sampleN.scABEL.ad: Sample size estimation for ABEL and iteratively adjusted alpha

Description

This function performs a sample size estimation for the BE decision via Average Bioequivalenc with Expanding Limits (ABEL) based on simulations. Simultaneously alpha is iteratively adjusted in order to maintain the consumer risk at the nominal level.

Usage

sampleN.scABEL.ad(alpha = 0.05, targetpower = 0.8, theta0, theta1,
                  theta2, CV = 0.3, design = c("2x3x3", "2x2x4", "2x2x3"),
                  regulator = c("EMA", "ANVISA"), nstart = NA, nsims = 1e6,
                  print = TRUE, details = FALSE, alpha.pre = 0.05,
                  setseed = TRUE)

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).

targetpower

Power to achieve at least. Must be {=>0,

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 Reference is assume

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 expanding the BE acceptance limits. Defaults to regulator = "EMA". This argument may be given also in lower case.

nstart

Best guess sample size. If not given (default), simulations start with the sample size estimated for alpha (or alpha.pre, if given), theta0, and targetpower. Can also be set to start t

nsims

Number of simulations to be performed to estimate the (empirical) TIE 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 (default), the steps during sample size search are shown. Additionally information about the impact on power by adjusting alpha and change of study costs due to the increased sample size is given.

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 data.frame with the input and results for adjusted alpha,
type I error, sample size, and achieved power.
The Sample size column contains the total sample size.
If no adjustment is necessary, NA will be returned in the
adj. alpha column and other results are identical to the ones
obtained by sampleN.scABEL.

`encoding`

utf-8

`Warning`

The sample size estimation for extreme theta0 (<0.83 or="">1.21) may be time
consuming and will eventually also fail since the start values chosen are
not really reasonable in that ranges.
If you really need sample sizes in that range be prepared to restart the sample
size estimation with nstart above the last one before failure.
Since the dependence of power from n is very flat in the mentioned region you may
also consider to adapt the number of simulations not to tap in the simulation
error trap.

See also 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 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 at least the target power is reached and 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`

Tóthfalusi{Tothfalusi}, L., Endrényi{Endrenyi}, L.
Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs
J Pharm Pharmaceut Sci. 2011;15(1):73-84
http://ejournals.library.ualberta.ca/index.php/JPPS/article/download/11612/9489{free download}

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`

scABEL.ad, sampleN.scABEL, power.scABEL, 
scABEL

`Examples`

Run this code# Not run: due to timing policy of CRAN for examples
# may run ten seconds or more
# using all the defaults:
# 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)
sampleN.scABEL.ad(CV = 0.3)
# should result in sample size n = 60, power = 0.8022
# Note: Without adjustment by sampleN.scABEL(): n = 54, power = 0.8159
# Easier to show the details:
sampleN.scABEL.ad(CV = 0.3, details = TRUE)
#
# same with ANVISA settings, CVswitch = 40\%
  sampleN.scABEL.ad(CV = 0.3, regulator = "anvisa")
# should result in n = 60, power = 0.8101; no adjustment necessary
#
# full replicate design, target power = 90\%, pre-specified alpha 0.025
sampleN.scABEL.ad(CV = 0.3, targetpower = 0.8, design = "2x2x4", alpha.pre = 0.025)
# should result in n = 44, power = 0.8040; pre-specified alpha justified
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