sampleN.RatioF {PowerTOST}

Sample size for equivalence of the ratio of two means with normality on original scale

Description

Estimates the necessary sample size to have at least a given power based on Fieller’s confidence (‘fiducial’) interval.

Usage

sampleN.RatioF(alpha = 0.025, targetpower = 0.8, theta1 = 0.8, theta2, 
               theta0 = 0.95, CV, CVb, design = "2x2", print = TRUE,
               details = FALSE, imax=100, setseed=TRUE)

Arguments

alpha

Type I error probability.
Defaults here to 0.025 because this function is intended for studies with clinical endpoints.

targetpower

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

theta1

Lower bioequivalence limit. Typically 0.8 (default).

theta2

Upper bioequivalence limit. Typically 1.25.
Is set to 1/theta1 if missing.

theta0

‘True’ or assumed T/R ratio. Typically set to 0.95.

CV

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).

CVb

CV of the between-subject variability. Only necessary for design="2x2".

design

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.

print

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

details

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

imax

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

setseed

If set to TRUE the dependence of the power from the state of the random number generator is avoided.

Details

The sample size is based on exact power calculated using the bivariate non-central t-distribution via function pmvt of the package mvtnorm.
Due to the calculation method used in package mvtnorm these probabilities are dependent from the state of the random number generator within the precision of the power.

The CV(within) and CVb(etween) in case of design="2x2" are obtained via an appropriate ANOVA from the error term and from the difference (MS(subject within sequence)-MS(error))/2.

The estimated sample size gives always the total number of subjects (not subject/sequence in crossovers or subjects/group in parallel designs – like in some other software packages).

Value

A data.frame with the input values and results will be returned.
The sample size n returned is the total sample size for both designs.

Note

This function is intended for studies with clinical endpoints.
In such studies the 95% confidence intervals are usually used for equivalence testing.
Therefore, alpha defaults here to 0.025 (see EMEA 2000).

Author(s)

D. Labes

References

Fieller EC. Some Problems in Interval Estimation. J Royal Stat Soc B. 1954;16(2):175–85. 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. 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

See Also

power.RatioF

Examples

# sample size for a 2x2 cross-over study
# with CVw=0.2, CVb=0.4
# alpha=0.025 (95% CIs), target power = 80%
# 'true' ratio = 95%, BE acceptance limits 80-125%
# using all the defaults:
sampleN.RatioF(CV = 0.2, CVb = 0.4)
# gives n=28 with an achieved power of 0.807774
# see Hauschke et.al. (2007) Table 10.3a

# sample size for a 2-group parallel study
# with CV=0.4 (total variability) 
# alpha=0.025 (95% CIs), target power = 90%
# 'true' ratio = 90%, BE acceptance limits 75-133.33%
sampleN.RatioF(targetpower = 0.9, theta1 = 0.75,
               theta0 = 0.90, CV = 0.4, design = "parallel")
# gives n=236 with an achieved power of 0.900685
# see Hauschke et.al. (2007) Table 10.2

# a rather strange setting of ratio0! have a look at n.
# it would be better this is not the sample size but your account balance ;-).
sampleN.RatioF(theta0 = 0.801, CV = 0.2, CVb = 0.4)