PowerTOST (version 1.4-7)

power.noninf: Power of the one-sided non-inferiority t-test

Description

Function calculates of the power of the one-sided non-inferiority t-test for normal or log-normal distributed data.

Usage

power.noninf(alpha = 0.025, logscale = TRUE, margin, theta0, CV, n, 
             design = "2x2", robust = FALSE)

Arguments

alpha

Type I error probability, significance level. Defaults here to 0.025.

logscale

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

margin

Non-inferiority margin. In case of logscale=TRUE it must be given as ratio, otherwise as diff. to 1. Defaults to 0.8 if logscale=TRUE or to -0.2 if logscale=FALSE.

theta0

'True' or assumed bioequivalence ratio or difference. 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.

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.

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 CV or theta0 are vectors. Other vector input is not tested yet.

Details

The power is calculated exact via non-central t-distribution.

Notes on the underlying hypotheses If the supplied margin is < 0 (logscale=FALSE) or < 1 (logscale=TRUE), then it is assumed higher response values are better. The hypotheses are H0: theta0 <= margin vs. H1: theta0 > margin where theta0 = mean(test)-mean(reference) if logscale=FALSE or H0: log(theta0) <= log(margin) vs. H1: log(theta0) > log(margin) where theta0 = mean(test)/mean(reference) if logscale=TRUE.

If the supplied margin is > 0 (logscale=FALSE) or > 1 (logscale=TRUE), then it is assumed lower response values are better. The hypotheses are H0: theta0 >= margin vs. H1: theta0 < margin where theta0 = mean(test)-mean(reference) if logscale=FALSE or H0: log(theta0) >= log(margin) vs. H1: log(theta0) < log(margin) where theta0 = mean(test)/mean(reference) if logscale=TRUE. This latter case may also be considered as 'non-superiority'.

References

Julious SA Sample sizes for clinical trials with Normal data Stat Med. 2004;23(12):1921--86. 10.1002/sim.1783

See Also

known.designs, sampleN.noninf

Examples

# NOT RUN {
# using all the defaults: margin=0.8, theta0=0.95, alpha=0.025
# log-transformed, design="2x2"
# should give: 0.4916748
power.noninf(CV=0.3, n=24)
# }