test_zmax_onesided: One-sided Zmax test

In targeted: Targeted Inference

One-sided Zmax test

Description

Calculating test statistics and p-values for the onesided Zmax / minP test.z

Given parameter estimates (\widehat{\theta}_1, \ldots, \widehat{\theta}_p)^\top with approximate assymptotic covariance matrix \widehat{S}, let Z_i = \frac{\widehat{\theta}_i - \delta_i}{\operatorname{SE}(\widehat{\theta}_i)} , where \operatorname{SE}(\widehat{\theta}_i) = \widehat{S}_{ii}. The Zmax test statistic is then Z_{max} = \max \{Z_1,\ldots,Z_p\}, and the null-hypothesis is H_0: \theta_i \leq \delta_i, i=1,\ldots,p with non-inferiority margin \delta_i, i=1,\ldots,p, for which the p-value is calculated as 1 - \Phi_R(Z_{max}) where \phi_R is the CDF of the multivariate normal distribution with mean zero and correlation matrix R = \operatorname{diag}(S_{11}^{-0.5}, \ldots, S_{pp}^{-0.5})S\operatorname{diag}(S_{11}^{-0.5}, \ldots, S_{pp}^{-0.5}).

Usage

test_zmax_onesided(par, vcov, noninf = 0, index = NULL, par.name = "theta")

Arguments

par	(numeric) parameter estimates or estimate object
vcov	(matrix) asymptotic variance estimate
noninf	(numeric) non-inferiority margins
index	(integer) subset of parameters to test
par.name	(character) parameter names in output

Value

htest object

Author(s)

Christian Bressen Pipper, Klaus Kähler Holst

See Also

test_intersection_sw() lava::test_wald() lava::closed_testing()

targeted documentation built on Jan. 12, 2026, 9:08 a.m.