## RSABE ⇒ ABEL [General Sta­tis­tics]

Hi VStus,

» I have limited data about partial replicate trial (2x3x3) with RSABE, which I want to use to assess the feasibility of same study under EMA regulation (assuming that EU has the same Reference product as US).
» Reported parameters:
» Number of subjects (observations per treatment arm)
» Swr estimated using PROC GLM
» Point Estimate (%) from RSABE-approach
» […]
» Is it feasible to try calculation of 90% CIs?

Yes.

» Can I apply the formula below?
» 90% CI = log(Point_Estimate) +/- Swr * qt(0.05, df))*100,

No (see this post). Let’s compare the EMA’s Q&A dataset II (n = 24; n1 = n2 = n3 = 8), evaluated by the FDA’s RSABE (PE = 1.022644, swR = 0.11397298) with results of the EMA’s methods: PE 102.26%; 90% CI: Methods A/B 97.32–107.46%, Method C 97.05–107.76%.

n   <- c(8, 8, 8) pe  <- 1.022644 swR <- 0.11397298 CI  <- exp(log(pe) + c(-1, +1)*qt(1-0.05, 2*sum(n)-3)*sqrt(1/6*swR^2*sum(1/n))) names(CI) <- c("lower", "upper") round(100*CI, 2) # lower  upper # 97.49 107.28

Alternatively:

library(PowerTOST) round(100*CI.BE(pe=pe, CV=se2CV(swR), n=n, design="2x3x3"), 2) # lower  upper # 97.49 107.28

Pretty close but in this case (swR <0.294) the FDA requires a mixed-effects model for ABE, where s²wR = 0.013246498 (PE 102.26%, 90% CI 97.05–107.76%). Hence, we have to take that into account.

library(PowerTOST) n    <- c(8, 8, 8) pe   <- 1.022644 s2wR <- 0.013246498 round(100*CI.BE(pe=pe, CV=mse2CV(s2wR), n=n, design="2x3x3", robust=TRUE), 2) # lower  upper # 97.32 107.46

Or the hard way:

 CI <- exp(log(pe) + c(-1, +1)*qt(1-0.05, sum(n)-3)*sqrt(1/6*s2wR*sum(1/n))) names(CI) <- c("lower", "upper") round(100*CI, 2) # lower  upper # 97.32 107.46

Bingo!

Dif-tor heh smusma 🖖
Helmut Schütz

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