MultPostP function

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

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

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.

Returns

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

Examples

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)

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.