## Problems with low variability [General Sta­tis­tics]

Hi Siva Krishna,

» I would like to say Thank you sir for your valuable information. This may be helpful to my question.

Welcome. Would you mind answering my previous questions:
» » I guess 100% was not contained in the 90% CI, right?
» » For which power did you plan the study?

Sometimes statistically significant differences are common, namely if the CV is low (say, <10%) and you plan for 80% power. Then you may end up with a sample size far below the regulatory minimum of twelve. Add more subjects to compensate for potential dropouts and…
In my protocols I state that extremely high power is expected and the CI might well contain not 100%.

script:

library(PowerTOST) balance <- function(x, seqs) { # gives complete sequences   x <- ceiling(x) + ceiling(x) %% seqs   return(x) } CV       <- 0.10    # assumed (here 10%) theta0   <- 0.925   # assumed T/R-ratio target   <- 0.80    # target (desired) power (here at least 80%) do.rate  <- 0.10    # anticipated dropout rate (here 10%) design   <- "2x2x2" # can be any one given by known.designs() seqs     <- as.integer(substr(design, 3, 3)) # sequences n        <- sampleN.TOST(CV = CV, theta0 = theta0, targetpower = target,                          design = design, details = FALSE,                          print = FALSE)[["Sample size"]] if (n < 12) n <- 12 # force to minimum acc. to GLs dosed    <- balance(n / (1 - do.rate), seqs) # adjust for dropout-rate & balance eligible <- dosed:n; dropouts <- rev(eligible - n) res      <- data.frame(dosed = dosed, dropouts = dropouts, eligible = eligible,                        power = NA, CL.lo = NA, CL.hi = NA,                        p.left = NA, p.right = NA) for (j in seq_along(eligible)) {   res\$power[j] <- suppressMessages(                     signif(power.TOST(CV = CV, theta0 = theta0,                                       design = design, n = eligible[j]), 4))   res[j, 5:6]  <- round(100*CI.BE(pe = theta0, CV = CV,                                   design = design, n = eligible[j]), 2)   res[j, 7:8]  <- suppressMessages(                     signif(pvalues.TOST(pe = theta0, CV = CV,                                         design = design, n = eligible[j]), 4)) } print(res, row.names = FALSE)

Gives (if the assumptions about the CV and T/R-ratio are realized in the study):

 dosed dropouts eligible  power CL.lo CL.hi   p.left   p.right     14        0       14 0.9760 86.49 98.93 0.001154 1.913e-06     14        1       13 0.9652 86.22 99.23 0.001752 4.846e-06     14        2       12 0.9521 85.92 99.59 0.002569 1.166e-05

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