## Validation of FDA's RSABE on NTIDs [RSABE / ABEL]

Hi, Helmut.
Thank you for your quick response.

» THX! Below my results obtained in Phoenix WinNonlin 7.0 in full precision.
» swR 0.124392768691665, swT 0.0557209092013223

Yes, sWR and sWT can be calculate manually. So my results are indentical to yours.

» lower CL 0.293238291752988, upper CL 0.684266752752176
Thay are identical to mine.

» The guidance might be confusing. See the last bullet point below the formula
• here α = 0.1.
Hence, 1–0.05 and 1–0.95 are correct.
I am not sure the guidance is correct or not.
But from the formula in the guidance (page 4, line 5) with Alpha=0.1, I guess the guidance is right, it calulates 90% CI of Swt/Swr, but not 95% CI.

Need your clarification? or FDA is wrong?

» I have only Excel 2000. Up to v2003 the inverse distributions were wrong. Maybe you have to use F.inv(alpha,df1,df1) or the old workaround Finv(2*alpha,df1,df1). Duno. The correct F-values (ν12=16) are:
» Fα∕2,ν12 2.33348362746764, F1−α∕2,ν12 0.428543825304327

In Excel 2003,
Finv(0.05,16,16) = 2.33348362835
Finv(0.95,16,16) = 0.428543825142279

In Excel 2013
Finv(0.05,16,16) = 2.33348362746764
Finv(0.95,16,16) = 0.428543825304327
F.inv(0.05,16,16) = 0.428543825304327
F.inv(0.95,16,16) = 2.33348362746764

» According to the guidance sWR and swT are estimated from complete data only (not an issue with this data set) ignoring its structure (solely 'sequence' in the linear model). Your values are correct. Hence, as usual $$CV = \sqrt{e^{s_{w}^{2}} - 1}$$. Therefore, we get CVwR 12.49% and CVwT 5.58%.

Thanks.

» Personally I would prefer to run a mixed effects model with restricted maximum likelihood which takes the entire information into account (i.e., the FDA’s code of the 2001 guidance and also in the ABE-part of the progesterone guidance). In this model you could have incomplete data and the variances of R and T are simultaneously estimated. I guess that’s impossible in Excel (as it is in R)…
» I got: CVwR 15.86% and CVwT 5.73%. Interesting.

I guess your result of 15.86% and 5.73% are obtain from the sheet of "Final Variance Parameters" from ABE results using PHX WNL.

let
a = Var(Period*Formulation*Subject)_21 (the value is 0.024828963992548 from PHX WNL)
b = Var(Period*Formulation*Subject)_22 (the value is 0.003281299568883 from PHX WNL)
CVwr = 100 * SQRT(EXP(a)-1)
CVwt = 100 * SQRT(EXP(b)-1)

I got the same results sa you.

Here the CVwr and CVwt are different from those calculated from Swr and Swt.
I prefer the result calculated from Swr and Swt.