PowerTOST (version 1.3-5)

power.2TOST: Power for two simultaneous TOST procedures

Description

Calculates the exact power of two simultaneous TOST procedures (where the two parameters of the two TOSTs are correlated with some correlation) for various study designs used in BE studies

Usage

power.2TOST(alpha = c(0.05, 0.05), logscale = TRUE, theta1, theta2, theta0, 
            CV, n, rho, design = "2x2", robust = FALSE, setseed = TRUE)

Arguments

alpha

Vector; contains one-sided significance level for each of the two TOSTs. For one TOST, by convention mostly set to 0.05.

logscale

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

theta1

Vector; contains lower bioequivalence limit for each of the two TOSTs. In case of logscale=TRUE it is given as ratio, otherwise as diff. to 1. Defaults to c(0.8, 0.8) if logscale=TRUE or to c(-0.2, -0.2)

theta2

Vector; contains upper bioequivalence limit for each of the two TOSTS. If not given theta2 will be calculated as 1/theta1 if logscale=TRUE or as -theta1 if logscale=FALSE.

theta0

Vector; contains 'true' assumed bioequivalence ratio for each of the two TOSTs. In case of logscale=TRUE each element must be given as ratio, otherwise as difference to 1. See examples. Defaults to c(0.95, 0.95) if logsca

CV

Vector of coefficient of variations (given as as ratio, e.g. 0.2 for 20%). 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. In case of logscale=FALSE CV is assum

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.

rho

Correlation between the two parameters under consideration. This is defined as correlation between the estimator of the treatment difference of parameter one and the estimator of the treatment difference of parameter two.

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

setseed

Calculation depends on pmvt() which is based on randomized quasi Monte Carlo methods. If setseed=TRUE a seed value is set, the default.

Value

• Value of power.

Details

The exact calculations of the power are performed via integration of the 4-dimensional non-central t-distribution via function pmvt() of package mvtnorm. An absolute error tolerance of 1e-04 is set within pmvt(). The formulas cover balanced and unbalanced studies w.r.t (sequence) groups. In case of parallel group design and higher order crossover designs (replicate crossover or crossover with more than two treatments) the calculations are based on the assumption of equal variances for Test and Reference products under consideration. The formulas for the paired means 'design' do not take an additional correlation parameter into account. They are solely based on the paired t-test (TOST of differences = zero).

References

Hua S. Y., Xu S., and D'Agostino Sr. R. B. "Multiplicity adjustments in testing for bioequivalence" Statistics in Medicine, Vol. 34, Issue 2, 215-231 (2015) Lang B., Fleischer F. (in press). "Letter to the Editor 'Comments on Multiplicity adjustments in testing for bioequivalence'". Statistics in Medicine. Phillips, K. F. (2009) "Power for Testing Multiple Instances of the Two One-Sided Tests Procedure" The International Journal of Biostatistics: Vol. 5: Iss. 1, Article 15.

See Also

sampleN.2TOST, known.designs

Examples

# Power for the 2x2x2 cross-over design with 24 subjects, intra-subject
# standard deviation of 0.3 (CV = 30.7\%) and assumed ratios of 1.05 for both
# parameters, and correlation 0.75 between parameters (using all the other
# default values)
power.2TOST(theta0 = rep(1.05, 2), CV = rep(se2CV(0.3), 2), n = 24, rho = 0.75)
# should give: [1] 0.3981441

# Setting as before but use rho = 1 to replicate result of power.TOST()
p1 <- power.2TOST(theta0 = rep(1.05, 2), CV = rep(se2CV(0.3), 2), n = 24, rho = 1)
p2 <- power.TOST(theta0 = 1.05, CV = se2CV(0.3), n = 24)
all.equal(p1, p2, tolerance = 1e-04)