Find the constant required such that the conditional error function meets the overall level condition.
getLevelConstant(design)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.
An object of class TrialDesignOptimalConditionalError created by getDesignOptimalConditionalErrorFunction(). Contains all necessary arguments to calculate the optimal conditional error function for the specified case.
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:
$$\alpha_1 + \int_{\alpha_1}^{\alpha_0} CP(p_1)dp_1>\alpha.$$
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