Bioequivalence and Bioavailability Forum • TIE for NTIDs

TIE for NTIDs [Power / Sample Size]

posted by d_labes – Berlin, Germany, 2018-02-04 13:40 (2266 d 13:17 ago) – Posting: # 18340
Views: 20,065

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 :cool:

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

Complete thread:

Sample size for 4-period 4-sequence crossover BE study Bryony Simmons 2018-02-01 12:16
- function sampleN.TOST of package PowerTOST Helmut 2018-02-01 13:01
  - Alpha adjustment in higher order crossover d_labes 2018-02-01 14:01
    - Deficiencies Helmut 2018-02-01 15:48
      - Deficiencies nobody 2018-02-01 17:10
      - Deficiencies d_labes 2018-02-01 18:57
        
        Deficiencies Relaxation 2018-02-02 11:12
        
        Deficiencies nobody 2018-02-02 12:49
        Deficiencies Helmut 2018-02-02 16:14
        
        Deficiencies Relaxation 2018-02-02 19:41
        
        alpha... where is omega? Astea 2018-02-02 21:45
        
        α and no ω Helmut 2018-02-02 23:39
        
        TIE for NTIDsd_labes 2018-02-04 12:40
        
        TIE for NTIDs Astea 2018-02-04 20:04
        
        TIE for NTIDs Helmut 2018-02-05 01:01
        
        TIE for NTIDs d_labes 2018-02-05 16:40
        
        TIE for NTIDs Helmut 2018-02-05 17:49
        
        TIE for NTIDs d_labes 2018-02-05 22:17
        
        TIE for NTIDs Helmut 2018-02-06 12:34
        
        TIE for NTIDs d_labes 2018-02-05 16:35
        
        bow TIE for NTIDs Astea 2018-02-05 17:52
        
        bow TIE for NTIDs Helmut 2018-02-05 18:10
        
        111.11 for NTIDs Astea 2018-02-05 19:27
        
        111.11 for NTIDs Helmut 2018-02-06 00:12
        
        bow TIE for NTIDs d_labes 2018-02-05 22:33