The predictive probability criterion function

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Description

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

Usage

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predprob(y, n, nmax, alpha_e, beta_e, p_s, theta_t)

Arguments

y

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.

alpha_e

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

beta_e

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

p_s

the the response rate for the standard drug.

theta_t

the prespecified target probability; tipically, θ_T = [0.85, 0.95].

Value

prob

the predictive probability: PP = ∑_{x=0}^{n_{max}-n} P(x | y) I(\Pr(p_E > p_S | y, x) ≥q θ_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

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# p. 97, PP = 0.5656
predprob(16, 23, 40, 0.6, 0.4, 0.6, 0.9)