mHP.btilde | 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!

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