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

## Description

The futility boundary btilde is computed by solving (under the alternative)

## Usage

 1 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!

## References

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

ASSISTant documentation built on May 6, 2019, 1:02 a.m.