## No ‘R1’ and ‘R2’ in replicate designs [General Sta­tis­tics]

Hi Brus,

❝ In a partial replicated design (3-periods, 3 sequences), only reference is replicated, with a sample size of 45, CRO sent to me the following with proc GLM for ANOVA for the R/R comparison:

❝ …

Least Squares Means:

R1: 2.522

R2: 2.419

❝ Also they sent to me the following 90% CI for the comparative R1/R2:

Ratio = 110.79

90% Confidence Interval = 87.31 - 140.57

Intra-subject CV% = 21.18

There can be only one.

There is no ‘R1’ and ‘R2’, only one R repeatedly administered in the sequences in different periods. Say, the sequences are TRR | RTR | RRT. Did the CRO call the first administration in each sequence R1 and the second R2 (while dropping T)?
This gives after recoding:   ░R1R2 | R1░R2 | R1R2░

❝ But I have several doubts:

❝ - It surprises me a 90% CI so wide for a relatively low, at least not high, ISCV.

As said above, such a ‘comparison’ will not work.

❝ - If I back-calculated the CV from this 90% CI with “CVfromCI” of PowerTOST, I obtain a CV of around 70%. Why?

You tried CI2CV(lower=0.8731, upper=1.4057, design="2x2x2", n=40), right? That’s not what you have. After recoding (wild guess) you have an Incomplete Block Design. Other degrees of freedom,

❝ - In addition, I have tried to calculate the ratio and 90% CI with MSE and LSM according to the Helmut example from Pamplona lecture on 2018 "Basic Statistic on BE", slide 16 and 17:

❝ …

❝ I obtained a ratio of 110,8 but a 90% CI of 102,44 – 119,94. Same ratio as CRO but different 90 % CI. This is strange although it is in line with the ISCV presented by the CRO.

These formulas are for a 2×2×2 crossover and are also implemented in CI2CV(). But again, there is only one R. A ‘PE’ and ‘CI’ doesn’t make sense.

❝ Furthermore, doing various tests, … why?

No idea.

❝ So, what is the correct 90% CI?

There is none. You can only calculate the CVwR according to the EMA’s or the FDA’s models. The results will be similar, though quite often the one of the FDA is a bit smaller.

If you want, send me the raw data off-list.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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