mHP.btilde {ASSISTant} | R Documentation |
The futility boundary btilde is computed by solving (under the alternative)
mHP.btilde(beta, cov.J)
beta |
the type II error |
cov.J |
the 3 x 3 covariance matrix |
P(\tilde{Z}_J^1≤\tilde{b} or \tilde{Z}_J^2≤\tilde{b}) = εβ
where the superscripts denote the stage and ε is the fraction of the type I error (α) spent and β is the type II error. We make use of the joint normal density of Z_{J} (the overall group) at each of the three stages and the fact that the \tilde{Z_J} is merely a translation of Z_J. So here the calculation is based on a mean of zero and has to be translated during use!
Adaptive Choice of Patient Subgroup for Comparing Two Treatments by Tze Leung Lai and Philip W. Lavori and Olivia Yueh-Wen Liao. Contemporary Clinical Trials, Vol. 39, No. 2, pp 191-200 (2014). http://www.sciencedirect.com/science/article/pii/S1551714414001311