joy_fm
☆    

Indonesia,
2014-11-03 09:19
(3434 d 02:36 ago)

Posting: # 13822
Views: 7,124
 

 SE Difference [General Sta­tis­tics]

Dear all,

Would you mind to answer my question related to Bioequivalence Statistical Analysis ?

Which one is the correct one for SE Difference ?

a. SE Difference = (MS residual x (1/nTR + 1/nRT)1/2

or

b. SE Difference = (MS residual x (2/n)1/2


Note : n = subject number of Bioequivalence study
nRT = subject number who get Reference Drug in Period 1, and get Test Drug in Period 2 = 1/2 n
nTR = subject number who get Test Drug in Period 1, and get Reference Drug in Period 2 = 1/2 n


If I calculate 2 formula from a and b, the results will be different.

a. SE Difference = (MS residual x (1/nTR+ 1/nRT)1/2
= (MS residual x (1/(1/2n)+ (1/(1/2n)1/2
= (MS residual x (2/n + 2/n)1/2
= (MS residual x (4/n)1/2

b. SE Difference = (MS residual x (2/n)1/2

Would you mind to share the guideline for SE Difference calculation ?

Thank you

Best Regards

joy_fm
Mahmoud
★    

Jordan,
2014-11-06 21:33
(3430 d 14:21 ago)

@ joy_fm
Posting: # 13834
Views: 6,168
 

 SE Difference

Dear Sir

1.SE Difference = (MS residual/2 x (1/nTR + 1/nRT)1/2
if nRT is not equal nTR

2.SE Difference = (MS residual x (2/n)1/2
if nRT = nTR=n/2

n = subject number of Bioequivalence study


Dr.Mahmoud Abdel Mohsen

Amman-Jordan
statistiain


Edit: You forgot closing brackets. Your formulas should read:
  1. SE Difference = (MS residual/2 × (1/nTR + 1/nRT))1/2
  2. SE Difference = (MS residual x (2/n))1/2
[Helmut]
joy_fm
☆    

Indonesia,
2014-11-07 05:05
(3430 d 06:49 ago)

@ Mahmoud
Posting: # 13836
Views: 5,984
 

 SE Difference

Dear Dr. Mahmoud Abdel Mohsen,

Thank you for answering my question.

Would you mind to share the guideline ?
Because I just have Canada Guideline "Guidance Document Conduct and Analysis of Comparative Bioavailability Studies" effective date May 22, 2012, that state:

SEDifference = (2MSResidual/n)0.5

Thank you

Best regards

Ms. Joy_fm
Mahmoud
★    

Jordan,
2014-11-07 06:42
(3430 d 05:12 ago)

@ joy_fm
Posting: # 13837
Views: 5,971
 

 SE Difference

Dear sir
No if you need any information i can send to you


Didn’t you realize? Ms. Joy = Madam Sir… Thankfully the BEBA Forum is not a boys-only club. [Helmut]
Helmut
★★★
avatar
Homepage
Vienna, Austria,
2014-11-07 15:29
(3429 d 20:26 ago)

@ joy_fm
Posting: # 13840
Views: 5,974
 

 Don’t trust in guidelines!

Hi Joy,

❝ Would you mind to share the guideline ?


It is not a particular good idea to rely on guidelines – especially when it comes to statistics. :stop:

❝ Because I just have Canada Guideline […]


❝ SEDifference = (2MSResidual/n)0.5


Not the sole error in Health Canada’s guidance; the formula – as Mahmoud wrote – is only correct in the balanced case. Always use $$SE=\sqrt{\frac{MSE}{2}\left(\frac{1}{n_\textrm{TR}}+\frac{1}{n_\textrm{RT}}\right)}\tag{1}$$ HC’s example dataset is balanced only by chance (one dropout in each sequence) and imbalanced studies are not uncommon in BE. BTW, it took HC 21 (‼) years to give the correct formula for the intra-subject CV:
$$CV_\textrm{intra}=\sqrt{\exp(MSE)-1}\tag{2}$$ In HC’s first (1991) guidance – and still in the 2009 (!) draft – the wrong $$CV_\textrm{intra}=\sqrt{MSE}\tag{3}$$ was given. For AUCT of the example data set one gets 0.275 by \(\small{(2)}\) and 0.270 by \(\small{(3)}\). So much about the “wisdom” of guidelines!

Get a statistical textbook relevant for BE (e.g., Hauschke et al.1 or Chow & Liu2).


  1. Hauschke D, Steinijans V, Pigeot I. Bioequivalence Studies in Drug Development. Chichester: John Wiley; 2007. doi:10.1002/9780470094778.
  2. Chow S-C Liu J-p. Design and Analysis of Bioavailability and Bioequivalence Studies.
    Boca Raton: Chapman & Hall/CRC Press; 3rd ed. 2009. doi:10.1201/9781420011678.

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joy_fm
☆    

Indonesia,
2014-11-10 02:49
(3427 d 09:05 ago)

@ Helmut
Posting: # 13847
Views: 5,782
 

 Don’t trust in guidelines!

Hi Helmut,
Thank you for your clear and helpful explanation :-)

And thank you for sharing your expertise with me.

Best Regards
joy_fm


Thank you for this statement too: Thankfully the BEBA Forum is not a boys-only club. [Helmut]
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