Don’t use the formula by Chow, Shao, Wang! [Power / Sample Size]
❝ For some reason, I can't see the image with the formula that you put on the first post.
I uploaded a copy. Should be visible by now.
❝ ❝ The only thing about what I'm not sure is CV. Because in formula that I used this is intra-subject variability, but in PowerTOST() this is coefficient of variation as ratio. In calculations in both cases I used СV - 0.3.
❝
❝ Within subject standard deviation and within subject CV are different parameters. Nevertheless, I think that this is not the only reason for such a big difference.
Chow used the standard deviation, whilst in
Power.TOST
the CV (fraction, not in %!) is used. However, no big difference since \(CV_w = \sqrt{e^{s_{w}^{2}} - 1}\) and the other way ’round \(s_w = \sqrt{\log{(CV_{w}^{2}) + 1}}\). In Power.TOST
for convenience you can use se2CV(foo)
for the former and CV2se(foo)
for the latter.❝ There is a sentence in one of the articles that is quoted on SampleNTOST formula that may clarify this issue: […]
❝ So by reading this, I am not sure if Chow formula might be appropriate to calculate sample size for BABE trials.
![[image]](img/uploaded/image4.gif)
Since the above equations do not have an explicit solution, for convenience, for a 2 × 2 crossover design, the total sample size needed to achieve a power of 80% or 90% at 5% level of significance with various combinations of ε and δ is given in Table 10.2.1.
However, in the example which follows on p.260 we read:By referring to Table 10.2.1, a total of 24 subjects per sequence is needed in order to achieve an 80% power at the 5% level of significance.
(my emphases)❝ […] Perhaps dlabes might clarify this, since he is the master that we all should thank for the amazing PowerTOST package
Detlew is on vacation. Some clarifications:
Zhang1
(5) where n = sample size per sequence
(9) with a correction term c
Hauschke et al.2
Chow & Liu (5.4.10)3
Using the formulas of Zhang or Chow & Liu, you get the sample size / sequence. To obtain the total, multiply by 2, which is already done it the right-hand side of Hauschke’s formulas.
Comparison with the references:
Table 2, untransformed data, 90% Power, Δ 0.2, σ 0.3, ∕θ 0.05 (p.5371): 37 / sequence
library(PowerTOST)
sampleN.TOST(CV=se2CV(0.3), theta0=0.05, theta1=-0.2, theta2=0.2,
logscale=FALSE, targetpower=0.90,
print=FALSE)[["Sample size"]]/2
[1] 37
Table 5.4.1, untransformed data, 80% Power, Δ 0.2μR, α 0.05 (p.1583): 52
library(PowerTOST)
sampleN.TOST(CV=0.30, theta0=0.05, theta1=-0.2, theta2=0.2,
logscale=FALSE, targetpower=0.80,
print=FALSE)[["Sample size"]]
[1] 52
Table 5.1, log-transformed data, 80% Power, (θ1, 1∕θ1) = (0.80, 1.25), θ 0.95, α 0.05 (p.1132): 40
library(PowerTOST)
sampleN.TOST(CV=0.30, theta0=0.95, theta1=0.8, theta2=1.25,
targetpower=0.80,
print=FALSE)[["Sample size"]]
[1] 40
Stop using the formula given by Chow, Shao, Wang! Sample sizes are way too small – which compromises power. If you used it in the past for 80% power – if all assumptions (CV, θ0) turned out to be “correct” – substantially more than 20% of studies should have failed. If not, you were lucky!
- Zhang P. A Simple Formula for Sample Size Calculation in Equivalence Studies. J Biopharm Stat. 2003;13(3):529-38. doi:10.1081/BIP-120022772
- Hauschke D, Steinijans V, Pigeot I. Bioequivalence Studies in Drug Development. Chichester: John Wiley; 2007. p.116. doi:10.1002/9780470094778
- Chow S-C Liu J-p. Design and Analysis of Bioavailability and Bioequivalence Studies.
Boca Raton: Chapman & Hall/CRC Press; 3rd ed. 2009. p.157. doi:10.1201/9781420011678
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
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Helmut Schütz
![[image]](https://static.bebac.at/img/CC by.png)
The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
Complete thread:
- sample size in bioequivalence studies daryazyatina 2017-08-03 09:34 [Power / Sample Size]
- sample size in bioequivalence studies BE-proff 2017-08-03 09:55
- sample size in bioequivalence studies daryazyatina 2017-08-03 10:08
- sample size in bioequivalence studies ElMaestro 2017-08-03 10:17
- sample size in bioequivalence studies daryazyatina 2017-08-03 10:58
- sample size in bioequivalence studies DavidManteigas 2017-08-03 12:40
- sample size in bioequivalence studies daryazyatina 2017-08-03 13:46
- Don’t use the formula by Chow, Shao, Wang!Helmut 2017-08-03 15:37
- Don’t use the formula by Chow, Shao, Wang! daryazyatina 2017-08-03 15:52
- Don’t use the formula by Chow, Shao, Wang! DavidManteigas 2017-08-03 16:12
- Don’t use the formula by Chow, Shao, Wang! Helmut 2017-08-03 16:33
- Don’t use the Book by Chow, Shao, Wang! d_labes 2017-08-16 16:01
- compromised power Helmut 2017-08-03 16:04
- compromised power daryazyatina 2017-08-04 08:15
- terminology Helmut 2017-08-04 12:41
- terminology daryazyatina 2017-08-16 10:12
- terminology Helmut 2017-08-16 18:54
- terminology daryazyatina 2017-08-16 10:12
- terminology Helmut 2017-08-04 12:41
- compromised power daryazyatina 2017-08-04 08:15
- sample size in bioequivalence studies DavidManteigas 2017-08-03 12:40
- sample size in bioequivalence studies daryazyatina 2017-08-03 10:58
- sample size in bioequivalence studies balinskyi 2018-06-03 12:58
- sample size in bioequivalence studies BE-proff 2017-08-03 09:55