Bioequivalence and Bioavailability Forum

Hi Zhang Yong,

❝ Hope you are well.

THX! Below my results obtained in Phoenix WinNonlin 7.0 in full precision.

❝ I manually calculate the sWR and sWT in Excel sheet, they are 0.124392769, 0.055720909, respectively. Are my results EXACTELY right?

s_wR 0.124392768691665, s_wT 0.0557209092013223

❝ In your slides, you have present the upper 95% CL of sWT/sWR 0.68427 ≤2.5.

❝ I have calculated

❝ lower 95% CL of sWT/sWR = 0.293238292

❝ upper 95% CL of sWT/sWR = 0.684266753 (this is nearly the same as your result)

lower CL 0.293238291752988, upper CL 0.684266752752176

❝ As US FDA's Guidance on Warfarin required, the upper 90% CI should be used, I also calculate the following:

❝ lower 90% CL of sWT/sWR = 0.322597242

❝ upper 90% CL of sWT/sWR = 0.621992961

❝ Are the above results right?

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 use the function Finv(0.1,16,16) and Finv(0.9,16,16) for the calculation of 90% CL of sWT/sWR,

❝ and Finv(0.05,16,16) and Finv(0.95,16,16) for the calculation of 95% CL of sWT/sWR. Do I use the right function?

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 (ν₁=ν₂=16) are:
F_{α∕2,ν1,ν2} 2.33348362746764, F_{1−α∕2,ν1,ν2} 0.428543825304327

❝ Would you please guide (step by step) me how to calculate CVwr CVwt? As shown in your slides, they are CVWR 12.49%, CVWT 5.58%. Although these two values are not used in calculation of "upper 90% CL of sWT/sWR".

According to the guidance s_WR and s_wT 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 CV_wR 12.49% and CV_wT 5.58%.

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: CV_wR 15.86% and CV_wT 5.73%. Interesting.

Hope that helps.