pvalue.TOST: p-value(s) of the TOST procedure

Description

Calculates the p-value(s) of the TOST procedure via students t-distribution given pe, CV and n.

Usage

pvalue.TOST(pe, CV, n, logscale = TRUE, theta1, theta2, design = "2x2", 
            robust = FALSE, both = FALSE)
pvalues.TOST(pe, CV, n, logscale = TRUE, theta1, theta2, design = "2x2", 
             robust = FALSE, both = TRUE)

Arguments

Observed point estimate of the ratio Test vs. Reference (if logscale=TRUE) or of the difference (if logscale=FALSE).

Obseved coefficient of variation as ratio (if logscale=TRUE) or residual error standard deviation (if logscale=FALSE).

Total number of subjects if given as scalar. Number of subjects in (sequence) groups if given as vector.

logscale

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

theta1

Lower bioequivalence limit. In case of logscale=TRUE it has to be given as ratio, otherwise as value < 0. Defaults to 0.8 if logscale=TRUE or to log(0.8)= -0.2231 if logscale=FALSE.

theta2

Upper bioequivalence limit. If not given theta2 will be calculated as 1/theta1 if logscale=TRUE or as -theta1 if logscale=FALSE.

design

Character string describing the study design. See known.designs() for designs covered in this package.

robust

If set to TRUE triggers the use of degrees of freedom according to the 'robust' evaluation (aka Senn's basic estimator). These df are calculated as n-seq. See known.designs()$df2.Has only effect for higher-order crossover designs. Defaults to FALSE. With that value the usual degrees of freedom will be used.

both

Indicates if both p-values (t-tests of pe>=theta1 and pe<=theta2) shall be given back or only the maximum. Defaults to FALSE for the function pvalue.TOST() and to TRUE for the function pvalues.TOST().

Value

Returns the p-value(s). Returns a vector with named elements "p.left", "p.right" if arguments pe and CV are scalars, else a matrix with columns "p.left", "p.right". p.left names the p-value of testing HA1: theta>=theta1, p.right the p-value of testing HA2: theta<=theta2 against their respective Nulls.

References

Schuirmann DJ. A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability J Pharmacokin Biopharm. 1987;15:657--80. 10.1007/BF01068419

Hauschke D, Steinijans V, Pigeot I. Bioequivalence Studies in Drug Development Chichester: Wiley; 2007.

Examples

Run this code

# NOT RUN {
# Defaults: 2x2 crossover, log-transformation
# BE acceptance limits 0.8 ... 1.25, usual df's
# interested in both p-values
pvalues.TOST(pe=0.95, CV=0.3, n=12)
# gives the vector (named elements)
#     p.left    p.right
# 0.09105601 0.02250985
# i.e. 'left' hypothesis H01: theta<=theta1 can't be rejected
# 'right' hypothesis H02: theta>=theta2 can be rejected

# max. p-value only as 'overall' pvalue, preferred by Benjamin
pvalue.TOST(pe=0.912, CV=0.333, n=24)
# should give 0.08777621, i.e inequivalence can't be rejected
# this is operationally identical to 
CI.BE(pe=0.912, CV=0.333, n=24)
# lower limit = 0.7766 outside 0.8 ... 1.25, i.e inequivalence can't be rejected
# }