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,
          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.

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.

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.

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 a significant inflation of the TIE is expected (i.e., exceeding
0.05036 for one million simulations), alpha is iteratively adjusted
until the consumer risk is maintained (n.s. > alpha0).
The significance limit is based on the one sided binomial test, e.g.,
binom.test(0.05*1e6, 1e6, alternative="less", conf.level=1-0.05)$conf.int[2]

`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., Fuglsang, A.
Perspectives on Scaled Average Bioequivalence Evaluation via Expanded Acceptance Limits (ABEL) and a Proposed Method to Control Type I Error
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 = 0.0339 (TIE 0.500, TIE for nominal alpha 0.0719)
#
# same with ANVISA settings, CVswitch=40\%
scABEL.ad(CV = 0.3, regulator = "anvisa")
# no adjustment necessary (TIE 0.0503, n.s. > 0.05)
#
# 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 = 0.0363 (TIE 0.500, TIE for nominal alpha 0.0654)
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