# mHP.btilde: Compute the futility boundary (modified Haybittle-Peto) for... In ASSISTant: Adaptive Subgroup Selection in Group Sequential Trials

 mHP.btilde R Documentation

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

### Description

The futility boundary btilde 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≤\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!

ASSISTant documentation built on Dec. 2, 2022, 5:12 p.m.