Bioequivalence and Bioavailability Forum

α adjustment? [RSABE / ABEL]

posted by Helmut  – Vienna, Austria, 2013-03-26 16:21 (4042 d 17:17 ago) – Posting: # 10286
Views: 20,540

Dear all!

❝ this behavior may be due to an adaptive choice of a statistical method in face of the data without any "adjustment" for this adaptation.

Yep. The acceptance range is data-driven (random variable dependent on CV_WR).

❝ PS.: no idea at the moment how to account for this.

Adjust α? Quick shot:

library(PowerTOST)
reg   <- "EMA"   # "EMA" for scABEL or "FDA" for RSABE
CV    <- 0.300   # intra-subject CV of reference
n     <- 24      # total sample size
                 # in case of imbalanced sequences use a vector:
                 # e.g., c(n1,n2,n3)
des   <- "2x3x3" # partial: "2x3x3" full: "2x2x4"
print <- FALSE   # intermediate results
if (reg == "EMA") { # scABEL
  ifelse (CV <= 0.5, GMR <- exp(0.7601283*CV2se(CV)),
    GMR <- exp(0.7601283*CV2se(0.5)))
  if (CV <= 0.3) GMR <- 1.25
    } else {        # RSABE
  ifelse (CV > 0.3, GMR <- exp(0.8925742*CV2se(CV)), GMR <- 1.25)
}
nsims <- 1e6
prec  <- 1e-8     # precision of bisection algo
x     <- 0.05     # target alpha
sig   <- binom.test(x*nsims, nsims,
           alternative='less')$conf.int[2] # significance limit of sim’s
nom   <- c(0.001, x)                # from conservative to target alpha
lower <- min(nom); upper <- max(nom)
delta <- upper - lower              # interval
ptm   <- proc.time()                # start timer
iter  <- 0
while (abs(delta) > prec) {         # until precision reached
  iter  <- iter + 1
  x.new <- (lower+upper)/2          # bisection
  if (reg == "EMA") {
    pBE <- power.scABEL(alpha=x.new, theta0=GMR, CV=CV, n=n,
                        design=des, nsims=nsims)
    } else {
    pBE <- power.RSABE(alpha=x.new, theta0=GMR, CV=CV, n=n,
                       design=des, nsims=nsims)
  }
  if (print == TRUE) cat(iter, x.new, pBE, "\n")
  if (abs(pBE - sig) <= prec) break # precision reached
  if (pBE > sig) upper <- x.new     # move limit downwards
  if (pBE < sig) lower <- x.new     # move limit upwards
  delta <- upper - lower            # new interval
}
if (print) cat("run-time:", round((proc.time()[3]-ptm[3]),1),
  "seconds  iterations:", iter, "\n")
cat("regulator:", reg, " CV:", CV, " n:", n, " design:", des,
  "\ntarget alpha:", x, " adjusted alpha:", x.new, " pBE:", pBE, "\n")

  CV   adj alpha pBE_scABEL  adj alpha pBE_RSABE
0.200  0.050000  0.050220    0.050000  0.050153
0.225  0.049730  0.050360    0.048467  0.050359
0.250  0.047370  0.050359    0.040790  0.050360
0.275  0.040833  0.050360    0.028606  0.050359
0.300  0.031124  0.050359    0.017999  0.050360
0.302  0.031612  0.050359    0.050000  0.048548
0.325  0.035545  0.050360    0.050000  0.047741
0.350  0.037636  0.050360    0.050000  0.046156
0.375  0.039190  0.050360    0.050000  0.043941
0.400  0.041417  0.050360    0.050000  0.041041
0.425  0.045221  0.050360    0.050000  0.037799
0.450  0.050000  0.049795    0.050000  0.034401
0.475  0.050000  0.043420    0.050000  0.031150
0.500  0.050000  0.036960    0.050000  0.028097
0.525  0.050000  0.040644    0.050000  0.025383
0.550  0.050000  0.043412    0.050000  0.022875
0.575  0.050000  0.045423    0.050000  0.020699
0.600  0.050000  0.046647    0.050000  0.018660
0.625  0.050000  0.047379    0.050000  0.016948
0.650  0.050000  0.047754    0.050000  0.015457
0.675  0.050000  0.047698    0.050000  0.014135
0.700  0.050000  0.047192    0.050000  0.012861
0.725  0.050000  0.046282    0.050000  0.011799
0.750  0.050000  0.045020    0.050000  0.010865
0.775  0.050000  0.043338    0.050000  0.010057
0.800  0.050000  0.041320    0.050000  0.009425





Take my code with a grain of salt. Cases where no adjustment is necessary agree with Detlew’s results.

---

Note: Any result <0.05035995 is not significantly >0.05 in 10⁶ simulations. However, if you want to get a more conservative estimate replace

sig   <- binom.test(x*nsims, nsims,
           alternative='less')$conf.int[2]

by

sig   <- 0.05

---

Edit: Much faster code in this post.

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


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Science Quotes

Complete thread:

• ‘alpha’ of scaled ABE? d_labes 2013-03-15 15:56 [RSABE / ABEL] 
  • ‘alpha’ of scaled ABE? Helmut 2013-03-15 17:27
    • ’alpha’ of scaled ABE: design d_labes 2013-03-16 20:10
      • N=24, 48 d_labes 2013-03-18 08:11
        • adaptive design without adjustment martin 2013-03-25 20:47
          • α adjustment?Helmut 2013-03-26 15:21
            • iteratively adjusted alpha martin 2013-03-26 16:19
              • throw away our sample size tables? Helmut 2013-03-26 18:02
                • if real martin 2013-03-26 19:44
                  • regulators don’t care? Helmut 2013-03-26 21:18
                • adjusting α Helmut 2013-08-11 16:19
              • target α in sim’s? Helmut 2013-03-27 15:38
                • target α in sim’s? martin 2013-03-27 16:36
                  • If it is real: results Helmut 2013-03-28 23:20
                • having alpha martin 2013-03-28 15:08
                  • fixed swr Helmut 2013-03-28 23:34
                    • fixed swr martin 2013-03-29 15:07
                      • Yes but no but yes but no but… Helmut 2013-03-29 16:10