# power.scABEL.sdsims: (Empirical) Power of BE decision via scaled (widened) BE... In PowerTOST: Power and Sample Size for (Bio)Equivalence Studies

 power.scABEL.sds R Documentation

## (Empirical) Power of BE decision via scaled (widened) BE acceptance limits

### Description

These function performs the power calculation of the BE decision via scaled (widened) BE acceptance limits based on subject data simulations.
This function has an alias power.scABEL.sds().

### Usage

```power.scABEL.sdsims(alpha = 0.05, theta1, theta2, theta0, CV, n,
design = c("2x3x3", "2x2x4", "2x2x3"), design_dta=NULL,
regulator, nsims = 1e+05, details = FALSE, setseed = TRUE,
progress)
```

### Arguments

 `alpha` Type I error probability, significance level. Conventionally mostly set to 0.05. `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. `theta0` ‘True’ or assumed T/R ratio. Defaults to 0.90 according to the two Lászlós 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` and the one of the Reference in the `CV`. `n` 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` is for sequence group 'TRT' and `n` is for sequence group 'RTR'. `design` Design of the study to be planned. `"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="2x3x3"`. `design_dta` 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. `regulator` Regulatory settings for the widening of the BE acceptance limits. May be given as `"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` must not be `"ISC"`. `nsims` 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. `details` If set to `TRUE` the computational time is shown as well as the components for the BE decision. p(BE-wABEL) is the probability that the CI is within (widened) limits. 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. `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()` is issued if `setseed=TRUE`, the default. `progress` Should a progressbar be shown? Defaults to `TRUE` if missing and nsims >5E5.

### Details

The methods rely on the analysis of log-transformed data, i.e., assume a log-normal 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 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`.
This feature is experimental in the sense that the data.frame is not checked for complying with the assumed structure.

### Value

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-wABEL) is the power of the widened ABEL criterion alone and p(BE-pe) is the power of the criterion 'point estimat within acceptance range' alone. p(BE-ABE) is the power of the conventional ABE test given for comparative purposes.

### Note

The function is mainly intended for crosscheck of `power.scABEL()` results.
But may be mandatory for cases where `power.scABEL()` results are inaccurate (low sample sizes and/or heteroscedasticity).
It is relatively slow. The run-time of this function doing 1 Mio sims is between ~ 7-8 sec for n=12 and ~ 3-4 min for n=120 on a machine with an Intel core i7 processor.
Thus be patient and go for a cup of coffee if you use this function with high sample sizes!

### Author(s)

D. Labes, B. Lang

### References

Tóthfalusi L, Endrényi L. Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs. J Pharm Pharmaceut Sci. 2011;15(1):73–84. open source

`power.scABEL, reg_const`

### Examples

```# using all the defaults:
# design="2x3x3", EMA regulatory settings
# PE constraint 0.8-1.25, cap on widening if CV>0.5
# true ratio=0.90, 1E+5 simulations
power.scABEL.sdsims(CV = 0.4, n = 36)
# should give:
#  0.74321
```

PowerTOST documentation built on March 18, 2022, 5:47 p.m.