sampleN.scABEL: Sample size estimation for BE decision via scaled (expanded)... In PowerTOST: Power and Sample Size for (Bio)Equivalence Studies

Description

This function performs the sample size estimation via power calculations of the BE decision via scaled (expanded) BE acceptance limits, based on simulations.

Usage

 ```1 2 3 4``` ```sampleN.scABEL(alpha = 0.05, targetpower = 0.8, theta0, theta1, theta2, CV, design = c("2x3x3", "2x2x4", "2x2x3"), regulator, nsims = 1e+05, nstart, imax = 100, print = TRUE, details = TRUE, setseed = TRUE) ```

Arguments

 `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 Lászlós 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 settings for the widening of the BE acceptance limits. May be given as character from the choices `"EMA"`, `"HC"`, `"GCC"`, `"FDA"` 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. `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 >=1.20. But see the warning section. `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` (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.

Details

The simulations are done via the distributional properties of the statistical quantities necessary for deciding BE based on ABEL (‘Average Bioequivalence with Expanded Limits’). For more details see a description in the `/doc` sub-directory of the package.

Function `sampleN.scABEL()` is based on power calculations via simulations using the distributional characteristics of the ‘key’ statistics obtained from the EMA recommended evaluation via ANOVA if `regulator="EMA"` or if the regulator component `est_method` is set to `"ANOVA"` if regulator is an object of class 'regSet'.
Otherwise, the simulations are based on the distributional characteristis of the ‘key’ statistics obtained from evaluation via intra-subject contrasts (ISC), as recommended by the FDA.

The estimated sample size gives always the total number of subjects (not subject/sequence – like in some other software packages).

Function `sampleN.scABEL2()` is solely based on power calculations via simulation using the distributional characteristics of the ‘key’ statistics obtained from evaluation via intra-subject contrasts (ISC). This function is deprecated.

Value

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.

Designs

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

Warning

The sample size estimation for 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. This is especially true in the range around 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 get caught in the simulation error trap.

If results of `power.scABEL` are expected to be inaccurate (partial replicate design with unbalanced sequences and/or heteroscedasticity in the case of CVwT&nbsp> CVwR, subject data via `sampleN.scABEL.sdsims` should be simulated instead. Very time consuming (easily 100times slower)! Subject data simulations are only supported for `regulator="EMA"` and `regulator="GCC"`.

Note

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.

In case of `regulator="FDA"` the sample size is only approximate since the BE decision method is not exactly what is expected by the FDA. But the two Lászlós state that the scABEL method should be ‘operationally’ equivalent to the FDA method. Thus the sample size should be comparable.
Consider in case of `regulator="FDA"` to use the function `sampleN.RSABE()` instead.

In case of `regulator="HC"` the underlying power is only approximative since the Health Canada recommends evaluation by a mixed model approach. But this could only implemented via subject data simulations which are very time consuming.

The minimum sample size is 6, even if the power is higher than the intended targetpower.

D. Labes

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 access

`power.scABEL`, `sampleN.scABEL.sdsims`, `sampleN.RSABE`, `reg_const`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26``` ```# using all 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 sampleN.scABEL(CV = 0.3) # should result in a sample size n=54, power=0.8159 # Now with former (inofficial) ANVISA settings, CVswitch=40% # (since 2016 ANVISA uses the same settings as EMA) reg <- reg_const("USER", r_const = 0.76, CVswitch = 0.4, CVcap = 0.5) reg\$name <- "Old ANVISA" sampleN.scABEL(CV = 0.3, regulator = reg) # should result in a sample size n=60, power=0.8101 # For the full replicate design, target power = 90% # true assumed ratio = 0.9, FDA regulatory settings # sims based on evalaution via ISC sampleN.scABEL(CV = 0.4, targetpower = 0.9, design = "2x2x4", regulator = "FDA") # should result in a sample size n=32, power=0.9125 # Fixed wider limits (0.7500 - 1.3333) for the GCC sampleN.scABEL(CV = 0.4, targetpower = 0.9, design = "2x2x4", regulator = "GCC") # should result in a sample size n=40, power=0.9039 ```