PowerTOST (version 1.3-5)

scABEL.ad: Iteratively adjusted alpha for ABEL

Description

This function iteratively adjusts alpha for the BE decision via Average Bioequivalence with Expanding Limits (ABEL) based on simulations in order to maintain the consumer risk at the nominal level.

Usage

scABEL.ad(alpha = 0.05, theta0, theta1, theta2, CV = 0.3,
          design = c("2x3x3", "2x2x4", "2x2x3"),
          regulator = c("EMA", "ANVISA"), n, alpha.pre = 0.05,
          imax = 100, tol, print = TRUE, details = FALSE,
          setseed = TRUE, nsims = 1e6)

Arguments

alpha

Type I error (TIE) probability (nominal level of the test). Per convention commonly set to 0.05. A lower value might be specified (e.g., in order to adjust for multiplicity in dose proportionality studies).

theta0

True or assumed bioavailability ratio. Defaults to 0.90 if not given explicitly.

theta1

Conventional lower ABE limit to be applied in the mixed procedure if CVwR = CVswitch. Also lower limit for the point estimate constraint. Defaults to 0.80 if not given explicitly.

theta2

Conventional upper ABE limit to be applied in the mixed procedure if CVwR = CVswitch. Also upper limit for the point estimate constraint. Defaults to 1.25 if not given explicitly.

CV

Coefficient(s) of variation as ratio (not percent). Defaults to 0.30 (i.e., the location of maximum inflation of the TIE for the EMA's ABEL. If length(CV) = 1 the same CV of Test and

design

Design of the study to be planned. "2x3x3" is the partial replicate design (RRT|RTR|TRR). "2x2x3" is the 2-sequence 3-period full replicate design (RTR|TRT). "2x2x4" is the 2-sequence 4-period full replicate design (

regulator

Regulatory body settings for the widening of the BE acceptance limits. Defaults to regulator = "EMA". This argument may be given also in lower case.

n

Total sample size of the study or a vector of sample size / sequences. If n leads to an unbalanced design (i.e., is not a multiple of two in the full replicate designs or not a multiple of three in the partial replicate), the code tries to

nsims

Number of simulations to be performed to estimate the (empirical) TIE error and in each iteration of adjusting alpha. The default value 1,000,000 = 1e+6 should not be lowered.

imax

Maximum number of steps in sample size search. Defaults to 100.

tol

Desired accuracy (convergence tolerance). Defaults to 1e-6 for regulator = "EMA" and to 1e-7 for regulator = "ANVISA".

print

If TRUE (default), the function prints its results.

details

If TRUE, the relative change of the consumer risk is shown. Additionally information about the impact on power (for specified theta0 and target power 0.80), runtime, and number of simulations (iterations) are given. Defaults t

alpha.pre

Pre-specified alpha (optional). Must be <=alpha. ABEL will be performed at level alpha.pre and the TIE assessed at level alpha. Less powerful than adjusting alpha but an alterna

setseed

Simulations are dependent on the starting point of the (pseudo) random number generator. To avoid differences in power for different runs a set.seed(123456) is issued if setseed=TRUE (default).

Value

• Returns a list with the input, adjusted alpha, and type I error (for nominal and adjusted alpha). If no adjustment is necessary, NA will be returned for adj. alpha and the TIE for alpha0 (or alpha1, if applicable) in TIE.unadj.

encoding

utf-8

Warning

See the Warning section of the function power.scABEL concerning the power value agreement to those obtained from simulations via subject data.

Details

The simulations are done via the distributional properties of the statistical quantities necessary for assessing BE based on ABEL. Simulations for the TIE are performed at the upper (expanded) limit U of the acceptance range. Examples of U at the EMA's CVswitch and CVcap: scABEL(CV=0.3, regulator="EMA")[["upper"]] [1] 1.25 scABEL(CV=0.5, regulator="EMA")[["upper"]] [1] 1.43191 Due to the symmetry around 1 results are valid for the lower (expanded) limit L as well. If an inflation of the TIE is expected (i.e., > alpha), alpha is iteratively adjusted until the consumer risk is maintained (<= alpha).

References

Wonnemann, M., Frömke{Froemke}, C., Koch, A. Inflation of the Type I Error: Investigations on Regulatory Recommendations for Bioequivalence of Highly Variable Drugs Pharm Res. 2015;32(1):135-43 Labes, D., Schütz{Schuetz}, H. Inflation of Type I Error in the Evaluation of Scaled Average Bioequivalence, and a Method for its Control in preparation 2016

See Also

sampleN.scABEL.ad, power.scABEL, scABEL

Examples

Run this code

# partial replicate design, target power=80\%,
# true assumed ratio = 0.90, 1E+6 simulated studies
# EMA regulatory settings (ABE limits, PE constraint 0.8 - 1.25)
# Not run: due to timing policy of CRAN for examples
scABEL.ad(CV = 0.3)
# should result in adjusted alpha 0.03389 (TIE 0.5000, TIE for nominal alpha 0.07189).
#
# EMA, full replicate design, CV 0.35, sample size 33 (unbalanced)
# Not run: due to timing policy of CRAN for examples
scABEL.ad(CV = 0.35, design = "2x2x4", n = c(16, 17))
# should result in adjusted alpha 0.03632 (TIE 0.5000, TIE for nominal alpha 0.06544).

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