These function performs the power calculation of the BE decision via
the reference scaled ABE based on subject data simulations.
Implemented are the methods ABEL, Hyslop and ‘exact’ as described in the
references.
The estimation method of the key statistics needed to perform the RSABE decision
is the usual ANOVA.
power.RSABE2L.sdsims(alpha = 0.05, theta1, theta2, theta0, CV, n,
design = c("2x3x3", "2x2x4", "2x2x3"), design_dta = NULL,
SABE_test = "exact", regulator, nsims = 1e+05,
details = FALSE, setseed = TRUE, progress)Returns the value of the (empirical) power if argument details=FALSE.
Returns a named vector if argument details=TRUE.
p(BE) is the power, p(BE-RSABE) is the power of using the reference
scaled ABE alone, and p(BE-pe) is the power of the criterion
‘point estimate within acceptance range’ alone. p(BE-ABE) is the power of
the conventional ABE test given for comparative purposes.
Type I error probability, significance level. Conventionally mostly set to 0.05.
Conventional lower ABE (Average Bioequivalence) limit to be applied
in the mixed procedure if CVsWR <= CVswitch. Also lower limit for the point
estimate constraint.
Defaults to 0.8 if not given explicitly.
Conventional upper ABE limit to be applied in the mixed procedure if
CVsWR <= CVswitch. Also upper limit for the point estimate constraint.
Defaults to 1.25 if not given explicitly.
‘True’ or assumed T/R ratio.
Defaults to 0.90 according to the two Lászlós if not given explicitly.
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), i.e., assuming
heteroscedasticity, the CV of the Test must be given in CV[1] and the one of the Reference in the CV[2].
Number of subjects under study.
May be given as vector. In that case it is assumed that n contains the number
of subjects in the sequence groups.
If n is given as single number (total sample size) and this number is not
divisible by the number of sequences of the design an unbalanced design is
assumed. A corresponding message is thrown (showing the numbers of subjects
in sequence groups).
Attention! In case of the "2x2x3" (TRT|RTR) design the order of sample sizes
per sequence is important if given as vector. n[1] is for sequence group
'TRT' and n[2] is for sequence group 'RTR'.
Design of the study.
"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 design="2x3x3". Details are given the section about Designs.
Alternatively to using the arguments design and n the design may
be defined via a data.frame with columns subject, sequence, period and
tmt. This feature is experimental in the sense that the data.frame is
not checked for complying with the assumed structure.
If you use the argument design_dta you don’t need to specify the arguments
design and n.
The default design_dta=NULL means that design and n are used
for the internal construction of the design data.frame.
This argument specifies the test method to be used for the reference scaled
ABE decision.
Default is the "exact" ‘ncTOST’ method of the two Laszlós. Other choices are "ABEL", "hyslop" and "fda". See Details.
Regulatory settings for the widening of the BE acceptance limits.
May be given as character "EMA" or as an object of
class 'regSet' (see reg_const).
Defaults to regulator="EMA" if missing.
This argument may be given also in lower case if given as character.
If given as object of class 'regSet' the component est_method can not be "ISC".
Number of simulations to be performed to obtain the empirical power.
Defaults to 100,000 = 1e+05.
If simulations are aimed for empirical alpha nsims=1e+06 is recommended.
If set to TRUE the computational time is shown as well as the components
for the BE decision.
p(BE-RSABE) is the probability of a positive outcome of the SABE test.
p(BE-PE) is the probability that the point estimate is within
theta1 ... theta2.
p(BE-ABE) is the simulated probability for the conventional ABE test.
Simulations are dependent on the starting point of the (pseudo) random number
generator. To avoid differences in power for different runs a set.seed()
is issued if setseed=TRUE, the default.
Should a progressbar be shown? Defaults to TRUE if missing and nsims >5e5.
D. Labes
Although some designs are more ‘popular’ than others, power calculations are valid for all of the following designs:
"2x2x4" | TRTR | RTRT |
| TRRT | RTTR | |
| TTRR | RRTT | |
"2x2x3" | TRT | RTR |
| TRR | RTT | |
"2x3x3" | TRR | RTR | RRT |
The methods rely on the analysis of log-transformed data, i.e., assumes a
log-normal distribution on the original scale.
The data.frame with columns subject, sequence, period and tmt
necessary for evalution of simulated subject data is constructed internally from
the arguments design and n or may be given user defined via the argument
design_dta. The last option is usefull if missing data have to be considered
or if designs have to be evaluated which are not in the list of argument
design.
The estimation method for obtaining the statistics necessary to perform the
reference scaled ABE decision is the usual ANOVA with effects treatment, period,
sequence and subject within sequence for the evaluation of all data and period,
sequence and subject within sequence for the evaluation of the Reference formulation
data only.
The SABE tests implemented are:
"exact" | ‘exact’ based method of the two Laszlós (see references, called there ‘ncTOST’) |
"ABEL" | Average bioequivalence with expanding limits |
"hyslop" | BE decision via the linearized RSABE criterion and its upper 95% CI |
"fda" | Hyslop with an additional bias correction term as implemented in the SAS code of the |
| FDA’s Guidance on Progesterone. |
Food and Drug Administration, Office of Generic Drugs (OGD). Draft Guidance on Progesterone. Recommended Apr 2010. Revised Feb 2011. download
Tóthfalusi L, Endrényi L. An Exact Procedure for the Evaluation of Reference-Scaled Average Bioequivalence. AAPS J. 2016;18(2):476--89. tools:::Rd_expr_doi("10.1208/s12248-016-9873-6").
Tóthfalusi L, Endrényi L. Algorithms for evaluating reference scaled average bioequivalence: power, bias, and consumer risk. Stat Med. 2017;36(27):4378--4390. tools:::Rd_expr_doi("10.1002/sim.7440")
power.RSABE, reg_const
# Not run due to timing policy of CRAN
# \donttest{
# pure EMA settings without mixed procedure, cap on widening and PE constraint
# as in the reference from 2017
reg <- reg_const("EMA")
reg$CVswitch <- 0
reg$CVcap <- Inf
reg$pe_constr <- FALSE
reg$name <- "EMA pure"
power.RSABE2L.sds(CV = 0.4, n = 12, theta0 = exp(0.05),
design = "2x2x4", regulator = reg, nsims = 50000)
# should give:
# [1] 0.46504 (compared to 47.1% in the 2017 reference)# }
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