Calculates the power of the test of equivalence of the ratio of two means
with normality on original scale.
This test is based on Fieller’s confidence (‘fiducial’) interval and Sasabuchi’s
test (a TOST procedure as well).
power.RatioF(alpha = 0.025, theta1 = 0.8, theta2, theta0 = 0.95,
CV, CVb, n, design = "2x2", setseed=TRUE)Value of power according to the input.
Type I error probability, aka significance level.
Defaults here to 0.025 because this function is intended for studies
with clinical endpoints.
Lower bioequivalence limit. Typically 0.8 (default).
Upper bioequivalence limit. Typically 1.25.
Is set to 1/theta1 if missing.
‘True’ or assumed T/R ratio. Typically set to 0.95 for planning.
Coefficient of variation as ratio. In case of design="parallel" this is
the CV of the total variability, in case of design="2x2" the
intra-subject CV (CVw in the reference).
CV of the between-subject variability. Only necessary for design="2x2".
Number of subjects to be planned.
n is for both designs implemented the total number of subjects.
A character string describing the study design.
design="parallel" or design="2x2" allowed for a two-parallel
group design or a classical TR|RT crossover design.
If set to TRUE the dependence of the power from the state of the random number
generator is avoided. With setseed = FALSE you may see the dependence
from the state of the random number generator.
D. Labes
The power is calculated exact using the bivariate non-central t-distribution
via function pmvt of the package mvtnorm.
Due to the calculation method of the used package mvtnorm -- randomized
Quasi-Monte-Carlo -- these probabilities are dependent from the state of the
random number generator within the precision of the power.
See argument setseed.
Fieller EC. Some Problems in Interval Estimation. J Royal Stat Soc B. 1954;16(2):175--85. tools:::Rd_expr_doi("10.1111/j.2517-6161.1954.tb00159.x")
Sasabuchi S. A test of a multivariate normal mean with composite hypotheses determined by linear inequalities. Biometrika. 1980;67(2):429--39. tools:::Rd_expr_doi("10.1093/biomet/67.2.429")
Hauschke D, Kieser M, Diletti E, Burke M. Sample size determination for proving equivalence based on the ratio of two means for normally distributed data. Stat Med. 1999;18(1):93--105.
Hauschke D, Steinijans V, Pigeot I. Bioequivalence Studies in Drug Development. Chichester: Wiley; 2007. Chapter 10.
European Agency for the Evaluation of Medicinal Products, CPMP. Points to Consider on Switching between Superiority and Non-Inferiority. London, 27 July 2000. CPMP/EWP/482/99
sampleN.RatioF
# power for alpha=0.025, ratio0=0.95, theta1=0.8, theta2=1/theta1=1.25
# within-subject CV=0.2, between-subject CV=0.4
# 2x2 crossover study, n=24
# using all the defaults:
power.RatioF(CV = 0.2, CVb = 0.4, n = 24)
# gives [1] 0.7315357
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