Imph
★    

Algeria,
2023-02-27 10:09
(25 d 18:46 ago)

Posting: # 23476
Views: 602
 

 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
★★★
avatar
Homepage
Vienna, Austria,
2023-02-27 14:00
(25 d 14:55 ago)

@ Imph
Posting: # 23477
Views: 536
 

 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! [image]
Helmut Schütz
[image]

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

Russia,
2023-02-27 21:45
(25 d 07:10 ago)

@ Helmut
Posting: # 23478
Views: 510
 

 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
★★★
avatar
Homepage
Vienna, Austria,
2023-02-28 11:24
(24 d 17:31 ago)

@ mittyri
Posting: # 23479
Views: 478
 

 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! [image]
Helmut Schütz
[image]

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

Algeria,
2023-03-06 13:42
(18 d 15:13 ago)

@ Helmut
Posting: # 23486
Views: 327
 

 CV ≈ s for low variances

Hello!

thanks a lot for all these informations.

Best regards.
UA Flag
Activity
 Admin contact
22,550 posts in 4,724 threads, 1,606 registered users;
18 visitors (0 registered, 18 guests [including 5 identified bots]).
Forum time: 04:56 CET (Europe/Vienna)

If there is an exception to any rule,
and if it can be proved by observation,
that rule is wrong.    Richard Feynman

The Bioequivalence and Bioavailability Forum is hosted by
BEBAC Ing. Helmut Schütz
HTML5