The alpha-TOST Corrective Procedure for (Bio)Equivalence Testing

Source: R/equiv.R

This functions is used to compute the alpha-TOST, a corrective procedure of the significance level applied to the Two One-Sided Test (TOST) for (bio)equivalence testing in the univariate framework.

atost(theta, sigma, nu, alpha, delta)

Arguments

theta

A numeric value corresponding to the difference of means.

sigma

A numeric value corresponding to the standard error.

nu

A numeric value corresponding to the number of degrees of freedom.

alpha

A numeric value specifying the significance level.

delta

A numeric value corresponding to (bio)equivalence limit. We assume symmetry, i.e, the (bio)equivalence interval corresponds to (-delta,delta)

Value

A tost object with the structure:

  • decision: A boolean variable indicating whether (bio)equivalence is accepted or not.

  • ci: Confidence interval at the 1 - 2*alpha level.

  • theta: The difference of means used for the test.

  • sigma: The standard error used for the test.

  • nu: The number of degrees of freedom used for the test.

  • alpha: The significance level used for the test.

  • delta: The (bio)equivalence limits used for the test.

  • method: The method used for the test (here the "alpha-TOST").

Author

Younes Boulaguiem, Stéphane Guerrier, Dominique-Laurent Couturier

Examples

data(skin)

theta_hat = diff(apply(skin,2,mean))
nu = nrow(skin) - 1
sig_hat = sd(apply(skin,1,diff))/sqrt(nu)
res_atost = atost(theta = theta_hat, sigma = sig_hat, nu = nu,
              alpha = 0.05, delta = log(1.25))
res_atost
#> ✔ Accept (bio)equivalence
#> Equiv. Region:  |----------------0----------------|
#> Estim. Inter.:     (---------------x--------------)
#> CI =  (-0.17654 ; 0.22194)
#> 
#> Method: alpha-TOST
#> alpha = 0.05; Equiv. lim. = +/- 0.22314
#> Corrected alpha = 0.07866
#> Mean = 0.02270; Stand. dev. = 0.13428; df = 16
compare_to_tost(res_atost)
#> TOST:       
#> ✖ Can't accept (bio)equivalence
#> alpha-TOST: 
#> ✔ Accept (bio)equivalence
#> 
#> Equiv. Region:  |---------------0---------------|  
#> TOST:            (---------------x----------------)
#> alpha-TOST:        (-------------x--------------)  
#> 
#>                  CI - low      CI - high
#> TOST:            -0.21174       0.25715
#> alpha-TOST:      -0.17654       0.22194
#> 
#> Equiv. lim. = +/- 0.22314