • note: these are the geometric means of untransformed data!
    • standard deviations: (1: 0.35950, 2: 0.42377)
    • variances = SD²: (1: 0.12924, 2: 0.17958)
    • n1,2 (group sizes): (1: 12, 2: 12)
    • Q1,2 = variance × (n1,2-1): (1: 1.42165, 2: 1.97539)
  3. calculate R = sqrt[(n1+n2)/(n1×n2)×(Q1+Q2)/(n1+n2-2)]: 0.16042
  4. look up the critical value of the t-distribution for alpha=0.05 with n1+n2-2 degrees of freedom: t 1.71714
  5. calculate t × R: 0.27547
  6. calculate Delta (difference of means Trt 2 - Trt 1): -0.17844
  7. antilog Delta (= point estimate): 0.83657
  8. calculate lower/upper 90% confidence limit = Delta ± t × R: lo: -0.45391, hi: 0.09702
  9. antilog lo and hi: exp(lo): 0.63514, exp(hi): 1.10189
So the final results are (point estimate and 90% confidence interval):
83.657% (63.514% - 110.189%)

I checked the 'manual' calculation in WinNonlin and EquivTest:
WinNonlin: 83.6572% (63.5100% - 110.1958%)
EquivTest: 83.66% (63.51% - 110.18%)

Slight differences seen in results are not uncommon... :-D

Regards, Jaime
Helmut
★★★
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Homepage
Vienna, Austria,
2007-04-04 15:31
(4953 d 08:10 ago)

@ Jaime_R
Posting: # 624
Views: 14,450
 

 BE parallel design

Hi Jaime!

You recycled my data! :clap:

» So the final results are (point estimate and 90% confidence interval):
» 83.657% (63.514% - 110.189%)
» WinNonlin: 83.6572% (63.5100% - 110.1958%)
» EquivTest: 83.66% (63.51% - 110.18%)
»
» Slight differences seen in results are not uncommon... :-D

Full ACK!
I don’t know which versions you were using; I'm getting exactly the same results in WinNonlin (v5.2) and EquivTest/PK.

Kinetica (v4.4.1) comes up with:
83.6572% (63.514% – 110.19%)

You never know when rounding will hit you – and don’t dare asking the software vendor for the algorithm…

Dif-tor heh smusma 🖖
Helmut Schütz
[image]

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

2007-04-04 17:32
(4953 d 06:09 ago)

@ Helmut
Posting: # 625
Views: 14,071
 

 BE parallel design

Thank you to all. It was a great help.

PKPDPKPD ;-)
Jaime_R
★★  

Barcelona,
2007-04-04 20:33
(4953 d 03:09 ago)

@ Helmut
Posting: # 626
Views: 14,042
 

 BE parallel design

Hi Helmut!

» You recycled my data!

Sure! You wrote:
You may use the data to 'play around' in your own piece of software.

» I don’t know which versions you were using…

WinNonlin (v5.1.1), EquivTest (v2.00)

Regards, Jaime
Sathya
☆    

India,
2008-09-01 07:21
(4437 d 16:20 ago)

@ Jaime_R
Posting: # 2291
Views: 13,368
 

 BE parallel design

HAI Jaime_R,

Your BE parallel design calculation is very useful to me.

This is the first time i am doing Parallel Design. Thank You.

I already did one BE cross over design.

there i Come across the Statistical calculation like

testmean
refmean
Standard Error
Mean Standard Error
diff
ratio
intra_cv
upper
lower
Power
P1 and P2

But in Paralled Design the Statistical calculation

testmean
refmean
SD
Variance
Delta
diff
Q
R
Point Estimate
Lower & Higher

I have a doubt that, is there no power calculation in Parallel design?

I don't know whether both parallel & crossover have same calculation or different Please Clarify. and also help me how to do power calculation in cross over?

Sathya
Sathya
☆    

India,
2008-09-04 12:37
(4434 d 11:04 ago)

@ Jaime_R
Posting: # 2314
Views: 13,235
 

 BE parallel design

Dear Jaime,

I tried your sample Data I got some clarity in Parallel study.

How can i Proceed it is in SAS?

Please Help me.

Please give me a sample for cross over study like parallel study especially for power calculation.

Then it will be very helpful to me.

can you please

Sathya
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