XH7081
☆

2022-09-21 22:22
(79 d 03:18 ago)

Posting: # 23311
Views: 821

## Bioequivalence Across 3 Different Injection Site [Power / Sample Size]

Hello! First of all thank you for the wonderful PowerTOST package!

If I want to design an injection site study to compare the relative bioavailability at 3 different injection site, say T1, T2 vs R, in either crossover design or parallel design, is it correct to use the R code below:

1. Crossover design (3x6x3), assuming true theta=1, intra-CV=0.3. R results indicate I need 42 total subjects (7 subjects per sequence), not considering drop out etc. Is it correct?

> sampleN.TOST(theta0=1, CV=0.3, design="3x6x3",targetpower=0.9)

+++++++++++ Equivalence test - TOST +++++++++++
Sample size estimation
-----------------------------------------------
Study design: 3x6x3 crossover
log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.9
BE margins = 0.8 ... 1.25
True ratio = 1, CV = 0.3

Sample size (total)
n power
42 0.929519

I also saw some posts suggest doing "two at a time" test, which will use the 2x2 design as follows (which gave essentially the same sample size as the 3x6x3 design above since I need to round up to 6X, so 40 becomes 42). Is this thought process correct?

> sampleN.TOST(theta0=1, CV=0.3, design="2x2",targetpower=0.9)

+++++++++++ Equivalence test - TOST +++++++++++
Sample size estimation
-----------------------------------------------
Study design: 2x2 crossover
log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.9
BE margins = 0.8 ... 1.25
True ratio = 1, CV = 0.3

Sample size (total)
n power
40 0.909560

2. Parallel design (3 arms, assuming true theta=1, pooled CV=0.4). R results indicate I need 132 total subjects (44 subjects per arm), not considering drop out etc. Is it correct, or the 132 is for 2 arms (66 per arm) and I actually need 198 total subjects?

> sampleN.TOST(alpha = 0.05,
+ CV = 0.40, theta0 = 1,
+ targetpower = 0.90, design = "parallel")

+++++++++++ Equivalence test - TOST +++++++++++
Sample size estimation
-----------------------------------------------
Study design: 2 parallel groups
log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.9
BE margins = 0.8 ... 1.25
True ratio = 1, CV = 0.4

Sample size (total)
n power
132 0.904103

Many thanks!
dshah
★★

India/United Kingdom,
2022-09-22 00:08
(79 d 01:32 ago)

@ XH7081
Posting: # 23312
Views: 727

## Bioequivalence Across 3 Different Injection Site

Dear XH7081!

Kindly consider True ratio as 0.9-1.111 instead of 1.

Regards,
Divyen
XH7081
☆

2022-09-22 19:14
(78 d 06:26 ago)

@ dshah
Posting: # 23316
Views: 650

## Bioequivalence Across 3 Different Injection Site

❝ Kindly consider True ratio as 0.9-1.111 instead of 1.

Hi Divyen, thank you for the input. Besides changing the true ratio, are the rest of the code in general correct?

Helmut
★★★

Vienna, Austria,
2022-09-22 11:30
(78 d 14:09 ago)

@ XH7081
Posting: # 23313
Views: 680

## Two at a Time

Hi XH7081,

❝ First of all thank you for the wonderful PowerTOST package!

Welcome. THX to Detlew Labes and Benjamin Lang. Both did much more than myself.

❝ If I want to design an injection site study to compare the relative bioavailability at 3 different injection site, say T1, T2 vs R, in either crossover design or parallel design, is it correct to use the R code below:

In principle yes but as already mentioned by Divyen, theta0 = 1 should not be used.

❝ I also saw some posts suggest doing "two at a time" test, which will use the 2x2 design as follows (which gave essentially the same sample size as the 3x6x3 design above since I need to round up to 6X, so 40 becomes 42). Is this thought process correct?

❝ Parallel design (3 arms, assuming true theta=1, pooled CV=0.4). R results indicate I need 132 total subjects (44 subjects per arm), not considering drop out etc. Is it correct, or the 132 is for 2 arms (66 per arm) and I actually need 198 total subjects?

Yes.

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
XH7081
☆

2022-09-22 19:13
(78 d 06:27 ago)

@ Helmut
Posting: # 23315
Views: 645

## Two at a Time

❝ ❝ Parallel design (3 arms, assuming true theta=1, pooled CV=0.4). R results indicate I need 132 total subjects (44 subjects per arm), not considering drop out etc. Is it correct, or the 132 is for 2 arms (66 per arm) and I actually need 198 total subjects?

❝ Yes.

Thank you for your reply. Just to clarify, when you say "Yes", do you mean that total of 132 subjects (44 per arm) is correct, or total of 198 subjects (66 per arm) is correct?
Helmut
★★★

Vienna, Austria,
2022-09-23 13:03
(77 d 12:37 ago)

@ XH7081
Posting: # 23317
Views: 608

## Two at a Time

Hi XH7081,

❝ Just to clarify, when you say "Yes", do you mean that total of 132 subjects (44 per arm) is correct, or total of 198 subjects (66 per arm) is correct?

The latter. The sample size functions of PowerTOST give always the total sample size. Therefore, 132 / 2 × 3 = 198. Sorry for the confusion caused.

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