## 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!  Ing. Helmut Schütz 