mHP.btilde {ASSISTant} | R Documentation |

## 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!

[Package

*ASSISTant*version 1.4.3 Index]