## Calculation of PE and 90% CI [General Sta­tis­tics]

Dear all,

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:

Source   / DF /       SS      /     MS       / P Seq      /  2 /  0.20523638   / 0.10261819   / 0.7686 Sbj(seq) / 40 / 15.497377771  / 0.3874344443 / <0.0001 Per      /  2 /  0.0922514826 / 0.0461257413 / 0.3597 Treat    /  1 /  0.0231184863 / 0.0231184863 / 0.4725 Error    / 37 /  1.6238230813 / 0.0438871103 / - 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

The number of observations used for the calculation were 40 due to drop outs.

But I have several doubts:
- It surprises me a 90% CI so wide for a relatively low, at least not high, ISCV.
- If I back-calculated the CV from this 90% CI with “CVfromCI” of PowerTOST, I obtain a CV of around 70%. Why?
- 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:

SE = √(MSE/nps), where nps = (n1 +n2)/2
∆ = LSM (T) – LSM (R)
PE (GMR = e∆)
90% CI = ∆ ± t(α = 0.05, df) × SE

I used 0.043 from first table as MSE and I used the formula from Helmut presentation to convert it in SE and then to calculate the ratio and 90% CI.

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.

Furthermore, doing various tests, I have noticed that if you add the mean square obtained in the Sbj(seq) from first table to the MSE and you use the formula from Helmut presentation to convert this sum in SE and then to calculate the ratio and 90% CI, you obtain the same 90% CI as CRO. But, If the subj(seq) is significant, should it be calculated in this way?, why?, and should it be taken into account and impact the 90% CI range?

So, what is the correct 90% CI?

Thank you so much

Best regards,  Ing. Helmut Schütz 