PowerTOST (version 1.1-08)

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. Conventionally 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.

design

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

method

Defaults to "exact" in which case the calculation is done based on formulas with Owen's Q. The exact calculation can also be choosen with method="owenq" Approximate calculations can be choosen via method="noncentral" or

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.

Warning

The function does not vectorize if design is a vector. The function vectorize properly if n or CV or theta0 are vectors. Other vector input is not tested yet.

Details

The exact calculations of power are based on Owen's Q-function. The approximate power is implemented via non-central t-distribution or via 'shifted' central t-distribution. The formulas used assume balanced studies, i.e. equal number of subjects in the (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" Journal 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 here for a short description: ../doc/BE_power_sample_size_excerpt.pdf.

See Also

sampleN.TOST, known.designs

Examples

# power for the 2x2 cross-over design with 24 subjects
# using all the other default values
# should give: [1] 0.7391155
power.TOST(CV=0.25, n=24)