## 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.

I think it’s crap. The formula Darya posted (10.2.6) of p.259 of the book gives the impression that

*n*is the total sample size. The text continues with:

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.

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:

Zhang^{1}

(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.537

^{1}): 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 0.2

*μ*

_{R},

*α*0.05 (p.158

^{3}): 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, (

*θ*

_{1}, 1∕

*θ*

_{1}) = (0.80, 1.25),

*θ*0.95,

*α*0.05 (p.113

^{2}): 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,

*θ*

_{0}) 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; 3^{rd}ed. 2009. p.157. doi:10.1201/9781420011678

*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

### 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