R: Power calculation of adaptive 2-stage BE studies in 2-group...

power.tsd.p {Power2Stage}

R Documentation

Power calculation of adaptive 2-stage BE studies in 2-group parallel designs

Description

This functions calculate the ‘empirical’ power of 2-stage BE studies with 2 parallel groups according to Fuglsang 2014 via simulations. The Potvin decision schemes are modified to include a futility criterion Nmax, a minimum number of subjects to be included in stage 2 and to allow the sample size estimation step to be done with point estimate and variabilities from stage 1 (fully adaptive).

Function ⁠power.tsd.pAF()⁠ performes exactly as described in Fuglsang’s paper, namely the power monitoring steps and the sample size estimation are based always on the pooled t-test.

Function power.tsd.p() with argument ⁠test="welch"⁠ on the other hand uses the genuine power of Welch’s test. Moreover it accepts unequal treatment groups in stage 1.

Usage

power.tsd.p(method = c("B", "C"), alpha0 = 0.05, alpha = c(0.0294, 0.0294),
            n1, GMR, CV, targetpower = 0.8, pmethod = c("nct", "exact", "shifted"),
            usePE = FALSE, Nmax = Inf, min.n2=0, test = c("welch", "t-test", "anova"),
            theta0, theta1, theta2, npct = c(0.05, 0.5, 0.95), nsims,
            setseed = TRUE, details = FALSE)

power.tsd.pAF(method = c("B", "C"), alpha0 = 0.05, alpha = c(0.0294, 0.0294),
              n1, GMR, CV, targetpower = 0.8, pmethod = c("shifted", "nct", "exact"),
              usePE = FALSE, Nmax = Inf, test = c("welch", "t-test", "anova"),
              theta0, theta1, theta2, npct = c(0.05, 0.5, 0.95), nsims,
              setseed = TRUE, details = FALSE)

Arguments

`method`	Decision schemes according to Potvin et.al. (defaults to `⁠"B"⁠`). Potvin’s ‘method D’ can be obtained by choosing `⁠"C"⁠` but setting `⁠alpha=c(0.028, 0.028)⁠`.
`alpha0`	Alpha value for the first step(s) in Potvin `⁠"C"⁠`, the power inspection and BE decision if power > targetpower. Defaults to 0.05.
`alpha`	Vector (two elements) of the nominal alphas for the two stages. Defaults to Pocock’s alpha setting `⁠alpha=c(0.0294, 0.0294)⁠`.
`n1`	Sample size of stage 1. Function `⁠power.tsd.p()⁠` accepts also a vector of stage 1 sample sizes with two elements, where the number of subjects in the in treatment group T should be given in the first element and the number of subjects in the treatment group R in the second. If given with one element, the total `⁠n1⁠` should be even.
`GMR`	Ratio T/R to be used in decision scheme (power calculations in stage 1 and sample size estimation for stage 2).
`CV`	Coefficient of variation of the total variability (use e.g., 0.3 for 30%) Can be a vector with two elements. In that case `⁠CV[1]⁠` is for the group under the Test treatment and `⁠CV[2]⁠` for the group under the Reference.
`targetpower`	Power threshold in the power monitoring steps and power to achieve in the sample size estimation step.
`pmethod`	Power calculation method, also to be used in the sample size estimation for stage 2. Implemented are `⁠"nct"⁠` (approximate calculations via non-central t-distribution, `⁠"exact"⁠` (exact calculations via Owen’s Q), and `⁠"shifted"⁠` (approximate calculation via shifted central t-distribution Defaults to `⁠"nct"⁠` for speed reasons in function `⁠power.tsd.p()⁠` as a reasonable compromise between speed and accuracy in the sample size estimation step. Defaults to `⁠"shifted"⁠` in function `⁠power.tsd.pAF()⁠` for consistancy with Fuglsang.
`usePE`	If `⁠TRUE⁠` the sample size estimation step is done with MSE and PE of stage 1. Defaults to `FALSE` i.e., the sample size is estimated with `⁠GMR⁠` and MSE (calculated from `⁠CV⁠`) of stage 1 analogous to Potvin et. al. NB: The power inspection steps in the Potvin methods are always done with the `⁠GMR⁠` argument and MSE (`⁠CV⁠`) of stage 1.
`Nmax`	Futility criterion. If set to a finite value, all studies simulated in which a sample size `⁠>Nmax⁠` is obtained will be regarded as BE=FAIL. Set this argument to `⁠Inf⁠`, the default, to work without that futility criterion.
`min.n2`	Minimum sample size of stage 2. If the sample size estimation step gives `⁠N < n1+min.n2⁠` the sample size for stage 2 will be forced to `⁠min.n2⁠`, i.e. the total sample size to `n1+min.n2`. Defaults to zero, i.e., no minimum sample size for stage 2 is applied.
`test`	Test on which the CI calculations are based on. Defaults to `⁠"welch"⁠` = Welch’s t-test accounting for heteroscedasticity in the variabilities of Test and Reference, but neglecting stage effects. `⁠"anova"⁠` calculates the 100(1–2α) confidence interval based on an ANOVA with treatment and stage in the model. `⁠"t-test"⁠` calculates the 100(1–2α) confidence interval based on the t-test assuming equal variabilities of Test and Reference and neglecting stage effects.
`theta0`	Assumed ratio of geometric means (T/R) for simulations. If missing, defaults to `⁠GMR⁠`.
`theta1`	Lower bioequivalence limit. Defaults to 0.8.
`theta2`	Upper bioequivalence limit. Defaults to 1.25.
`npct`	Percentiles to be used for the presentation of the distribution of `⁠n(total)=n1+n2⁠`. Defaults to `⁠c(0.05, 0.5, 0.95)⁠` to obtain the 5% and 95% percentiles and the median.
`nsims`	Number of studies to simulate. If missing, `⁠nsims⁠` is set to 1E+05 = 100,000 or to 1E+06 = 1 Mio if estimating the empiric Type I Error (`⁠'alpha'⁠`), i.e., with `⁠theta0⁠` at the border or outside the acceptance range `⁠theta1⁠` ... `⁠theta2⁠`.
`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(1234567)` is issued if `⁠setseed=TRUE⁠`, the default. Set this argument to `⁠FALSE⁠` to view the variation in power between different runs.
`details`	If set to `⁠TRUE⁠` the function prints the results of time measurements of the simulation steps. Defaults to `⁠FALSE⁠`.

Details

The calculations follow in principle the simulations as described by Fuglsang.
The underlying subject data are assumed to be evaluated after log-transformation. But instead of simulating subject data the statistics (mean and variance of Test and Reference of stage 1 and stage 2) are simulated via their associated distributions (normal and χ²).

Value

Returns an object of class ⁠"pwrtsd"⁠ with all the input arguments and results as components.
The class ⁠"pwrtsd"⁠ has an S3 print method.
The results are in the components:

`pBE`	Fraction of studies found BE.
`pBE_s1`	Fraction of studies found BE in stage 1.
`pct_s2`	Percentage of studies continuing to stage 2.
`nmean`	Mean of n(total).
`nrange`	Range (min, max) of n(total).
`nperc`	Percentiles of the distribution of n(total).
`ntable`	Object of class `⁠"table"⁠` summarizing the discrete distribution of n(total) via its distinct values and counts of occurences of these values. This component is only given back if `⁠usePE==FALSE⁠` or otherwise if `⁠is.finite(Nmax)⁠`, i.e., a futility criterion is used.

Author(s)

D. Labes

References

Fuglsang A. Sequential Bioequivalence Approaches for Parallel Design.
AAPS J. 2014; 16(3):373–8. doi: 10.1208/s12248-014-9571-1

Potvin D, DiLiberti CE, Hauck WW, Parr AF, Schuirmann DJ, Smith RA. Sequential design approaches for bioequivalence studies with crossover designs.
Pharm Stat. 2008; 7(4):245–62. doi: 10.1002/pst.294

Examples

# using all the defaults
power.tsd.p(n1=48, CV=0.25)

[Package Power2Stage version 0.5-4 Index]