## TIE for NTIDs [Power / Sample Size]

Dear Astea, dear Helmut,

❝ ❝ I suspect TIE will be also inflated in studies of NTDs also (by using FDA approach or by using different confidence limits for two metrics).

❝ Might well be.

There is no reason to speculate. Fire up the all-in-one device suitable for every purpose PowerTOST
and use function power.NTIDFDA().

Try this (for the homoscedastic case swR=swT):
library(PowerTOST) # number of subjects n <- 12 design <- "2x2x4" # theta is the reguatory constant for widening/shrinking the acceptance limits # (see Warfarin guidance, but note: the theta there is theta^2) theta <- -(log(0.9)/0.1) # function to obtain the upper limit of the implied acceptance range UL <- function(CV, theta){   upper <- exp(theta* CV2se(CV))   if (upper>1.25) upper <- 1.25   upper } CVs <- seq(0.03, 0.4, by=0.01) # reserve memory GMR <- vector("numeric", length= length(CVs)) TIE <- vector("numeric", length= length(CVs)) ns  <- vector("numeric", length= length(CVs)) for (i in seq_along(CVs)){   GMR[i] <- UL(CVs[i], theta)   ns[i]  <- n   # instead of a constant n we may use n obtained via sampleN.NTIDFDA()   # then uncomment next line   # ns[i]  <- sampleN.NTIDFDA(CV=CVs[i], print=FALSE, details=FALSE)[["Sample size"]]   TIE[i] <- power.NTIDFDA(CV=CVs[i], theta0 = GMR[i], n=n, design=design, nsims=1E6) } print(data.frame(CV=CVs, GMR=GMR, n=ns, TIE=TIE), row.names=FALSE)

With n=12 we get:
   CV      GMR      TIE  0.03 1.032106 0.049529  0.04 1.043027 0.049529  0.05 1.054058 0.049529  0.06 1.065197 0.049529  0.07 1.076443 0.049529  0.08 1.087796 0.049529  0.09 1.099256 0.049529  0.10 1.110820 0.049529  0.11 1.122489 0.049529  0.12 1.134261 0.049529  0.13 1.146135 0.049513  0.14 1.158110 0.049401  0.15 1.170186 0.048949  0.16 1.182360 0.047774  0.17 1.194633 0.045520  0.18 1.207001 0.041949  0.19 1.219466 0.037606  0.20 1.232024 0.032688  0.21 1.244675 0.027556  0.22 1.250000 0.027744  0.23 1.250000 0.031157  0.24 1.250000 0.034106  0.25 1.250000 0.036487  0.26 1.250000 0.038232  0.27 1.250000 0.039669  0.28 1.250000 0.040685  0.29 1.250000 0.041398  0.30 1.250000 0.041859

But if we use n obtained to have a targetpower of 0.8, using theta0=0.975 we get:
  0.03 214 1.032106 0.051258  0.04 54 1.043027 0.051405  0.05 32 1.054058 0.051804  0.06 24 1.065197 0.051418  0.07 22 1.076443 0.051395  0.08 20 1.087796 0.051232  0.09 18 1.099256 0.051158  0.10 18 1.110820 0.051158  0.11 16 1.122489 0.050734  0.12 16 1.134261 0.050734  0.13 16 1.146135 0.050732  0.14 16 1.158110 0.050705  0.15 16 1.170186 0.050552  0.16 16 1.182360 0.049877  0.17 16 1.194633 0.048183  0.18 16 1.207001 0.044852  0.19 16 1.219466 0.040159  0.20 16 1.232024 0.034550  0.21 16 1.244675 0.028581  0.22 16 1.250000 0.028871  0.23 16 1.250000 0.033203  0.24 16 1.250000 0.036778  0.25 16 1.250000 0.039643  0.26 16 1.250000 0.041844  0.27 18 1.250000 0.044551  0.28 18 1.250000 0.045817  0.29 18 1.250000 0.046739  0.30 20 1.250000 0.048178
Indeed a small alpha-inflation at low CVs'.
If we were Potvin-adepts this is a negligible alpha inflation, namely below 0.052.

Regards,

Detlew