The SEQDESIGN Procedure

Haybittle-Peto Method

The Haybittle-Peto method (Haybittle, 1971; Peto et al., 1976) uses a value of 3 for the critical values in interim stages, so that the critical value at the final stage is close to the original design without interim monitoring.

In the SEQDESIGN procedure, the Haybittle-Peto method has been generalized to allow for different boundary values at different stages. That is, with the standardized normal scale, the boundary values are given by the following:

$Z_{\alpha u}({\Pi }_{k}) = z_{\alpha uk}$
$Z_{\beta u}({\Pi }_{k}) = {\theta }_{1u} \, I^{\frac{1}{2}}_{k} - z_{\beta uk}$
$Z_{\beta l}({\Pi }_{k}) = {\theta }_{1l} \, I^{\frac{1}{2}}_{k} + z_{\beta lk}$
$Z_{\alpha l}({\Pi }_{k}) = - z_{\alpha lk}$

where ${\theta }_{1l}$ and ${\theta }_{1u}$ are the lower and upper alternative references and the boundary values $z_{\alpha uk}$ , $z_{\beta uk}$ , $z_{\beta lk}$ , and $z_{\alpha lk}$ are specified either explicitly with the HP( Z= numbers) option or implicitly with the HP( PVALUE= numbers) option. The HP( PVALUE= numbers) option specifies the nominal p-values $p_{k}$ for the corresponding boundary values $z_{k}$ :

$z_{k} = {\Phi }^{-1} ( 1 - p_{k})$

The Haybittle-Peto method is illustrated in Example 83.5.