mHP.btilde {ASSISTant}

Compute the futility boundary (modified Haybittle-Peto) for the first two stages

Description

The futility boundary \tilde{b} is computed by solving (under the alternative)

Usage

mHP.btilde(beta, cov.J)

Arguments

beta

the type II error

cov.J

the 3 x 3 covariance matrix

Details

P(\tilde{Z}_J^1\le\tilde{b} or \tilde{Z}_J^2\le\tilde{b}) = \epsilon\beta

where the superscripts denote the stage and \epsilon is the fraction of the type I error (\alpha) spent and \beta 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!