Description Usage Arguments Details Value Warning Note Author(s) References See Also Examples
View source: R/samplesize_RSABE_NTID.R
This function performs the sample size estimation for the BE decision for the FDA’s method for NTIDs based on simulations. The study design is the full replicate design 2x2x4 (TRTRRTRT) or the 3period replicate design with sequences TRTRTR.
1 2 3 
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 FDA procedure. 
theta2 
Conventional upper ABE limit to be applied in the FDA procedure. 
CV 
Intrasubject coefficient(s) of variation as ratio (not percent).

design 
Design of the study to be planned. 
nsims 
Number of simulations to be performed to obtain the empirical power. Defaults to 100,000 = 1e+5. 
nstart 
Set this to a start value for the sample size 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 values for different runs a

The linearized scaled ABE criterion is calculated according to the SAS code
given in the FDA Warfarine guidance. For deciding BE the study must pass that criterion,
the conventional ABE test and additional the test that the ratio of
sWT/sWR <= 2.5.
The simulations are done via the distributional properties of the statistical
quantities necessary for deciding BE based on these method.
Details can be found in a document Implementation_scaledABE_sims
located in
the /doc
subdirectory of the package.
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.
For some input constellations the sample size search may be very time
consuming and will eventually also fail since the start values chosen may
not really reasonable for them. This applies especially for theta0 values
near to the implied scaled (tightened/widened) ABE limits according to
exp(±1.053605*swR)
.
In case of a failed sample size search you may restart with setting the argument
nstart
.
In case of theta0 values outside the implied scaled (tightened/widened) ABE limits
no sample size estimation is possible and the function throws an error
(f.i. CV=0.04, theta0=0.95).
The design recommended by the FDA is the full replicate design "2x2x4"
.
The sample size estimation is done only for balanced studies since the
break down of the total subject number in case of unbalanced sequence groups
is not unique. Moreover the formulas used are only valid for balanced designs.
The FDA method is described for the ABE limits 0.8 ... 1.25 only. Setting theta1,
theta2 to other values may not be reasonable and is not tested.
The results for the design "2x2x3"
are to be considered as experimental since
at present not thorougly tested.
The minimum sample size is 6, even if the power is higher than the intended
targetpower.
D. Labes
Food and Drug Administration, Office of Generic Drugs (OGD). Draft Guidance on Warfarin Sodium. Recommended Dec 2012. download
Yu LX, Jiang W, Zhang X, Lionberger R, Makhlouf F, Schuirmann DJ, Muldowney L, Chen ML, Davit B, Conner D, Woodcock J. Novel bioequivalence approach for narrow therapeutic index drugs. Clin Pharmacol Ther. 2015;97(3):286–91. doi: 10.1002/cpt.28
Jiang W, Makhlouf F, Schuirmann DJ, Zhang X, Zheng N, Conner D, Yu LX, Lionberger R. A Bioequivalence Approach for Generic Narrow Therapeutic Index Drugs: Evaluation of the ReferenceScaled Approach and Variability Comparison Criterion. AAPS J. 2015;17(4):891–901. doi: 10.1208/s1224801597535
Endrényi L, Tóthfalusi L. Determination of Bioequivalence for Drugs with Narrow Therapeutic Index: Reduction of the Regulatory Burden. J Pharm Pharm Sci. 2013;16(5):676–82. open access
power.NTIDFDA
and power.HVNTID
, sampleN.HVNTID
for NTIDs with
high variability
1 2 3 4 5 6 7 8 9 10 11 12 13  sampleN.NTIDFDA(CV = 0.04,theta0 = 0.975)
# should give
# n=54 with an (empirical) power of 0.809590
#
# Test formulation with lower variability
sampleN.NTIDFDA(CV = c(0.04,0.06),theta0 = 0.975)
# should give
# n=20 with an (empirical) power of 0.0.814610
#
# alternative 3period design
sampleN.NTIDFDA(CV = 0.04,theta0 = 0.975, design="2x2x3")
# should give
# n=86 with power = 0.80364

+++++++++++ FDA method for NTIDs ++++++++++++
Sample size estimation

Study design: 2x2x4
logtransformed data (multiplicative model)
1e+05 studies for each step simulated.
alpha = 0.05, target power = 0.8
CVw(T) = 0.04, CVw(R) = 0.04
True ratio = 0.975
ABE limits = 0.8 ... 1.25
Implied scABEL = 0.9587 ... 1.0430
Regulatory settings: FDA
 Regulatory const. = 1.053605
 'CVcap' = 0.2142
Sample size search
n power
52 0.795040
54 0.809590
+++++++++++ FDA method for NTIDs ++++++++++++
Sample size estimation

Study design: 2x2x4
logtransformed data (multiplicative model)
1e+05 studies for each step simulated.
alpha = 0.05, target power = 0.8
CVw(T) = 0.04, CVw(R) = 0.06
True ratio = 0.975
ABE limits = 0.8 ... 1.25
Implied scABEL = 0.9388 ... 1.0652
Regulatory settings: FDA
 Regulatory const. = 1.053605
 'CVcap' = 0.2142
Sample size search
n power
18 0.775080
20 0.814610
+++++++++++ FDA method for NTIDs ++++++++++++
Sample size estimation

Study design: 2x2x3
logtransformed data (multiplicative model)
1e+05 studies for each step simulated.
alpha = 0.05, target power = 0.8
CVw(T) = 0.04, CVw(R) = 0.04
True ratio = 0.975
ABE limits = 0.8 ... 1.25
Implied scABEL = 0.9587 ... 1.0430
Regulatory settings: FDA
 Regulatory const. = 1.053605
 'CVcap' = 0.2142
Sample size search
n power
84 0.793660
86 0.803640
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