PowerTOST (version 1.4-7)

sampleN.noninf: Sample size for the non-inferiority t-test

Description

Function for calculating the sample size needed to have a pre-specified power for the one-sided non-inferiority t-test for normal or log-normal distributed data.

Usage

sampleN.noninf(alpha = 0.025, targetpower = 0.8, logscale = TRUE, margin, 
               theta0, CV, design = "2x2", robust = FALSE, 
               details = FALSE, print = TRUE, imax=100)

Arguments

alpha

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

targetpower

Power to achieve at least. Must be >0 and <1. Typical values are 0.8 or 0.9.

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.

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.

details

If TRUE the design characteristics and the steps during sample size calculations will be shown. Defaults to FALSE.

print

If TRUE (default) the function prints its results. If FALSE only the data.frame with the results will be returned.

imax

Maximum number of steps in sample size search. Defaults to 100. Adaption only in rare cases needed.

Value

A data.frame with the input settings and results will be returned. Explore it with str(sampleN.noninf(...)

Warning

The function does not vectorize properly. If you need sample sizes with varying CVs f.i. use for-loops or the apply-family.

Details

The sample size is calculated via iterative evaluation of power.noninf(). Start value for the sample size search is taken from a large sample approximation. The sample size is bound to 4 as minimum.

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, power.noninf

Examples

# NOT RUN {
# using all the defaults: margin=0.8, theta0=0.95, alpha=0.025
# log-transformed, design="2x2"
sampleN.noninf(CV=0.3)
# should give n=48
#
# 'non-superiority' case, log-transformed data
# with assumed 'true' ratio somewhat above 1
sampleN.noninf(CV=0.3, targetpower=0.9, margin=1.25, theta0=1.05)
# should give n=62
# }