Bioequivalence and Bioavailability Forum

Dear Raveendranath!

❝ As per Canadian guidance the formula for Intra subject CV% is

❝ Intra-subject CV = 100 x (MSResidual)^0.5

The formula in Canada’s guideline is only a rough approximation. For correct formulas and references see this post.
See also Section 6.2 in Julious’ paper:*

[…] all statistical inference for bioequivalence trials are undertaken on the log scale and back transformed to the original scale for interpretation. Thus, the within-subject estimate of variability on the log scale is used both for inference and sample size estimation. However, for the interpretation of the mean effect on the original scale it is optimal to have a measure of variability also on the original scale. A measure of variability that could be used is the coefficient of variability (CV) as this parameter is not scale dependent. Now, for log-Normally distributed data the following exact relationship between the CV on the arithmetic scale and the standard deviation sigma on the log scale holds:

$$CV=\sqrt{e^{\sigma^2}-1}$$

For small estimates of σ² [σ < 0.30] the CV can be approximated by

$$CV \sim \sigma$$σ is the square root of the residual MSE from a parametric model (ANOVA, LMEM).

See Table 8-H from the Canadian Guideline:
MSE:           0.0729
exact:         100 × sqrt(exp(0.0729)-1) = 27.5%
approximation: 100 × sqrt(0.0729)        = 27.0%

BTW, I ran AUC_t data of Table 8-G and got an MSE of 0.073161 (CV_intra 27.55%, CV_inter 55.01%). Maybe they cheated in order to get a nice square root (0.27²=0.0729)? Table 8-H is weird anyhow. How the hell do they get for Sequence MS=0.09 from SS=0.0535 (df=1)?! Ah, I see, it was a copy-and-paste error from the next column with the F-value (only the HTML-version of the guideline, PDF-version is correct).

WinNonlin / Phoenix-Beta (and the other pieces of software specialized in BE: Kinetica and EquivTest) give only the exact CV-values (intra- and inter-). Consider writing a polite letter to Eric Ormsby and/or calculate the approximate CV (if you are a guideline-addict)… Don’t use the approximation in sample size estimation for another study! So far about trustworthiness of guidelines.

It’s true that the bias of the approximate formula is acceptable for small CVs, but increases gradually. Might be a killer if you have to deal with an HVD/HVDP:



Another plot of the increasing deviation:



It’s getting nasty when you base the sample size estimation of another study on the approximate formula. Sample sizes will be too small - or in other words the true power of the study might be (substanially) smaller than expected:



For an MSE of 0.2231 CV is 50%, but the approximation gives just 47.24%. In a full replicate design you would need 50 subjects (power 81.28%). If you use 47.24% you might plan the study with only 44 subjects (expecting a power of 80.26%). But your estimation is based on a wrong CV! If you perform the study in 44 subjects, power is only 76.07%.
For an even more extreme example (think about a bisphosphonate with CV 80%) you would perform the study in 88 subjects instead of 108. Power will be 71.69%…

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• Julious SA. TUTORIAL IN BIOSTATISTICS. Sample sizes for clinical trials with Normal data. Stat Med. 2004;23(12):1921–86. doi:10.1002/sim.1783.