PowerTOST (version 1.4-5)

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

Description

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

Usage

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)

Arguments

alpha

Vector; contains one-sided significance level for each of the two TOSTs. For one TOST, by 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.

logscale

Should the data used on log-transformed or on original scale? TRUE or FALSE. Defaults to TRUE.

theta0

Vector; contains 'true' assumed bioequivalence 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.

theta1

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.

theta2

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.

CV

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.

rho

Correlation between the two parameters under consideration. This is defined as correlation between the estimator of the treatment difference of parameter one and the estimator of the treatment difference of parameter two.

design

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

setseed

Calculation depends on pmvt() which is based on randomized quasi Monte Carlo methods. If setseed=TRUE a seed value is set, the default.

robust

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 df are calculated as n-seq. See known.designs()$df2 for designs covered in this package. Has only effect for higher-order crossover designs.

print

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

details

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

imax

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

Value

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

Warning

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

Details

The sample size is calculated via iterative evaluation of power of the 2 TOSTs. Start value for the sample size search is taken from a large sample approximation (1 TOST) according to Zhang, modified. The sample size is bound to 4 as minimum.

References

Hua SY, Xu S, D'Agostino RB Sr. Multiplicity adjustments in testing for bioequivalence Stat Med. 2015;34(2):215--31. 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. 10.1002/sim.6488

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

See Also

power.2TOST, known.designs

Examples

# NOT RUN {
# 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=0.808840
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=52 with power=0.801250
sampleN.2TOST(logscale=FALSE, theta0 = rep(-0.05, 2), CV = c(0.2, 0.2), 
              rho = 0.9, design = "parallel")
# }