PredP {ph2bye}

The predictive probability criterion function for Phase II single-arm design

Description

Lee and Liu's criterion function for determining the trial decision cutoffs based on the predictive probability.

Usage

PredP(x, n, nmax, a, b, p0, theta_t)

Arguments

x

the number of responses among n patients treated by the experimental drug at a certain stage of the trial.

n

the number of patients treated by the experimental drug at a certain stage of the trial.

nmax

the maximum number of patients treated by the experimental drug.

a

the hyperparameter (shape1) of the Beta prior for the experimental drug.

b

the hyperparameter (shape2) of the Beta prior for the experimental drug.

p0

the the response rate for the standard drug.

theta_t

the cutoff probability for efficacy including future patients; typically, \theta_T = [0.85, 0.95]. Set 0.9 by default.

Value

prob

the predictive probability: PP = \sum\limits_{y=0}^{n_{max}-n} Pr(Y=y | x) I(\Pr(p > p_0 | Y=y, x) \geq \theta_T)

References

Lee, J. J., Liu, D. D. (2008). A predictive probability design for phase II cancer clinical trials. Clinical Trials 5: 93-106.

Yin, G. (2012). Clinical Trial Design: Bayesian and Frequentist Adaptive Methods. New York: Wiley.

Examples

# Using vague prior Uniform(0,1), i.e. Beta(1,1)
PredP(16, 23, 40, 1, 1, 0.5, 0.9)