PowerTOST (version 1.2-09)

power.TOST: Power of the classical TOST procedure

Description

Calculates the exact or approximate power of the two-one-sided t-tests (TOST) procedure for various study designs used in BE studies.

Usage

power.TOST(alpha = 0.05, logscale = TRUE, theta1, theta2, theta0, CV, n, 
           design = "2x2", method="exact", robust=FALSE)

Arguments

alpha

Type I error probability, significance level. By convention mostly set to 0.05.

logscale

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

theta1

Lower bioequivalence limit. In case of logscale=TRUE it is given as ratio, otherwise as diff. to 1. Defaults to 0.8 if logscale=TRUE or to -0.2 if logscale=FALSE.

theta2

Upper bioequivalence limit. If not given theta2 will be calculated as 1/theta1 if logscale=TRUE or as -theta1 if logscale=FALSE.

theta0

'True' or assumed bioequivalence ratio. In case of logscale=TRUE it must be given as ratio, otherwise as difference to 1. See examples. Defaults to 0.95 if logscale=TRUE or to 0.05 if logscale=FALSE

CV

Coefficient of variation as ratio. 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.

n

Number of subjects under study. Is total number if given as scalar, else number of subjects in the (sequence) groups. In the latter case the length of n vector has to be equal to the number of (sequence) groups.

design

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

method

Method for calculation of the power. Defaults to "exact" in which case the calculation is done based on formulas with Owen's Q. The calculation via Owen's Q can also be choosen with method="owenq". Another exact method via direct integrat

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

Value

• Value of power according to the input arguments.

Details

The exact calculations of power are based on Owen's Q-function or via direct integration of the bivariate non-central t-distribution via function pmvt() of package mvtnorm. The approximate power is implemented via non-central t-distribution or via 'shifted' central t-distribution. The formulas cover now balanced and unbalanced studies w.r.t (sequence) groups. In case of parallel group design and higher order crossover designs (replicate crossover or crossover with more than two treatments) the calculations are based on the assumption of equal variances for Test and Reference products under consideration. The formulas for the paired means 'design' do not take a correlation parameter into account. They are solely based on the paired t-test (TOST of differences = zero).

References

Phillips, K. F. (1990) "Power of the Two One-Sided Tests Procedure in Bioequivalence" J. of Pharmacokinetics and Biopharmaceutics, 18, 137-144. Diletti D., Hauschke D., and Steinijans V. W. (1991) "Sample Size Determination for Bioequivalence Assessment by Means of Confidence Intervals" Int. J. of Clinical Pharmacology, Therapy and Toxicology, 29, 1-8

See Also

sampleN.TOST, known.designs

Examples

# power for the 2x2 cross-over design with 24 subjects and CV 25\%
# using all the other default values
power.TOST(CV=0.25, n=24)
# should give: [1] 0.7391155
# nct approximation very good for this configuration
power.TOST(CV=0.25, n=24, method="nct")
# gives also: [1] 0.7391155
# shifted-central-t  approximation 
power.TOST(CV=0.25, n=24, method="shifted")
# gives:      [1] 0.7328894

# power for the 2x2 cross-over study with 24 subjects, CV 25\%
# and 2 drop-outs in the same sequence group (unbalanced study)
power.TOST(CV=0.25, n=c(10,12))
# should give: [1] 0.6912935
# not the same compared to the balanced setting
power.TOST(CV=0.25, n=22)
# should give: [1] 0.6953401