The package contains functions to calculate power and estimate sample size for various study designs used in (not only bio-) equivalence studies. Power and sample size can be obtained based on different methods, amongst them prominently the TOST procedure (Two One-Sided t-Tests).
Version 1.5.3 built 2021-01-18 with R 4.0.3.
For an overview of supported designs, methods, and defaults together with some basic examples see
2x2x2
or 2x2
for short.
3x3
and 3x6x3
. Both have the same degrees of freedom (2n–4) in the conventional approach and therefore, require the same number of subjects.
sampleN.RatioF()
and for non-inferiority/-superiority in function sampleN.noninf()
, where it is 0.025). In the functions alpha
.
beta0
.
CV
.
CV
.
CV
). If heteroscedasticity is assumed, CV
has to given as a vector with two elements CV = c(x, y)
, where CV[1]
is CV_{wT} and CV[2]
is CV_{wR}.
CVb
is required in function sampleN.RatioF()
and in function sampleN.dp()
if design = "IBD"
(incomplete block design).
ABEL: Based on the switching coefficient of variation \(\small{CV_0=30\%}\). \(\small{k=\log_{e}1.25/\sqrt{\log_{e}(CV_{0}^{2}+1)}\approx 0.760}\).
\(\small{\left[ {L,\,U} \right]=\left[1+\log_{e}0.80/\log_{e}rd,\:1+\log_{e}1.25/\log_{e}rd \right]}\)
logscale = TRUE
where \(\theta_0=\mu_\textrm{T}/\mu_\textrm{R}\)).Non-inferiority: If margin < 1, higher responses are are assumed to be better. \[\small{H_0:\,\theta_0 \leq \log_{e}\textrm{margin}\:vs\:H_1:\,\theta_0>\log_{e}\textrm{margin}}\]
targetpower
.
rd
.
robust
logscale = TRUE
) or difference T – R (logscale = FALSE
). In the functions theta0
.
theta1
and theta2
.
theta0 = theta2
or theta0 = theta1
.power.scABEL()
, power.RSABE()
, power.NTIDFDA()
, power.HVNTID()
).
In all functions sample sizes are estimated based on equivalence margins [\(\small{\theta_1,\theta_2}\)] in full numeric precision. The widened margins for highly variable C_{max} are \(\small{\theta_1=0.75,}\) \(\small{\theta_2=1/\theta_1=1.\dot{3}}\) and not the rounded 75.00 – 133.33% according to the guidelines of the Russian Federation, the EEU, and the GCC. If for a NTID theta1 = 0.90
is specified, \(\small{\theta_2=1/\theta_1=1.\dot{1}}\) and not the rounded 111.11% as in the guidelines. Health Canada requires rounding to only one decimal place with bioequivalence margins for NTIDs of 90.0 – 112.0%.
Estimated sample sizes are generally not affected or – in extremely rare cases – conservative.
Example for a HVDP (\(\small{\theta_0}\) 0.90, design 2x2x4) and a NTID (\(\small{\theta_0}\) 0.975, design 2x2x2):
# CV agency method L U n theta1 theta2 n
# 0.574 EMA ABEL 69.84% 143.19% 30 0.698368 1.431910 30
# 0.574 HC ABEL 66.7 % 150.0 % 28 0.666667 1.500000 28
# 0.574 RU/EEU/GGC ABE 75.00% 133.33% 34 0.750000 1.333333 34
# 0.100 EMA ABE 90.00% 111.11% 22 0.900000 1.111111 22
# 0.100 HC ABE 90.0 % 112.0 % 22 0.900000 1.111111 22
You can install the released version of PowerTOST from CRAN with …
package <- "PowerTOST"
inst <- package %in% installed.packages()
if (length(package[!inst]) > 0) install.packages(package[!inst])
… and the development version from GitHub with
# install.packages("remotes")
remotes::install_github("Detlew/PowerTOST")
Skips installation from a github remote if the SHA-1 has not changed since last install. Use force = TRUE
to force installation.
Inspect this information for reproducibility. Of particular importance are the versions of R and the packages used to create this workflow. It is considered good practice to record this information with every analysis.
options(width = 80)
devtools::session_info()
# - Session info ---------------------------------------------------------------
# setting value
# version R version 4.0.3 (2020-10-10)
# os Windows 10 x64
# system x86_64, mingw32
# ui RTerm
# language EN
# collate C
# ctype German_Germany.1252
# tz Europe/Berlin
# date 2021-01-18
#
# - Packages -------------------------------------------------------------------
# package * version date lib source
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# magrittr 2.0.1 2020-11-17 [2] CRAN (R 4.0.3)
# memoise 1.1.0 2017-04-21 [2] CRAN (R 4.0.0)
# mvtnorm 1.1-1 2020-06-09 [2] CRAN (R 4.0.0)
# pkgbuild 1.2.0 2020-12-15 [2] CRAN (R 4.0.3)
# pkgload 1.1.0 2020-05-29 [2] CRAN (R 4.0.0)
# PowerTOST * 1.5-3 2021-01-18 [1] local
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# ps 1.5.0 2020-12-05 [2] CRAN (R 4.0.3)
# purrr 0.3.4 2020-04-17 [2] CRAN (R 4.0.0)
# R6 2.5.0 2020-10-28 [2] CRAN (R 4.0.3)
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# rlang 0.4.9 2020-11-26 [2] CRAN (R 4.0.3)
# rmarkdown 2.6 2020-12-14 [2] CRAN (R 4.0.3)
# rprojroot 2.0.2 2020-11-15 [2] CRAN (R 4.0.3)
# sessioninfo 1.1.1 2018-11-05 [2] CRAN (R 4.0.0)
# stringi 1.5.3 2020-09-09 [2] CRAN (R 4.0.2)
# stringr 1.4.0 2019-02-10 [2] CRAN (R 4.0.0)
# TeachingDemos 2.12 2020-04-07 [2] CRAN (R 4.0.0)
# testthat 3.0.1 2020-12-17 [2] CRAN (R 4.0.3)
# tufte 0.9 2020-12-02 [2] CRAN (R 4.0.3)
# usethis 2.0.0 2020-12-10 [2] CRAN (R 4.0.3)
# withr 2.4.0 2021-01-16 [2] CRAN (R 4.0.3)
# xfun 0.19 2020-10-30 [2] CRAN (R 4.0.3)
# yaml 2.2.1 2020-02-01 [2] CRAN (R 4.0.0)
#
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# [3] C:/Program Files/R/R-4.0.3/library