PowerTOST (version 1.3-5)

type1error.2TOST: Type I error rate for two simultaneous TOST procedures

Description

Calculates the exact type I error rate 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

type1error.2TOST(alpha = c(0.05, 0.05), logscale = TRUE, theta1, theta2, 
                 CV, n, rho, design = "2x2", robust = FALSE, setseed = TRUE, 
                 details = FALSE)

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.

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.

details

logical; if TRUE, P(Type I error) will be returned for all eight intersection null sets, otherwise the maximum (default).

Value

• Value of Type I Error rate if argument details = FALSE. A data.frame with the TIE for each of the eight nullhypothesis regions if details = TRUE.

Details

The exact calculations of the type 1 error rate are performed via integration of the 4-dimensional non-central t-distribution via function pmvt() of package mvtnorm. An absolute error tolerance of 1e-05 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.

See Also

sampleN.2TOST, known.designs

Examples

# Replicate type 1 error rate for scenario S2 from Hua et al.
# runs 6-7 seconds, more than allowed for examples on CRAN
n <- 24
cv <- se2CV(c(0.0490 / sqrt(2/n), 0.0657 / sqrt(2/n)))
type1error.2TOST(CV = cv, n = n, rho = 0.6794, details = FALSE)