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Two One-Sided Tests (TOST) for (Bio)Equivalence Assessment

Source: R/internal_average_univariate.R
tost.Rd

Performs the Two One-Sided Tests (TOST) procedure for (bio)equivalence assessment in both univariate and multivariate settings.

Usage

tost(theta, sigma, nu, delta, alpha = 0.05, ...)

Arguments

theta

A numeric value or vector representing the estimated difference(s) (e.g., between a generic and reference product).

sigma

A numeric value (univariate) or matrix (multivariate) corresponding to the estimated variance of theta.

nu

A numeric value specifying the degrees of freedom. In the multivariate case, it is assumed to be the same across all dimensions.

delta

A numeric value or vector defining the (bio)equivalence margin(s). The procedure assumes symmetry, i.e., the (bio)equivalence region is \((-\delta, \delta)\). In the multivariate case, it is assumed to be the same across all dimensions.

alpha

A numeric value specifying the significance level (default: alpha = 0.05).

...

Additional arguments.

Value

A tost object with the following elements:

  • decision: Logical; indicates whether (bio)equivalence is accepted.

  • ci: Confidence region at the \(1 - 2\alpha\) level.

  • theta: The estimated difference(s) used in the test.

  • sigma: The estimated variance of theta; a numeric value (univariate) or matrix (multivariate).

  • nu: The degrees of freedom used in the test.

  • alpha: The significance level used in the test.

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

  • method: A character string describing the method used ("TOST").

  • setting: The setting used ("univariate" or "multivariate").

Examples

# Univariate case
data(skin)
theta_hat = diff(colMeans(skin))
nu = nrow(skin) - 1
sig_hat = sd(apply(skin, 1, diff)) / sqrt(nu)
tost(theta = theta_hat, sigma = sig_hat, nu = nu,
     alpha = 0.05, delta = log(1.25))
#> Error in tost(theta = theta_hat, sigma = sig_hat, nu = nu, alpha = 0.05,     delta = log(1.25)): could not find function "tost"

# Multivariate case
data(ticlopidine)
n = nrow(ticlopidine)
nu = n - 1
theta_hat = colMeans(ticlopidine)
Sigma_hat = cov(ticlopidine) / n
tost(theta = theta_hat, sigma = Sigma_hat, nu = nu, delta = log(1.25))
#> Error in tost(theta = theta_hat, sigma = Sigma_hat, nu = nu, delta = log(1.25)): could not find function "tost"