Bioequivalence and Bioavailability Forum

Imph
★

2023-02-27 10:09
(802 d 10:42 ago)

Posting: # 23476
Views: 4,111

Variance VS Coefficient of variation [General Statistics]

Hello!

In the formulas for calculating the number of subjects on logarithmic scale, should we use the variance or the coefficient of variation? In Chow's paper (On Sample Size Calculation in Bioequivalence Trials, 2001) we see the variance in the formula on log-sclae while in his book (Design and Analysis of Bioavailability and Bioequivalence Studies, 2009) we see th coefficient of variation in the formula on log-scale.

Thank you in advance.

Helmut
★★★

Vienna, Austria,
2023-02-27 14:00
(802 d 06:50 ago)

@ Imph
Posting: # 23477
Views: 3,303

s² ↔ CV

Post reply

Hi Imph,

❝ […] should we use the variance or the coefficient of variation? In Chow's paper (On Sample Size Calculation in Bioequivalence Trials, 2001) we see the variance in the formula on log-sclae while in his book (Design and Analysis of Bioavailability and Bioequivalence Studies, 2009) we see th coefficient of variation in the formula on log-scale.

Both are fine. From the ANOVA of the study’s data you get the residual variance. However, the CV is more common. If you use software, make sure to use the correct input. $$\eqalign{
CV&=\sqrt{\exp(s^2)-1}⁠\\
s^2&=\log_{e}(CV^2+1)
}$$ PS: If you want to perform the estimation manually, be aware that the formulas in Chow & Wang’s 2001 paper are only approximate and contain typos (I warned you already). See the errata: J Pharmacokinet Pharmacodyn. 2002; 29(2): 101-102.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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Science Quotes

mittyri ★★ Russia, 2023-02-27 21:45 (801 d 23:06 ago) @ Helmut Posting: # 23478 Views: 3,333	CV ≈ s for low variances Post reply
	Hi Imph, Helmut and All! some history porn `CV ≈ sqrt(MSE) # for low MSE only!!!` Historical interest only (but still popular in NONMEM wild forests) — Kind regards, Mittyri

Helmut
★★★

Vienna, Austria,
2023-02-28 11:24
(801 d 09:26 ago)

@ mittyri
Posting: # 23479
Views: 3,319

CV ≈ s for low variances

Post reply

Hi mittyri,

❝ some history porn

Hey, that’s a nice one!

❝ Historical interest only (but still popular in NONMEM wild forests)

The Canadian guidances (from 1992 to the draft of 2009) contained these goodies:$$\eqalign{
\text{Intrasubject CV}&=100\times\text{(MSResidual)}^{0.5}\\
\text{Intersubject CV}&=100\times\text{(MSSubj}\,\text{(Seq))}^{0.5}}$$ When using the wrong formula, estimated sample sizes will be too small. Example for 2×2×2, T/R 0.95, target power 0.8:

library(PowerTOST) CV <- seq(0.14, 0.4, 0.02) mse <- CV2mse(CV) x <- data.frame(mse = mse, CV.right = CV, n.right = NA_integer_, CV.wrong = sqrt(mse), n.wrong = NA_integer_) for (j in seq_along(CV)) { x[j, c(3, 5)] <- c(sampleN.TOST(CV = CV[j], print = FALSE)[["Sample size"]], sampleN.TOST(CV = x$CV.wrong[j], print = FALSE)[["Sample size"]]) } names(x) <- c("MSE", "CV", "n", "CV ~ sqrt(MSE)", "~ n") print(signif(x, 4), row.names = FALSE) MSE CV n CV ~ sqrt(MSE) ~ n 0.01941 0.14 12 0.1393 10 0.02528 0.16 14 0.1590 14 0.03189 0.18 16 0.1786 16 0.03922 0.20 20 0.1980 20 0.04727 0.22 22 0.2174 22 0.05600 0.24 26 0.2366 26 0.06541 0.26 30 0.2558 30 0.07548 0.28 34 0.2747 34 0.08618 0.30 40 0.2936 38 0.09749 0.32 44 0.3122 42 0.10940 0.34 50 0.3307 46 0.12190 0.36 54 0.3491 52 0.13490 0.38 60 0.3673 56 0.14840 0.40 66 0.3853 62

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

Imph ★ 2023-03-06 13:42 (795 d 07:08 ago) @ Helmut Posting: # 23486 Views: 3,107	CV ≈ s for low variances Post reply
	Hello! thanks a lot for all these informations. Best regards.

Variance VS Coefficient of variation [General Sta­tis­tics]

s² ↔ CV

CV ≈ s for low variances

CV ≈ s for low variances

CV ≈ s for low variances

Variance VS Coefficient of variation [General Statistics]