getNuPrime: Calculate the Derivate of Nu

In optconerrf: Optimal Monotone Conditional Error Functions

Calculate the Derivate of Nu

Description

Calculates the derivative of nu for a given conditional error and conditional power.

Usage

getNuPrime(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

The function \nu' is defined as

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

Note that in this implementation, the the factor -2 is used instead of -4, which is used in by Brannath & Bauer (2004), who explicitly investigate the setting of a balanced two-group trial. The argument conditionalPower is either the fixed target conditional power or the value of the conditional power function at the corresponding first-stage p-value.

Value

Value for nu prime.

References

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

Examples

getNuPrime(alpha = 0.05, conditionalPower = 0.9)

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