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

Description

Thall, Simon and Estey's criterion function for determining the trial decision boundaries for efficacy (futility) and safety (toxicity).

Usage

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MultPostP(x, n, a.vec, p0)

Arguments

x

the value of observed data. It can be x_{E}=y_{ET}+y_{E T^C} i.e. number of responses for efficacy among n patients treated by the experimental drug, or x_{T}= y_{ET}+y_{E^C T} i.e. number of responses for toxicity among n patients treated by the experimental drug, where y = (y_{ET}, y_{E^C T}, y_{ET^C}, y_{E^C T^C}), that is, among n patients treated by the experimental drug, y_{ET} of them have experienced both toxicity and efficacy, y_{E^C T} have experienced toxicity only, y_{ET^C} have experienced efficacy only, y_{E^C T^C} have neither experienced toxicity nor efficacy.

n

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

a.vec

the hyperparameter vector of the Dirichlet prior for the experimental drug.

p0

the prespecified reseponse rate for efficacy, futility or toxicity.

Value

prob

the posterior probability: Pr(p_E > p_0 | X=x_E) or Pr(p_T > p_0 | X=x_T)

References

Berry, S. M., Carlin, B. P., Lee, J. J., & Muller, P. (2010). Bayesian adaptive methods for clinical trials. CRC press.

Thall, Peter F., Richard M. Simon, and Elihu H. Estey. (1995). Bayesian sequential monitoring designs for single-arm clinical trials with multiple outcomes. Statistics in medicine 14.4: 357-379.

Yin, G. (2013). Clinical Trial Design: Bayesian and Frequentist Adaptive Methods. New York: Wiley.

Examples

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n <- 30; x.eff <- 5; x.tox <- 8; param <- c(1,1,1,1); p0.eff <- 0.9; p0.tox <- 0.95
MultPostP(x=x.eff, n=n, a.vec=param, p0=p0.eff)
MultPostP(x=x.tox, n=n, a.vec=param, p0=p0.tox)