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

In PowerTOST: Power and Sample Size for (Bio)Equivalence Studies

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, design = c("2x3x3", "2x2x4", "2x2x3"), regulator,
                  nstart = NA, nsims = 1e+06, imax = 100, tol,
                  print = TRUE, details = FALSE, alpha.pre = 0.05,
                  setseed = TRUE, sdsims = FALSE, progress)

Arguments

alpha	Type I error (TIE) probability (nominal level of the test). Per convention commonly set to 0.05.
targetpower	Power to achieve at least. Must be >0 and <1. Typical values are 0.80 to 0.90 (i.e., 80% to 90%). Defaults to 0.80 if not given explicitly.
theta0	‘True’ or assumed T/R ratio. Defaults to 0.90 according to the two Lászlós 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	Intra-subject coefficient(s) of variation as ratio (not percent). If given as a scalar (length(CV) == 1) the same CV of Test and Reference is assumed (homoscedasticity: CVwT = CVwR). If given as a vector (length(CV) == 2) – assuming heteroscedasticity – the CV of Test must be given in the first element and the one of Reference in the second.
design	Design of the study to be planned. "2x3x3" is the partial replicate design. "2x2x4" is a full replicate design with 2 sequences and 4 periods. "2x2x3" is a full replicate design with 2 sequences and 3 periods. Defaults to "2x3x3". Details are given the section about Designs.
regulator	Regulatory settings for the widening of the BE acceptance limits. Choose from "EMA" (default), "HC", or "GCC". 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 the sample size search if a previous run failed. According to regulatory requirements must be >=12 for the EMA and >=24 for ANVISA.
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.
imax	Maximum number of steps in sample size search. Defaults to 100.
tol	Desired accuracy (convergence tolerance). Defaults to 1E-6.
print	If TRUE (default), the function sends its results to the console.
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 alternative in the critical region of maximum inflation of the TIE. In certain scenarios Bonferroni’s 0.025 is not sufficient to preserve the Type I Error. Not recommended if CVwR ≥ 0.45 due to poor power characteristics.
setseed	Simulations are dependent on the starting point of the (pseudo) random number generator. To avoid differences in power for different runs set.seed(123456) is issued if setseed = TRUE (default).
sdsims	If FALSE (default) power is estimated by the respective ‘key’ statistics. Recommended for speed reasons. Set to TRUE if results of power.scABEL are expected to be inaccurate (partial replicate design with unbalanced sequences and/or heteroscedasticity where CVwT > CVwR) and subject data via power.scABEL.sdsims should be simulated instead. Very time consuming (easily 100times slower)! Subject data simulations are only supported for regulator = "EMA" and regulator = "GCC".
progress	Set to TRUE if a progress bar should be displayed. Defaults to FALSE. Ignored if sdsims = FALSE.

Details

The simulations are done via the distributional properties of the statistical quantities necessary for assessing BE based on ABEL. Simulations of the TIE are performed at the upper (expanded) limit U of the acceptance range. Due to the symmetry around 1 results are valid for the lower (expanded) limit L as well.
U at the EMA’s and Health Canada’s CVcap, the GCC’s for any CV_wR > 0.30:

scABEL(CV = 0.5, reg = "EMA")[["upper"]]
[1] 1.43191
scABEL(CV = 0.57382, reg = "HC")[["upper"]]
[1] 1.5
scABEL(CV = 0.31, reg = "GCC")[["upper"]]
[1] 1.333333

Simulated studies are evaluated by ANOVA (Method A) as recommended in the EMA’s Q&A-document and by intra-subject contrasts if regulator="HC". Health Canada requires a mixed effects model which cannot be implemented in R. However, intra-subjects contrasts are a sufficiently close approximation.

If an inflation of the TIE is expected (i.e., >alpha), alpha is iteratively adjusted until at least the target power is reached and the consumer risk is maintained (<=alpha). For details about the algorithm see the respective section of scABEL.ad.

The estimated sample size gives always the total number of subjects (not subject/sequence – like in some other software packages).

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 alpha.adj column and other results are identical to the ones obtained by sampleN.scABEL.

Designs

Although some designs are more ‘popular’ than others, sample size estimations are valid for all of the following designs:

"2x2x4"	TRTR | RTRT
	TRRT | RTTR
	TTRR | RRTT
"2x2x3"	TRT | RTR
	TRR | RTT
"2x3x3"	TRR | RTR | RRT

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.

For the GCC and CV_wR ≤ 0.30 simulations will be time consuming and may result in large sample sizes.

Note

We are doing the sample size estimation only for balanced designs since the break down of the total subject number in case of unbalanced sequences is not unique. Moreover the formulas used are only for balanced designs.

Author(s)

H. Schütz

References

Tóthfalusi L, Endrényi L. Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs. J Pharm Pharmaceut Sci. 2011;15(1):73–84. open access

Wonnemann M, Frömke 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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11095-014-1450-z")}

Muñoz J, Alcaide D, Ocaña J. Consumer’s risk in the EMA and FDA regulatory approaches for bioequivalence in highly variable drugs. Stat Med. 2015;35(12):1933–43. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sim.6834")}

Labes D, Schütz H. Inflation of Type I Error in the Evaluation of Scaled Average Bioequivalence, and a Method for its Control. Pharm Res. 2016;33(11):2805–14. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11095-016-2006-1")}

See Also

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

Examples

# --- Not run due to timing policy of CRAN for examples
# each may run some ten seconds or more
# using all the defaults:
# TRR|RTR|RRT, target power 80%, 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 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)
#
# TRTR|RTRT, target power 90%, pre-specified alpha 0.025

sampleN.scABEL.ad(CV = 0.3, targetpower = 0.9, design = "2x2x4", alpha.pre = 0.025)
# should result in n 60, power 0.9021; pre-specified alpha justified.

PowerTOST documentation built on May 29, 2024, 4:40 a.m.