PowerTOST (version 1.1-08)

power2.TOST: Power of the classical TOST procedure with unbalanced (sequence) groups

Description

Calculates the exact or approximate power of the two-one-sided t-tests procedure for various study designs used in BE studies in case of unbalanced number of subjects in the (sequence) groups.

Usage

power2.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 in the (sequence) groups under study. Must be a vector of length = (sequence) groups.

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 chosen with method="owenq". Approximate calculations can be chosen 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.

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. 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.

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 Also

power.TOST, known.designs

Examples

# power for the 2x2 cross-over design with 24 subjects balanced,
# CV=25\% using all the other default values
# should give: [1] 0.7391155
power2.TOST(CV=0.25, n=c(12,12))
# the same result 
power.TOST(CV=0.25, n=24)

# power for the 2x2 cross-over study with 24 subjects, same CV 
# and 2 drop-outs in the same sequence group
# should give: [1] 0.6912935
power2.TOST(CV=0.25, n=c(10,12))
# not the same compared to
power.TOST(CV=0.25,n=22)
power2.TOST(CV=0.25,n=c(11,11))
# both should give: [1] 0.6953401