BDP2 {BDP2}  R Documentation 
Operating characteristics of a singlearm trial with a binary endpoint
Description
Determines the operating characteristics of a singlearm trial with a binary endpoint (response, success) and interim efficacy and futility analyses. Declaration of efficacy and futility (including possibly early stopping) is based on the posterior probability that the true response rate is at least pE , pF respectively.
Usage
BDP2(n, interim.at, ptrue,
eff.stop = FALSE,
pF, cF, pE = NULL, cE = NULL,
type="PostProb", alpha=0.05,
shape1F, shape2F, shape1E = NULL, shape2E = NULL,
simulate = FALSE, nsim = 10000)
Arguments
n 
sample size at the final analysis 
interim.at 
vector of sample sizes at the interim analyses 
ptrue 
true (assumed) response rate used for analytical evaluations or simulating the trial 
eff.stop 

pF 
response rate used for the futility criterion (may be identical to pE) 
cF 
critical level of posterior probabilities used for declaring futility 
pE 
response rate used for the efficacy criterion 
cE 
critical level of posterior probabilities used for declaring efficacy 
type 
"PostProb" for decisions based on posterior probabilities (default) or "PredictivePower" for decisions based on predictive power (currently only implemented for 
alpha 
significance level for final test (only for 
shape1F 
first parameter of the Beta prior for futility analysis 
shape2F 
second parameter of the Beta prior for futility analysis 
shape1E 
first parameter of the Beta prior for efficacy analysis 
shape2E 
second parameter of the Beta prior for efficacy analysis 
simulate 

nsim 
number of simulation runs (only used if 
Details
Assumptions: Endpoint (response/no response) data available for all study patients. Betabinomial model. Prior distribution = Beta(shape1, shape2).
Decisions based on posterior probabilities
The posterior distribution at interim analysis with n.int patients and k.int successes is Beta(k.int + shape1F, n.int + shape2F  k.int) and Beta(k.int + shape1E, n.int + shape2E  k.int), respectively. Efficacy is declared if the posterior probability P(true response rate > pE) is >= cE. Futility is declared if the posterior probability P(true success rate > pF) is < cF. cF, cE translate into futility/efficacy boundaries (maximum number of responses leading to early termination for futility/ minimum number of responses leading to declaring of, or early termination for, efficacy).
Decisions based on predictive power
Given the results of the interim analysis, the predictive power at the final analysis (n patients, critical number of successes k.crit) is P(X >= k.crit  k.int), where X follows a betabinomial distribution with parameters n'= n  n.int, a = k.int + shape1, and b = n.int  k.int + shape2.
Efficacy is declared if the predictive power is >= cE (cE must be high, e.g. 0.70). Futility is declared if the predictive power is < cF (cF must be small, e.g. 0.10). cE, cF translate into futility/efficacy boundaries (maximum number of responses leading to early termination for futility/ minimum number of responses leading to declaring of, or early termination for, efficacy).
References
KoppSchneider, A., Wiesenfarth, M., Witt, R., Edelmann, D., Witt, O. and Abel, U. (2018).
Monitoring futility and efficacy in phase II trials with Bayesian
posterior distributions  a calibration approach.
Biometrical Journal, to appear.
Examples
# Operating characteristics with calling for efficacy
BDP2(n=20, interim.at = c(3,9,13,18), ptrue = 0.3,
eff.stop = "call",
pF=0.3, cF=0.01, pE=0.12, cE = 0.9,
type="PostProb",
shape1F=0.3, shape2F=0.7, shape1E=0.12, shape2E=0.88)
# Operating characteristics with stopping for efficacy
BDP2(n=20, interim.at = c(3,9,13,18), ptrue = 0.3,
eff.stop = "stop",
pF=0.3, cF=0.01, pE=0.12, cE = 0.9,
type="PostProb",
shape1F=0.3, shape2F=0.7, shape1E=0.12, shape2E=0.88)