## Reference-scaling: Don’t use FARTSSIE! [Power / Sample Size]

Hi Astea,

❝ Just few words in defence of FARTSSIE. May be the approximations are rude, far from exact PowerTOST (see #), but the results overally seems to be correlated for CV>30%:

Nope. The EMA’s ABEL not only means extending the limits (based on the observed – not the assumed CVwR) but also assessing the GMR-restriction. It’s a complex framework and therefore, no simple formula exists to calculate power. Try this one:

library(PowerTOST) CV         <- c(30, 40, 50) n          <- c(40, 27, 23) n.FARTSSIE <- n + n %% 2 # round to next even res        <- data.frame(CV=CV, n.FARTSSIE=n.FARTSSIE, pwr.FARTSSIE=NA,                          n.ABE=NA, pwr.ABE=NA, n.ABEL=NA, pwr.ABEL=NA) names(res)[1] <- "CV%" EL         <- scABEL(CV=CV/100) for (j in seq_along(CV)) {   # power for ABEL with n of FARTSSIE   res[j, "pwr.FARTSSIE"] <- power.scABEL(CV=CV[j]/100, design="2x2x4",                                          n=n.FARTSSIE[j])   # PowerTOST's function for ABE mimicking FARTSSIE   tmp <- sampleN.TOST(CV=CV[j]/100, theta0=0.9, theta1=EL[[j, "lower"]],                       design="2x2x4", print=FALSE, details=FALSE)   res[j, "n.ABE"]   <- tmp[["Sample size"]]   res[j, "pwr.ABE"] <- tmp[["Achieved power"]]   # PowerTOST's function for ABEL (1e5 simulations)   tmp <- sampleN.scABEL(CV=CV[j]/100, theta0=0.9, design="2x2x4",                         print=FALSE, details=FALSE)   res[j, "n.ABEL"]   <- tmp[["Sample size"]]   res[j, "pwr.ABEL"] <- tmp[["Achieved power"]] } print(signif(res, 5), row.names=FALSE)  CV% n.FARTSSIE pwr.FARTSSIE n.ABE pwr.ABE n.ABEL pwr.ABEL   30         40      0.85247    40 0.80999     34  0.80281   40         28      0.78286    28 0.81790     30  0.80656   50         24      0.75363    24 0.83042     28  0.81428

For all CVs FARTSSIE’s sample sizes will give the desired power for ABE (column pwr.ABE) but not for ABEL (column pwr.FARTSSIE). For CV 30% it will be too high (since only 34 subjects are required) but for CV >30% too low (more subjects are required). Only sampleN.scABEL() will give sample sizes (n.ABEL) with at least the desired power (pwr.ABEL).

As expected, FARTSSIE screws completely up if one wants to assess the Type I Error. Set “Method C1” and the 4-period replicate. Try with CV 30%, T/R 125%, sample size 34. I got

version power   2.2   5%      1.8   4.99%   1.7   4.99%

Sorry, Dave!

library(PowerTOST) cat(paste0(100*power.scABEL(CV=0.3, design="2x2x4", theta0=1.25,                             n=34, nsims=1e6), "%\n")) 8.1626%

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Helmut Schütz

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