Imph
★

Algeria,
2023-02-27 10:09
(26 d 08:21 ago)

Posting: # 23476
Views: 611

## 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
(26 d 04:30 ago)

@ Imph
Posting: # 23477
Views: 545

## s² ↔ CV

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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mittyri
★★

Russia,
2023-02-27 21:45
(25 d 20:45 ago)

@ Helmut
Posting: # 23478
Views: 519

## CV ≈ s for low variances

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
(25 d 07:05 ago)

@ mittyri
Posting: # 23479
Views: 487

## CV ≈ s for low variances

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. 🚮
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Imph
★

Algeria,
2023-03-06 13:42
(19 d 04:48 ago)

@ Helmut
Posting: # 23486
Views: 336

## CV ≈ s for low variances

Hello!

thanks a lot for all these informations.

Best regards.
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