PowerTOST (version 1.3-5)

exppower.noninf: 'Expected' power of non-inferiority test

Description

Calculates the 'expected' power for a variety of study designs used in bioequivalence studies.

Usage

exppower.noninf(alpha = 0.025, logscale=TRUE, theta0, margin, CV, dfCV, n, 
                design = "2x2", robust=FALSE, method=c("exact", "approx"))

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.

theta0

'True' or assumed bioequivalence ratio or difference. Typically set to 0.95 (default if missing) if logscale=TRUE. Defaults to -0.05 if logscale=FALSE.

margin

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

CV

Coefficient of variation as ratio.

dfCV

Degrees of freedom for the CV (error/residual degree of freedom). dfCV=Inf is allowed and will result give the same result as power.noninf(...).

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. 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

method

Defaults to code{method="exact"}. In that case the expected power will be calculated as expected value of the power with respect to the (prior) distribution of sigma^2 (inverse gamma distribution). Set to method="approx" will calculate the

Value

• Value of expected power according to the input.

Details

This function calculates the so-called 'expected' power taking into account that usually the CV is not known but estimated from a previous study / studies with an uncertainty. See references.

References

A.P. Grieve "Confidence Intervals and Sample Sizes" Biometrics 47, 1597-1603 December 1991 O'Hagan et al. "Assurance in Clinical Trial Design" Pharmaceut. Statist. 2005; 4: 187-201 S.A. Julious, R.J. Owen "Sample size calculations for clinical studies allowing for uncertainty in variance" Pharmaceutical Statistics (2006), 5, 29-37 S.A. Julious "Sample sizes for Clinical Trials" CRC Press, Chapman & Hall 2010 Bertsche et al. "The predictive distribution of the residual variability in the linear-fixed effects model for clinical cross-over trials" Biometrical Journal 00 (2016) 0, 1-13 Article first published online: 22 MAR 2016

See Also

expsampleN.noninf, power.noninf, exppower.TOST

Examples

# expected power for non-inferiority test of a 2x2 crossover
# CV 30\% known from a pilot study with 12 subjects (-> dfCV=10)
# using all the defaults for other parameters
# should give: [1] 0.6761068
exppower.noninf(CV=0.3, dfCV=10, n=40)
# Julious approximation
exppower.noninf(CV=0.3, dfCV=10, n=40, method="approx")
# should give: [1] 0.6751358

# Compare this to the usual power (CV assumed known, "carved in stone")
power.noninf(CV=0.3, n=40)
# should give: [1] 0.7228685
# same as 'expected' power with dfCV=Inf
exppower.noninf(CV=0.3, dfCV=Inf, n=40)

# may also calculated via exppower.TOST() after setting upper acceptance limit 
# to Inf and alpha=0.025: settings of first example above
exppower.TOST(CV=0.3, dfCV=10, n=40, theta2=Inf, alpha=0.025)