optconerrf (version 1.0.1)

getOptimalConditionalError: Calculate the Optimal Conditional Error

Description

Calculate the Optimal Conditional Error

Usage

getOptimalConditionalError(firstStagePValue, design)

Value

Value of the optimal conditional error function.

Arguments

firstStagePValue

First-stage p-value or p-values. Must be a numeric vector between 0 and 1.

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 optimal conditional error \(\alpha_2\) given a first-stage p-value \(p_1\) is calculated as: $$\alpha_2(p_1)=\psi(-e^{c_0} \cdot \frac{\Delta_1^2}{l(p_1)}).$$

The level constant \(c_0\) as well as the specification of the effect size \(\Delta_1\) and the likelihood ratio \(l(p_1)\) must be contained in the design object (see ?getDesignOptimalConditionalErrorFunction). Early stopping rules are supported, i.e., for \(p_1 \leq \alpha_1\), the returned conditional error is 1 and for \(p_1 > \alpha_0\), the returned conditional error is 0.

References

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

See Also

getDesignOptimalConditionalErrorFunction()

Examples

# Create a design
design <- getDesignOptimalConditionalErrorFunction(
alpha = 0.025, alpha1 = 0.001, alpha0 = 0.5, conditionalPower = 0.9,
delta1 = 0.5, firstStageInformation = 40, useInterimEstimate = FALSE,
likelihoodRatioDistribution = "fixed", deltaLR = 0.5)

# Calculate optimal conditional error
getOptimalConditionalError(
firstStagePValue = c(0.1, 0.2, 0.3), design = design
)