Bioequivalence and Bioavailability Forum

Dear FI,

❝ Unfortunately I get a different value for the variance of the differences of the pooled formulation data:

❝ MSE=0.165897781 in EXCEL and

❝ 0.1662119811 from SAS, if I take the „stderr“-value from „iout2“ to calculate MSE using: MSE=stderr²*69;

❝ (accordingly: SE in EXCEL: 0.0490338, in SAS 0.49080)

(emphasis by me)

"Hier liegt der Hund begraben!" (That's the crux of the matter.)
The formula you use to relate MSE and stderr of the difference T-R is only appropriate if the study is balanced with respect to the number of subjects within the sequences.

If this is not the case you have to use ⁽¹⁾
   stderr2 = MSE*(0.25*(1/n1 + 1/n2))
for the 'full replicate' design (2-sequence-4period).
Only if you set n₁=n₂=N/2 (N=total number of subjects) you get
   stderr2 = MSE*(1/N)
or the other way round
   MSE = N*stderr2
you have used.

Since here for the EMA I dataset n₁=36 (RTRT), n₂=33 (TRTR)and MSE=0.1658977 you get stderr=0.04908023, that value you obtain from 'iout2' regardless if you use Proc GLM or Proc MIXED.

BTW: The formula for the partial replicate design (3-sequence-3-period) is
   stderr2 = MSE*((1/6)*(1/n1 + 1/n2 + 1/n3))

❝ My knowledge in SAS is not enough, to draw the formula somewhere.

As you see: It's a question of the power to know and not of knowledge in SAS .

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⁽¹⁾S-C Chow and J-P Liu
Design and Analysis of Bioavailability and Bioequivalence Studies
Chapman & Hall / CRC, Boca Raton, 3rd Ed. (2009)
Chapter 9.4 (but cave! model without carry over for the 2x2x4, formula 9.4.12)

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Hope this helps.