Description Usage Arguments Details Value Designs Warning Note Author(s) See Also Examples
View source: R/sampleN.RSABE2L.sdsims.R
These functions performs the sample size estimation of the BE decision via
the reference scaled ABE based on subject data simulations.
Implemented are the methods ABEL, Hyslop and ‘exact’ (see the References in
power.RSABE2L.sdsims
).
The estimation method of the key statistics needed to perform the RSABE decision
is the usual ANOVA.
This function has an alias sampleN.RSABE2L.sds().
1 2 3 4 5 6 
alpha 
Type I error probability. Per convention mostly set to 0.05. 
targetpower 
Power to achieve at least. Must be >0 and <1. 
theta0 
‘True’ or assumed T/R ratio. 
theta1 
Conventional lower ABE limit to be applied in the mixed procedure if

theta2 
Conventional upper ABE limit to be applied in the mixed procedure if

CV 
Intrasubject coefficient(s) of variation as ratio (not percent).

design 
Design of the study to be planned. 
SABE_test 
This argument specifies the test method to be used for the reference scaled
ABE decision. 
regulator 
Regulatory settings for the widening of the BE acceptance limits. 
nsims 
Number of simulations to be performed to obtain the (empirical) power. The default value 100,000 = 1e+5 is usually sufficient. Consider to rise this value if theta0<=0.85 or >=1.25. But see the warning section. 
nstart 
Set this to a start for the sample size search if a previous run failed. 
imax 
Maximum number of steps in sample size search. Defaults to 100. 
print 
If 
details 
If set to 
setseed 
Simulations are dependent on the starting point of the (pseudo) random number
generator. To avoid differences in power for different runs a 
progress 
Should a progressbar be shown? Defaults to 
The methods rely on the analysis of logtransformed data, i.e., assume a
lognormal distribution on the original scale.
The widened BE acceptance limits will be calculated by the formula
[L, U] = exp(± r_const * sWR)
with r_const
the regulatory constant and sWR
the standard deviation of the within
subjects variability of the Reference. r_const = 0.76
(~log(1.25)/0.29356) is used
in case of regulator="EMA"
.
If the CVwR of the Reference is < CVswitch=0.3 the conventional ABE limits
apply (mixed procedure).
In case of regulator="EMA"
a cap is placed on the widened limits if
CVwr>0.5, i.e., the widened limits are held at value calculated for CVwR=0.5.
The simulations are done by simulating subject data (all effects fixed except the
residuals) and evaluating these data via ANOVA of all data to get the point estimate
of T vs. R along with its 90% CI and an ANOVA of the data under R(eference) only
to get an estimate of s2wR.
The estimated sample size gives always the total number of subjects (not subject/sequence – like in some other software packages).
Returns a data.frame with the input settings and sample size results.
The Sample size
column contains the total sample size.
The nlast
column contains the last n
value. May be useful for restarting.
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 
The sample size estimation for very extreme theta0 (<0.83 or >1.21) may be very
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 via the argument nstart.
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.
We are doing the sample size estimation only for balanced designs since the
break down of the total subject number in case of unbalanced sequence groups
is not unique. Moreover the formulas used are only for balanced designs.
The minimum sample size is 6, even if the power is higher than the intended
targetpower.
Subject simulations are relatively slow. Thus be patient and go for a cup of coffee if you use this function with high sample sizes!
H. Schütz
power.RSABE2L.sdsims
, sampleN.scABEL
, reg_const
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21  # using the defaults:
# partial replicate design, targetpower=80%,
# true assumed ratio = 0.90, 1E+5 simulated studies
# ABE limits, PE constraint 0.8  1.25
# EMA regulatory settings
# compare results
CV < 0.4
method < c("exact", "abel", "hyslop", "fda")
res < data.frame(SABE_test = c("ncTOST", "ABEL",
"Hyslop", "FDA"),
n = NA, power = NA)
for (i in 1:nrow(res)) {
res[i, 2:3] < sampleN.RSABE2L.sdsims(CV = CV,
SABE_test = method[i],
details = FALSE,
print = FALSE)[8:9]
}
print(res, digits = 4, row.names = FALSE)
# should result in a sample size n=48 with all methods,
# power=0.8197 (ncTOST), 0.8411 (ABEL), 0.8089 (Hyslop), 0.8113 (FDA)

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