## TIE for NTIDs [Power / Sample Size]

Hi Astea,

❝ My thoughts are as follows: according to some product specific EMA guideline (sirolimus for example) we should shorten the limit only for AUC but not for Cmax. May it leed to TIE inflation or not?

❝ Then by using Power.2TOST for CV=0.3 I get TIE very slightly upper than 0.05

power.2TOST(CV=c(0.3,0.25), n=122, theta1=c(0.8, 0.9), theta2=c(1.25, 1.11), theta0=c(1, 1.11), rho=0)

❝ [1] 0.05000002

❝ In this case the diference from 0.05 is negligible, but may be one could find more rude example? Or am I using or interpretate power.2TOST uncorrectly?

You are using it correctly but this function underwent a minor revision. In the development version 1.4.6.9000 you would get
[1] 0.05003
or better with nsims=1e6 for the TIE:
[1] 0.050059
IMHO, AUC and Cmax generally are highly correlated.
power.2TOST(CV=c(0.3, 0.25), n=122, theta1=c(0.8, 0.9),             theta2=c(1.25, 1/0.9), theta0=c(1, 1/0.9),             rho=0.9, nsims=nsims) [1] 0.050092

❝ ❝ Try this (for the homoscedastic case swR=swT):

❝ And what to do if variances are different (non-negotiable word heteroscedasticity)?

Extending Detlew’s code for swT=2swR:
library(PowerTOST) design <- "2x2x4" theta  <- log(1/0.9)/0.1 nsims  <- 1e6 bt.sig <- binom.test(0.05*nsims, nsims, alternative="less")\$conf.int[2] sw.r   <- 2     # ratio of swT/swR min.n  <- FALSE # TRUE to force FDA's minimum sample of 24 UL <- function(CVwR, theta) {   upper <- exp(theta* CV2se(CVwR))   if (upper > 1.25) upper <- 1.25   return(upper) } CVwR <- seq(0.03, 0.25, 0.01) CVwT <- se2CV(CV2se(CVwR)*sw.r) CVs  <- data.frame(CVwT, CVwR, stringsAsFactors=FALSE) res  <- cbind(CVs, n=NA, forced=FALSE, GMR=NA, TIE=NA,               signif=" n. s.", stringsAsFactors=FALSE) for (j in seq_along(CVwR)){   res[j, "GMR"] <- UL(CVs[j, "CVwR"], theta)   res[j, "n"]   <- sampleN.NTIDFDA(CV=as.numeric(CVs[j, ]), print=FALSE,                                    details=FALSE)[["Sample size"]]   if (min.n & as.numeric(res[j, "n"]) < 24) {     res[j, "n"]      <- 24     res[j, "forced"] <- TRUE   }   res[j, "TIE"] <- power.NTIDFDA(CV=as.numeric(CVs[j, ]),                                  theta0=as.numeric(res[j, "GMR"]),                                  n=as.numeric(res[j, "n"]),                                  design=design, nsims=nsims)   res[j, "CVwT"] <- sprintf("%.4f", as.numeric(res[j, "CVwT"]))   res[j, "CVwR"] <- sprintf("%.4f", as.numeric(res[j, "CVwR"]))   if (res[j, "TIE"] > bt.sig) res[j, "signif"] <- "p<0.05" } if (!min.n) res <- res[ , -which(names(res) == "forced")] cat("swT/swR:", sw.r, "\n"); print(res, row.names=FALSE) swT/swR: 2    CVwT   CVwR   n      GMR      TIE signif  0.0600 0.0300 430 1.032106 0.050580 p<0.05  0.0801 0.0400 156 1.043027 0.048675  n. s.  0.1002 0.0500 134 1.054058 0.048292  n. s.  0.1203 0.0600 130 1.065197 0.047557  n. s.  0.1405 0.0700 128 1.076443 0.047594  n. s.  0.1608 0.0800 128 1.087796 0.047594  n. s.  0.1811 0.0900 128 1.099256 0.047594  n. s.  0.2015 0.1000 128 1.110820 0.047594  n. s.  0.2220 0.1100 128 1.122489 0.047594  n. s.  0.2426 0.1200 128 1.134261 0.047594  n. s.  0.2633 0.1300 128 1.146135 0.047594  n. s.  0.2841 0.1400 128 1.158110 0.047594  n. s.  0.3051 0.1500 128 1.170186 0.047594  n. s.  0.3262 0.1600 128 1.182360 0.047594  n. s.  0.3474 0.1700 128 1.194633 0.047594  n. s.  0.3688 0.1800 128 1.207001 0.047572  n. s.  0.3904 0.1900 128 1.219466 0.047074  n. s.  0.4121 0.2000 128 1.232024 0.043871  n. s.  0.4341 0.2100 128 1.244675 0.035001  n. s.  0.4562 0.2200 128 1.250000 0.034496  n. s.  0.4785 0.2300 128 1.250000 0.038751  n. s.  0.5011 0.2400 128 1.250000 0.039936  n. s.  0.5239 0.2500 128 1.250000 0.040172  n. s.

For swT=swR:
swT/swR: 1    CVwT   CVwR   n      GMR      TIE signif  0.0300 0.0300 214 1.032106 0.051258 p<0.05  0.0400 0.0400  54 1.043027 0.051405 p<0.05  0.0500 0.0500  32 1.054058 0.051804 p<0.05  0.0600 0.0600  24 1.065197 0.051418 p<0.05  0.0700 0.0700  22 1.076443 0.051395 p<0.05  0.0800 0.0800  20 1.087796 0.051232 p<0.05  0.0900 0.0900  18 1.099256 0.051158 p<0.05  0.1000 0.1000  18 1.110820 0.051158 p<0.05  0.1100 0.1100  16 1.122489 0.050734 p<0.05  0.1200 0.1200  16 1.134261 0.050734 p<0.05  0.1300 0.1300  16 1.146135 0.050732 p<0.05  0.1400 0.1400  16 1.158110 0.050705 p<0.05  0.1500 0.1500  16 1.170186 0.050552 p<0.05  0.1600 0.1600  16 1.182360 0.049877  n. s.  0.1700 0.1700  16 1.194633 0.048183  n. s.  0.1800 0.1800  16 1.207001 0.044852  n. s.  0.1900 0.1900  16 1.219466 0.040159  n. s.  0.2000 0.2000  16 1.232024 0.034550  n. s.  0.2100 0.2100  16 1.244675 0.028581  n. s.  0.2200 0.2200  16 1.250000 0.028871  n. s.  0.2300 0.2300  16 1.250000 0.033203  n. s.  0.2400 0.2400  16 1.250000 0.036778  n. s.  0.2500 0.2500  16 1.250000 0.039643  n. s.

And for swT=½swR:
swT/swR: 0.5    CVwT   CVwR   n      GMR      TIE signif  0.0150 0.0300 160 1.032106 0.051551 p<0.05  0.0200 0.0400  40 1.043027 0.052274 p<0.05  0.0250 0.0500  24 1.054058 0.052155 p<0.05  0.0300 0.0600  18 1.065197 0.052223 p<0.05  0.0350 0.0700  16 1.076443 0.051795 p<0.05  0.0400 0.0800  14 1.087796 0.051311 p<0.05  0.0449 0.0900  14 1.099256 0.051311 p<0.05  0.0499 0.1000  12 1.110820 0.050936 p<0.05  0.0549 0.1100  12 1.122489 0.050936 p<0.05  0.0598 0.1200  12 1.134261 0.050935 p<0.05  0.0648 0.1300  12 1.146135 0.050930 p<0.05  0.0697 0.1400  12 1.158110 0.050855 p<0.05  0.0747 0.1500  12 1.170186 0.050450 p<0.05  0.0796 0.1600  12 1.182360 0.049208  n. s.  0.0845 0.1700  12 1.194633 0.046557  n. s.  0.0895 0.1800  10 1.207001 0.040180  n. s.  0.0944 0.1900  10 1.219466 0.035008  n. s.  0.0993 0.2000  10 1.232024 0.029501  n. s.  0.1042 0.2100  10 1.244675 0.024305  n. s.  0.1090 0.2200  10 1.250000 0.024381  n. s.  0.1139 0.2300  12 1.250000 0.029092  n. s.  0.1187 0.2400  12 1.250000 0.032756  n. s.  0.1236 0.2500  12 1.250000 0.035953  n. s.

Apart from the CVs there is a dependency of the TIE on the sample size (common to the FDA’s scaling methods). If we force the minimum sample size to 24 dosed subjects (required by the FDA for RSABE) we get with min.n <- TRUE:
swT/swR: 1    CVwT   CVwR   n forced      GMR      TIE signif  0.0300 0.0300 214  FALSE 1.032106 0.051258 p<0.05  0.0400 0.0400  54  FALSE 1.043027 0.051405 p<0.05  0.0500 0.0500  32  FALSE 1.054058 0.051804 p<0.05  0.0600 0.0600  24  FALSE 1.065197 0.051418 p<0.05  0.0700 0.0700  24   TRUE 1.076443 0.051418 p<0.05  0.0800 0.0800  24   TRUE 1.087796 0.051418 p<0.05  0.0900 0.0900  24   TRUE 1.099256 0.051418 p<0.05  0.1000 0.1000  24   TRUE 1.110820 0.051418 p<0.05  0.1100 0.1100  24   TRUE 1.122489 0.051418 p<0.05  0.1200 0.1200  24   TRUE 1.134261 0.051418 p<0.05  0.1300 0.1300  24   TRUE 1.146135 0.051418 p<0.05  0.1400 0.1400  24   TRUE 1.158110 0.051415 p<0.05  0.1500 0.1500  24   TRUE 1.170186 0.051390 p<0.05  0.1600 0.1600  24   TRUE 1.182360 0.051193 p<0.05  0.1700 0.1700  24   TRUE 1.194633 0.050291  n. s.  0.1800 0.1800  24   TRUE 1.207001 0.047754  n. s.  0.1900 0.1900  24   TRUE 1.219466 0.043035  n. s.  0.2000 0.2000  24   TRUE 1.232024 0.036599  n. s.  0.2100 0.2100  24   TRUE 1.244675 0.029193  n. s.  0.2200 0.2200  24   TRUE 1.250000 0.029453  n. s.  0.2300 0.2300  24   TRUE 1.250000 0.034602  n. s.  0.2400 0.2400  24   TRUE 1.250000 0.038978  n. s.  0.2500 0.2500  24   TRUE 1.250000 0.042264  n. s. swT/swR: 0.5    CVwT   CVwR   n forced      GMR      TIE signif  0.0150 0.0300 160  FALSE 1.032106 0.051551 p<0.05  0.0200 0.0400  40  FALSE 1.043027 0.052274 p<0.05  0.0250 0.0500  24  FALSE 1.054058 0.052155 p<0.05  0.0300 0.0600  24   TRUE 1.065197 0.052155 p<0.05  0.0350 0.0700  24   TRUE 1.076443 0.052155 p<0.05  0.0400 0.0800  24   TRUE 1.087796 0.052155 p<0.05  0.0449 0.0900  24   TRUE 1.099256 0.052155 p<0.05  0.0499 0.1000  24   TRUE 1.110820 0.052155 p<0.05  0.0549 0.1100  24   TRUE 1.122489 0.052155 p<0.05  0.0598 0.1200  24   TRUE 1.134261 0.052155 p<0.05  0.0648 0.1300  24   TRUE 1.146135 0.052155 p<0.05  0.0697 0.1400  24   TRUE 1.158110 0.052155 p<0.05  0.0747 0.1500  24   TRUE 1.170186 0.052144 p<0.05  0.0796 0.1600  24   TRUE 1.182360 0.052008 p<0.05  0.0845 0.1700  24   TRUE 1.194633 0.051177 p<0.05  0.0895 0.1800  24   TRUE 1.207001 0.048438  n. s.  0.0944 0.1900  24   TRUE 1.219466 0.042814  n. s.  0.0993 0.2000  24   TRUE 1.232024 0.034901  n. s.  0.1042 0.2100  24   TRUE 1.244675 0.025993  n. s.  0.1090 0.2200  24   TRUE 1.250000 0.026019  n. s.  0.1139 0.2300  24   TRUE 1.250000 0.031621  n. s.  0.1187 0.2400  24   TRUE 1.250000 0.036474  n. s.  0.1236 0.2500  24   TRUE 1.250000 0.040374  n. s.
Hence, the TIE gets larger for studies forced to n 24 as compared to the ones designed for the target power.

Edit: Corrected code there.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

23,153 posts in 4,862 threads, 1,647 registered users;
108 visitors (2 registered, 106 guests [including 14 identified bots]).
Forum time: 11:33 CEST (Europe/Vienna)

If I find 10,000 ways something won’t work, I haven’t failed.
I am not discouraged, because every wrong attempt discarded
is another step forward.    Thomas Alva Edison

The Bioequivalence and Bioavailability Forum is hosted by
Ing. Helmut Schütz