Calculate the Optimal Conditional Error

Usage

getConditionalError(design, pValue, stage = 1)

Arguments

design: An object of class TrialDesignOptimalConditionalError created by getDesignOptimalConditionalError(). Contains all necessary arguments to calculate the optimal conditional error function for the specified case.
pValue: First-stage p-value or p-values. Must be a numeric vector between 0 and 1.
stage: Completed interim stage. Currently only 1 is supported.

Value

A numeric vector of conditional errors, one per first-stage p-value.

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 ?getDesignOptimalConditionalError). Early stopping rules are supported, i.e., for $p_1 \leq \alpha_1$ with $\alpha_1 > 0$, 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, 60(3), 715-723. doi:10.1111/j.0006-341X.2004.00221.x

Brannath, W., zur Verth, J., Dreher, M. & Scharpenberg, M. (2024; revised 2026). Optimal monotone conditional error functions. doi:10.48550/arXiv.2402.00814

The related R package optconerrf: Optimal Monotone Conditional Error Functions provides a standalone implementation of this methodology. The rpact implementation uses rpact design objects and interfaces; optconerrf is not required to run these functions.

Examples

# Create a design
design <- getDesignOptimalConditionalError(
    alpha = 0.025, efficacyBounds = 0.001, futilityBounds = 0.5, conditionalPower = 0.9,
    thetaH1 = 0.5, firstStageInformation = 40, useInterimEstimate = FALSE,
    likelihoodRatioDistribution = "fixed", thetaLR = 0.5
)

# Early efficacy gives 1, continuation gives the stage-two threshold,
# and binding futility gives 0.
getConditionalError(
    pValue = c(0.0005, 0.1, 0.3, 0.8), design = design
)
#> [1] 1.000000000 0.029470114 0.002541869 0.000000000