getLevelConstant: Get Level Constant for Optimal Conditional Error Function

In optconerrf: Optimal Monotone Conditional Error Functions

Get Level Constant for Optimal Conditional Error Function

Description

Find the constant required such that the conditional error function meets the overall level condition.

Usage

getLevelConstant(design)

Arguments

design

An object of class TrialDesignOptimalConditionalError created by getDesignOptimalConditionalErrorFunction(). Contains all necessary arguments to calculate the optimal conditional error function for the specified case.

Details

The level condition is defined as:

\alpha = \alpha_1 + \int_{\alpha_1}^{\alpha_0} \alpha_2(p_1)dp_1.

The constant c_0 of the optimal conditional error function is calibrated such that it meets the level condition. For a valid design, the additional following condition must be met to be able to exhaust the level \alpha:

\alpha_1 + CP(\alpha_0-\alpha_1)>\alpha.

This condition is checked by getLevelConstant() and the execution is terminated if it is not met.
In case a conditional power function is used, the condition is instead:

\alpha_1 + \int_{\alpha_1}^{\alpha_0} CP(p_1)dp_1>\alpha.

Value

A list that contains the constant (element $root) and other components provided by uniroot(). The level constant is calculated corresponding to the mean difference scale.

References

Brannath, W. & Bauer, P. (2004). Optimal conditional error functions for the control of conditional power. Biometrics. https://www.jstor.org/stable/3695393

Brannath, W., Dreher, M., zur Verth, J., Scharpenberg, M. (2024). Optimal monotone conditional error functions. https://arxiv.org/abs/2402.00814

optconerrf documentation built on Sept. 9, 2025, 5:29 p.m.