getNu: Calculate Nu

In optconerrf: Optimal Monotone Conditional Error Functions

Calculate Nu

Description

Calculate the factor which relates \alpha_2 to the second-stage information for given conditional power.

Usage

getNu(alpha, conditionalPower)

Arguments

alpha	The (conditional) type I error rate of the design. Must be a numeric vector with values between 0 and 1.
conditionalPower	The target conditional power CP of the design. Must be a numeric value.

Details

Note that this function uses factor 1 instead of factor 2 (Brannath & Bauer 2004). This has no impact on the optimal conditional error function, as constant factors are absorbed by the level constant c_0.
The calculation is:

\nu(\alpha_2(p_1)) = (\Phi^{-1}(1-\alpha_2(p_1)) + \Phi^{-1}(CP))^2.

Value

Factor linking information and \alpha_2.

References

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

Examples

getNu(alpha = 0.05, conditionalPower = 0.9)

# Returns 0 if alpha exceeds conditionalPower
getNu(alpha = 0.8, conditionalPower = 0.7)

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