optconerrf (version 1.0.1)

getNu: Calculate Nu

Description

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

Usage

getNu(alpha, conditionalPower)

Value

Factor linking information and \(\alpha_2\).

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

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)