sampleN.2TOST: Sample size based on power of two TOSTs

View source: R/sampleN_2TOST_sim.R

sampleN.2TOSTR Documentation

Sample size based on power of two TOSTs


Estimates the necessary sample size to have at least a given power when two parameters are tested simultaneously.


sampleN.2TOST(alpha = c(0.05, 0.05), targetpower = 0.8, logscale = TRUE, 
              theta0, theta1, theta2, CV, rho, design = "2x2", setseed = TRUE,
              robust = FALSE, print = TRUE, details = FALSE, imax = 100,
              nsims = 1e+05)



Vector; contains one-sided significance level for each of the two TOSTs.
For one TOST, by convention mostly set to 0.05.


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


Should the data used on log-transformed or on original scale? TRUE (default) or FALSE.


Vector; contains ‘true’ assumed T/R ratio for each of the two TOSTs.
In case of logscale=TRUE each element must be given as ratio,
otherwise as difference to 1. See examples.
Defaults to c(0.95, 0.95) if logscale=TRUE or to c(0.05, 0.05) if logscale=FALSE.


Vector; contains lower bioequivalence limit for each of the two TOSTs.
In case of logscale=TRUE it is given as ratio, otherwise as diff. to 1.
Defaults to c(0.8, 0.8) if logscale=TRUE or to c(-0.2, -0.2) if logscale=FALSE.


Vector; contains upper bioequivalence limit for each of the two TOSTs.
If not given theta2 will be calculated as 1/theta1 if logscale=TRUE
or as -theta1 if logscale=FALSE.


Vector of coefficient of variations (given as as ratio, e.g., 0.2 for 20%).
In case of cross-over studies this is the within-subject CV,
in case of a parallel-group design the CV of the total variability.
In case of logscale=FALSE CV is assumed to be the respective standard deviation.


Correlation between the two PK metrics (e.g., AUC and Cmax) under consideration. This is defined as correlation between the estimator of the treatment difference of PK metric one and the estimator of the treatment difference of PK metric two. Has to be within {–1, +1}.


Character string describing the study design.
See known.designs() for designs covered in this package.


Logical; if TRUE, the default, a seed of 1234567 is set.


Defaults to FALSE. With that value the usual degrees of freedom will be used.
Set to TRUE will use the degrees of freedom according to the ‘robust’ evaluation (aka Senn’s basic estimator). These degrees of freedom are calculated as n-seq.
See known.designs()$df2 for designs covered in this package.
Has only effect for higher-order crossover designs.


If TRUE (default) the function prints its results.
If FALSE only the result list will be returned.


If TRUE the design characteristics and the steps during sample size calculations will be shown.
Defaults to FALSE.


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


Number of studies to simulate. Defaults to 100,000 = 1E5.


The sample size is estimated via iterative evaluation of power of the two TOSTs.
Start value for the sample size search is taken from a large sample approximation (one TOST) according to Zhang, modified.
The sample size is bound to 4 as minimum.

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


A list with the input and results will be returned.
The element name "Sample size" contains the total sample size.


The function does not vectorize properly.
If you need sample sizes with varying CVs, use f.i. for-loops or the apply-family.


If both theta0 are near the acceptance limits then the starting value may not be a good approximation resulting in a lot of iteration steps; imax may need to be increased to obtain the required sample size.


B. Lang, D. Labes


Phillips KF. Power for Testing Multiple Instances of the Two One-Sided Tests Procedure. Int J Biostat. 2009;5(1):Article 15.

Hua SY, Xu S, D’Agostino RB Sr. Multiplicity adjustments in testing for bioequivalence. Stat Med. 2015;34(2):215–31. doi: 10.1002/sim.6247

Lang B, Fleischer F. Letter to the Editor: Comments on ‘Multiplicity adjustments in testing for bioequivalence’. Stat Med. 2016;35(14):2479–80. doi: 10.1002/sim.6488

Zhang P. A Simple Formula for Sample Size Calculation in Equivalence Studies. J Biopharm Stat. 2003;13(3):529–538. doi: 10.1081/BIP-120022772

See Also

power.2TOST, known.designs


# Sample size for 2x2x2 cross-over design, intra-subject CV = 30% and assumed
# ratios of 0.95 for both parameters, and correlation 0.9 between parameters
# (using all the other default values)
# Should give n=44 with power=0.80684
sampleN.2TOST(theta0 = rep(0.95, 2), CV = rep(0.3, 2), rho = 0.9)

# Sample size for a parallel group design,
# evaluation on the original (untransformed) scale
# BE limits 80 ... 120% = -20% ... +20% of reference,
# assumed true BE ratio 0.95% = -5% to reference mean for both parameters,
# total CV=20% for both parameters, and correlation 0.9 between parameters
# should give n=54 with power=0.8149
sampleN.2TOST(logscale=FALSE, theta0 = rep(-0.05, 2), CV = c(0.2, 0.2), 
              rho = 0.9, design = "parallel")

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