The power is obtained via subject data simulations.
Three models are implemented:
gmodel==1 is full FDA model for testing group-by-treatment interaction followed by gmodel==2 or gmodel==3 with data of the biggest group depending on the test of the treatment by group interaction
gmodel==2 is full FDA model but without group-by-treatment interaction
gmodel==3 is model with pooled groups, i.e. without any group term
power.TOST.sds(alpha = 0.05, theta1, theta2, theta0, CV, n,
design = c("2x2", "2x2x2", "2x3x3", "2x2x4", "2x2x3"),
design_dta = NULL, grps = 2, ngrp = NULL, gmodel = 2, p.level=0.1,
nsims = 1e+05, details = FALSE, setseed = TRUE, progress)Returns the value of the (empirical) power
Type I error probability, significance level. Conventionally mostly set to 0.05.
Lower BE limit. Defaults to 0.8 if not given explicitely.
Upper BE limit. Defaults to 1.25 if not given explicitely.
‘True’ or assumed T/R ratio.
Defaults to 0.95 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 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 to be planned.
"2x2" or "2x2x2" is the conventional cross-over design.
"2x3x3" is the partial replicate design (TRR|RTR|RRT).
"2x2x4" is the full replicate design with 2 sequences and 4 periods.
"2x2x3" is the 3-period design with sequences TRT|RTR.
Defaults to design="2x2".
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.
Number of (logistical) groups. Defaults to 2.
Vector of number of subjects in groups.
Number describing the model incorporating group effects
gmodel=1 is full FDA model for testing group-by-treatment interaction
followed by gmodel=2 or gmodel=3 with data of the biggest group
depending on the test of the treatment by group interaction
gmodel=2 is full FDA model but without group-by-treatment interaction
gmodel=3 is model with pooled groups, i.e. without any group term
Defaults to gmodel=2.
Significance level of the test of a group-by-treatment interaction.
Defaults to p.level=0.1.
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.
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, the default.
Should a progressbar be shown? Defaults to TRUE if missing and nsims >5E5.
D. Labes
The power is calculated via subject data sims.
The evaluation of BE is done via 1-2*alpha confidence interval using classical ANOVA
for the models with group effects.
The data.frame with columns subject, sequence, period and tmt
necessary for evaluation 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.
This feature is experimental in the sense that the data.frame is not checked
for complying with the assumed structure.
The p.value of the test of the group-by-treatment interaction in case of gmodel=1
defaults to p.level = 0.1, the value originally used by the FDA. Later on a value of
p.level = 0.05 was used.
If the group-by-treatment interaction is significant the subsequent BE decision is done with the data of the largest group. If there are more than one with the same size, one gets a warning that this feature -- showing BE in all that groups -- is not implemented yet. Only the first of the largest groups is tested for BE.
Schütz H.
Multi-Group Studies in Bioequivalence. To pool or not to pool?
Presentation at BioBriges 2018, Prague. https://bebac.at/lectures/Prague2018.pdf
# power for gmodel=2, 2x2 crossover, grps=3 with even number of subjects
power.TOST.sds(CV=0.2, n=18, grps=3)
# gives [1] 0.78404
# without considering groups
power.TOST.sds(CV=0.2, n=18, gmodel=3)
# gives [1] 0.7887
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