This function performs the Sample size estimation for the BE decision via linearized scaled ABE criterion based on simulations.

```
sampleN.RSABE(alpha = 0.05, targetpower = 0.8, theta0, theta1, theta2, CV,
design = c("2x3x3", "2x2x4", "2x2x3"), regulator = c("FDA", "EMA"),
nsims = 1e+05, nstart, imax=100, print = TRUE,
details = TRUE, setseed=TRUE)
```

alpha

Type I error probability. Per convention mostly set to 0.05.

targetpower

Power to achieve at least. Must be >0 and <1. Typical values are 0.8 or 0.9.

theta0

‘True’ or assumed T/R ratio. Defaults to 0.90 according to the two Laszl<U+00F3>s if not given explicitly.

theta1

Conventional lower ABE 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.

theta2

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.

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`

),*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]`

.

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 `design="2x3x3"`

. Details are given the section about Designs.

regulator

Regulatory body settings for the scaled ABE criterion.
Defaults to `design="FDA"`

.
Also the scaled ABE criterion is usually calculated with the FDA constant
`r_const=log(1.25)/0.25`

you can override this behavior to use the EMA setting
`r_const=0.76`

to avoid the discontinuity at CV=30% and be more stringent.

nsims

Number of simulations to be performed to obtain the (empirical) power.

nstart

Set this to a start for the sample size search if a previous run failed. After reworking the start n in version 1.1-05 rarely needed.

imax

Maximum number of steps in sample size search. Defaults to 100.

print

If `TRUE`

(default) the function prints its results. If `FALSE`

only the result data.frame will be returned.

details

If set to `TRUE`

, the default, the steps during sample size search are shown.

setseed

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.

Returns a data.frame with the input 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 |

The sample size estimation for theta0 >1.2 and <0.85 may be very time consuming and will eventually also fail since the start values chosen are not really reasonable in that ranges. This is especially true in the range about CV = 0.3 and regulatory constant according to FDA. 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.

The linearized scaled ABE criterion is calculated according to the SAS code
given in the FDA progesterone guidance.
The simulations are done via the distributional properties of the statistical
quantities necessary for deciding BE based on scaled ABE.
For more details see a document `Implementation_scaledABE_simsVx.yy.pdf`

in the `/doc`

sub-directory of
the package.
If a CVcap is defined for the regulator, the BE decision is based on the inclusion
of the CI in the capped widened acceptance limits in case of CVwR > CVcap. This
resembles method ‘Howe-EMA’ in Mu<U+00F1>oz *et al.* and is the standard behavior now if
`regulator="EMA"`

is choosen.

Food and Drug Administration, Office of Generic Drugs (OGD). *Draft Guidance on Progesterone.* Recommended Apr 2010. Revised Feb 2011. download

T<U+00F3>thfalusi, L, Endr<U+00E9>nyi, L. *Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs.* J Pharm Pharmaceut Sci. 2011;15(1):73--84.
open access

T<U+00F3>thfalusi L, Endr<U+00E9>nyi L, Garc<U+00ED>a Arieta A. *Evaluation of Bioequivalence for Highly Variable Drugs with Scaled Average Bioequivalence.* Clin Pharmacokin. 2009;48(11):725--43. 10.2165/11318040-000000000-00000

Mu<U+00F1>oz J, Alcaide D, Oca<U+00F1>a J. *Consumer<U+2019>s risk in the EMA and FDA regulatory approaches for bioequivalence in highly variable drugs.* Stat Med. 2015;35(12):1933--43. 10.1002/sim.6834

```
# NOT RUN {
# using all the defaults:
# design=2x3x3 (partial replicate design), theta0=0.90,
# ABE limits, PE constraint 0.8 - 1.25
# targetpower=80%, alpha=0.05, 1E5 simulations
sampleN.RSABE(CV = 0.3)
# should result in a sample size n=45, power=0.80344
# }
```

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