PowerTOST (version 1.5-4)

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

Description

Estimates the necessary sample size to have at least a given power when two parameters are 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,
              nsims = 1e+05)

Value

A list with the input and results will be returned.

The element name "Sample size" contains the total sample size.

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 (default) or FALSE.

theta0

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.

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 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}.

design

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

setseed

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

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 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.

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.

nsims

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

Warning

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

Author

B. Lang, D. Labes

Details

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).

References

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. tools:::Rd_expr_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. tools:::Rd_expr_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. tools:::Rd_expr_doi("10.1081/BIP-120022772")

See Also

power.2TOST, known.designs

Examples

# 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")